The Electronic and Superconducting Properties of Oxygen-Ordered MgB2 compounds of the form

The electronic properties of grapheneA.H.Castro NetoDepartment of Physics,Boston University,590Commonwealth Avenue,Boston,Massachusetts02215,USAF.GuineaInstituto de Ciencia de Materiales de Madrid,CSIC,Cantoblanco,E-28049Madrid,SpainN.M.R.PeresCenter of Physics and Department of Physics,Universidade do Minho,P-4710-057,Braga,PortugalK.S.Novoselov and A.K.GeimDepartment of Physics and Astronomy,University of Manchester,Manchester,M139PL,United Kingdom͑Published14January2009͒This article reviews the basic theoretical aspects of graphene,a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations.The Dirac electrons can be controlled by application of external electric and magneticfields,or by altering sample geometry and/or topology.The Dirac electrons behave in unusual ways in tunneling,confinement,and the integer quantum Hall effect.The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers.Edge͑surface͒states in graphene depend on the edge termination͑zigzag or armchair͒and affect the physical properties of nanoribbons.Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties.The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.DOI:10.1103/RevModPhys.81.109PACS number͑s͒:81.05.Uw,73.20.Ϫr,03.65.Pm,82.45.MpCONTENTSI.Introduction110II.Elementary Electronic Properties of Graphene112A.Single layer:Tight-binding approach1121.Cyclotron mass1132.Density of states114B.Dirac fermions1141.Chiral tunneling and Klein paradox1152.Confinement and Zitterbewegung117C.Bilayer graphene:Tight-binding approach118D.Epitaxial graphene119E.Graphene stacks1201.Electronic structure of bulk graphite121F.Surface states in graphene122G.Surface states in graphene stacks124H.The spectrum of graphene nanoribbons1241.Zigzag nanoribbons1252.Armchair nanoribbons126I.Dirac fermions in a magneticfield126J.The anomalous integer quantum Hall effect128 K.Tight-binding model in a magneticfield128 ndau levels in graphene stacks130 M.Diamagnetism130 N.Spin-orbit coupling131 III.Flexural Phonons,Elasticity,and Crumpling132 IV.Disorder in Graphene134A.Ripples135B.Topological lattice defects136C.Impurity states137D.Localized states near edges,cracks,and voids137E.Self-doping138F.Vector potential and gaugefield disorder1391.Gaugefield induced by curvature1402.Elastic strain1403.Random gaugefields141G.Coupling to magnetic impurities141H.Weak and strong localization142I.Transport near the Dirac point143J.Boltzmann equation description of dc transport indoped graphene144 K.Magnetotransport and universal conductivity1451.The full self-consistent Born approximation͑FSBA͒146 V.Many-Body Effects148A.Electron-phonon interactions148B.Electron-electron interactions1501.Screening in graphene stacks152C.Short-range interactions1521.Bilayer graphene:Exchange1532.Bilayer graphene:Short-range interactions154D.Interactions in high magneticfields154VI.Conclusions154 Acknowledgments155 References155REVIEWS OF MODERN PHYSICS,VOLUME81,JANUARY–MARCH20090034-6861/2009/81͑1͒/109͑54͒©2009The American Physical Society109I.INTRODUCTIONCarbon is the materia prima for life and the basis of all organic chemistry.Because of the flexibility of its bond-ing,carbon-based systems show an unlimited number of different structures with an equally large variety of physical properties.These physical properties are,in great part,the result of the dimensionality of these structures.Among systems with only carbon atoms,graphene—a two-dimensional ͑2D ͒allotrope of carbon—plays an important role since it is the basis for the understanding of the electronic properties in other allotropes.Graphene is made out of carbon atoms ar-ranged on a honeycomb structure made out of hexagons ͑see Fig.1͒,and can be thought of as composed of ben-zene rings stripped out from their hydrogen atoms ͑Pauling,1972͒.Fullerenes ͑Andreoni,2000͒are mol-ecules where carbon atoms are arranged spherically,and hence,from the physical point of view,are zero-dimensional objects with discrete energy states.Fullerenes can be obtained from graphene with the in-troduction of pentagons ͑that create positive curvature defects ͒,and hence,fullerenes can be thought as wrapped-up graphene.Carbon nanotubes ͑Saito et al.,1998;Charlier et al.,2007͒are obtained by rolling graphene along a given direction and reconnecting the carbon bonds.Hence carbon nanotubes have only hexa-gons and can be thought of as one-dimensional ͑1D ͒ob-jects.Graphite,a three dimensional ͑3D ͒allotrope of carbon,became widely known after the invention of the pencil in 1564͑Petroski,1989͒,and its usefulness as an instrument for writing comes from the fact that graphite is made out of stacks of graphene layers that are weakly coupled by van der Waals forces.Hence,when one presses a pencil against a sheet of paper,one is actually producing graphene stacks and,somewhere among them,there could be individual graphene layers.Al-though graphene is the mother for all these different allotropes and has been presumably produced every time someone writes with a pencil,it was only isolated 440years after its invention ͑Novoselov et al.,2004͒.The reason is that,first,no one actually expected graphene to exist in the free state and,second,even with the ben-efit of hindsight,no experimental tools existed to search for one-atom-thick flakes among the pencil debris cov-ering macroscopic areas ͑Geim and MacDonald,2007͒.Graphene was eventually spotted due to the subtle op-tical effect it creates on top of a chosen SiO 2substrate ͑Novoselov et al.,2004͒that allows its observation with an ordinary optical microscope ͑Abergel et al.,2007;Blake et al.,2007;Casiraghi et al.,2007͒.Hence,graphene is relatively straightforward to make,but not so easy to find.The structural flexibility of graphene is reflected in its electronic properties.The sp 2hybridization between one s orbital and two p orbitals leads to a trigonal planar structure with a formation of a ␴bond between carbon atoms that are separated by 1.42Å.The ␴band is re-sponsible for the robustness of the lattice structure in all allotropes.Due to the Pauli principle,these bands have a filled shell and,hence,form a deep valence band.The unaffected p orbital,which is perpendicular to the pla-nar structure,can bind covalently with neighboring car-bon atoms,leading to the formation of a ␲band.Since each p orbital has one extra electron,the ␲band is half filled.Half-filled bands in transition elements have played an important role in the physics of strongly correlated systems since,due to their strong tight-binding charac-ter,the Coulomb energies are large,leading to strong collective effects,magnetism,and insulating behavior due to correlation gaps or Mottness ͑Phillips,2006͒.In fact,Linus Pauling proposed in the 1950s that,on the basis of the electronic properties of benzene,graphene should be a resonant valence bond ͑RVB ͒structure ͑Pauling,1972͒.RVB states have become popular in the literature of transition-metal oxides,and particularly in studies of cuprate-oxide superconductors ͑Maple,1998͒.This point of view should be contrasted with contempo-raneous band-structure studies of graphene ͑Wallace,1947͒that found it to be a semimetal with unusual lin-early dispersing electronic excitations called Dirac elec-trons.While most current experimental data in graphene support the band structure point of view,the role of electron-electron interactions in graphene is a subject of intense research.It was P .R.Wallace in 1946who first wrote on the band structure of graphene and showed the unusual semimetallic behavior in this material ͑Wallace,1947͒.At that time,the thought of a purely 2D structure was not reality and Wallace’s studies of graphene served him as a starting point to study graphite,an important mate-rial for nuclear reactors in the post–World War II era.During the following years,the study of graphite culmi-nated with the Slonczewski-Weiss-McClure ͑SWM ͒band structure of graphite,which provided a description of the electronic properties in this material ͑McClure,1957;Slonczewski and Weiss,1958͒and was successful in de-scribing the experimental data ͑Boyle and Nozières 1958;McClure,1958;Spry and Scherer,1960;Soule et al.,1964;Williamson et al.,1965;Dillon et al.,1977͒.From 1957to 1968,the assignment of the electron and hole states within the SWM model were oppositetoFIG.1.͑Color online ͒Graphene ͑top left ͒is a honeycomb lattice of carbon atoms.Graphite ͑top right ͒can be viewed as a stack of graphene layers.Carbon nanotubes are rolled-up cylinders of graphene ͑bottom left ͒.Fullerenes ͑C 60͒are mol-ecules consisting of wrapped graphene by the introduction of pentagons on the hexagonal lattice.From Castro Neto et al.,2006a .110Castro Neto et al.:The electronic properties of grapheneRev.Mod.Phys.,V ol.81,No.1,January–March 2009what is accepted today.In1968,Schroeder et al.͑Schroeder et al.,1968͒established the currently ac-cepted location of electron and hole pockets͑McClure, 1971͒.The SWM model has been revisited in recent years because of its inability to describe the van der Waals–like interactions between graphene planes,a problem that requires the understanding of many-body effects that go beyond the band-structure description ͑Rydberg et al.,2003͒.These issues,however,do not arise in the context of a single graphene crystal but they show up when graphene layers are stacked on top of each other,as in the case,for instance,of the bilayer graphene.Stacking can change the electronic properties considerably and the layering structure can be used in order to control the electronic properties.One of the most interesting aspects of the graphene problem is that its low-energy excitations are massless, chiral,Dirac fermions.In neutral graphene,the chemical potential crosses exactly the Dirac point.This particular dispersion,that is only valid at low energies,mimics the physics of quantum electrodynamics͑QED͒for massless fermions except for the fact that in graphene the Dirac fermions move with a speed v F,which is300times smaller than the speed of light c.Hence,many of the unusual properties of QED can show up in graphene but at much smaller speeds͑Castro Neto et al.,2006a; Katsnelson et al.,2006;Katsnelson and Novoselov, 2007͒.Dirac fermions behave in unusual ways when compared to ordinary electrons if subjected to magnetic fields,leading to new physical phenomena͑Gusynin and Sharapov,2005;Peres,Guinea,and Castro Neto,2006a͒such as the anomalous integer quantum Hall effect ͑IQHE͒measured experimentally͑Novoselov,Geim, Morozov,et al.,2005a;Zhang et al.,2005͒.Besides being qualitatively different from the IQHE observed in Si and GaAlAs͑heterostructures͒devices͑Stone,1992͒, the IQHE in graphene can be observed at room tem-perature because of the large cyclotron energies for “relativistic”electrons͑Novoselov et al.,2007͒.In fact, the anomalous IQHE is the trademark of Dirac fermion behavior.Another interesting feature of Dirac fermions is their insensitivity to external electrostatic potentials due to the so-called Klein paradox,that is,the fact that Dirac fermions can be transmitted with probability1through a classically forbidden region͑Calogeracos and Dombey, 1999;Itzykson and Zuber,2006͒.In fact,Dirac fermions behave in an unusual way in the presence of confining potentials,leading to the phenomenon of Zitter-bewegung,or jittery motion of the wave function͑Itzyk-son and Zuber,2006͒.In graphene,these electrostatic potentials can be easily generated by disorder.Since dis-order is unavoidable in any material,there has been a great deal of interest in trying to understand how disor-der affects the physics of electrons in graphene and its transport properties.In fact,under certain conditions, Dirac fermions are immune to localization effects ob-served in ordinary electrons͑Lee and Ramakrishnan, 1985͒and it has been established experimentally that electrons can propagate without scattering over large distances of the order of micrometers in graphene͑No-voselov et al.,2004͒.The sources of disorder in graphene are many and can vary from ordinary effects commonly found in semiconductors,such as ionized impurities in the Si substrate,to adatoms and various molecules ad-sorbed in the graphene surface,to more unusual defects such as ripples associated with the soft structure of graphene͑Meyer,Geim,Katsnelson,Novoselov,Booth, et al.,2007a͒.In fact,graphene is unique in the sense that it shares properties of soft membranes͑Nelson et al.,2004͒and at the same time it behaves in a metallic way,so that the Dirac fermions propagate on a locally curved space.Here analogies with problems of quantum gravity become apparent͑Fauser et al.,2007͒.The soft-ness of graphene is related with the fact that it has out-of-plane vibrational modes͑phonons͒that cannot be found in3D solids.Theseflexural modes,responsible for the bending properties of graphene,also account for the lack of long range structural order in soft mem-branes leading to the phenomenon of crumpling͑Nelson et al.,2004͒.Nevertheless,the presence of a substrate or scaffolds that hold graphene in place can stabilize a cer-tain degree of order in graphene but leaves behind the so-called ripples͑which can be viewed as frozenflexural modes͒.It was realized early on that graphene should also present unusual mesoscopic effects͑Peres,Castro Neto, and Guinea,2006a;Katsnelson,2007a͒.These effects have their origin in the boundary conditions required for the wave functions in mesoscopic samples with various types of edges graphene can have͑Nakada et al.,1996; Wakabayashi et al.,1999;Peres,Guinea,and Castro Neto,2006a;Akhmerov and Beenakker,2008͒.The most studied edges,zigzag and armchair,have drastically different electronic properties.Zigzag edges can sustain edge͑surface͒states and resonances that are not present in the armchair case.Moreover,when coupled to con-ducting leads,the boundary conditions for a graphene ribbon strongly affect its conductance,and the chiral Dirac nature of fermions in graphene can be used for applications where one can control the valleyflavor of the electrons besides its charge,the so-called valleytron-ics͑Rycerz et al.,2007͒.Furthermore,when supercon-ducting contacts are attached to graphene,they lead to the development of supercurrentflow and Andreev pro-cesses characteristic of the superconducting proximity effect͑Heersche et al.,2007͒.The fact that Cooper pairs can propagate so well in graphene attests to the robust electronic coherence in this material.In fact,quantum interference phenomena such as weak localization,uni-versal conductancefluctuations͑Morozov et al.,2006͒, and the Aharonov-Bohm effect in graphene rings have already been observed experimentally͑Recher et al., 2007;Russo,2007͒.The ballistic electronic propagation in graphene can be used forfield-effect devices such as p-n͑Cheianov and Fal’ko,2006;Cheianov,Fal’ko,and Altshuler,2007;Huard et al.,2007;Lemme et al.,2007; Tworzydlo et al.,2007;Williams et al.,2007;Fogler, Glazman,Novikov,et al.,2008;Zhang and Fogler,2008͒and p-n-p͑Ossipov et al.,2007͒junctions,and as“neu-111Castro Neto et al.:The electronic properties of graphene Rev.Mod.Phys.,V ol.81,No.1,January–March2009trino”billiards ͑Berry and Modragon,1987;Miao et al.,2007͒.It has also been suggested that Coulomb interac-tions are considerably enhanced in smaller geometries,such as graphene quantum dots ͑Milton Pereira et al.,2007͒,leading to unusual Coulomb blockade effects ͑Geim and Novoselov,2007͒and perhaps to magnetic phenomena such as the Kondo effect.The transport properties of graphene allow for their use in a plethora of applications ranging from single molecule detection ͑Schedin et al.,2007;Wehling et al.,2008͒to spin injec-tion ͑Cho et al.,2007;Hill et al.,2007;Ohishi et al.,2007;Tombros et al.,2007͒.Because of its unusual structural and electronic flex-ibility,graphene can be tailored chemically and/or struc-turally in many different ways:deposition of metal at-oms ͑Calandra and Mauri,2007;Uchoa et al.,2008͒or molecules ͑Schedin et al.,2007;Leenaerts et al.,2008;Wehling et al.,2008͒on top;intercalation ͓as done in graphite intercalated compounds ͑Dresselhaus et al.,1983;Tanuma and Kamimura,1985;Dresselhaus and Dresselhaus,2002͔͒;incorporation of nitrogen and/or boron in its structure ͑Martins et al.,2007;Peres,Klironomos,Tsai,et al.,2007͓͒in analogy with what has been done in nanotubes ͑Stephan et al.,1994͔͒;and using different substrates that modify the electronic structure ͑Calizo et al.,2007;Giovannetti et al.,2007;Varchon et al.,2007;Zhou et al.,2007;Das et al.,2008;Faugeras et al.,2008͒.The control of graphene properties can be extended in new directions allowing for the creation of graphene-based systems with magnetic and supercon-ducting properties ͑Uchoa and Castro Neto,2007͒that are unique in their 2D properties.Although the graphene field is still in its infancy,the scientific and technological possibilities of this new material seem to be unlimited.The understanding and control of this ma-terial’s properties can open doors for a new frontier in electronics.As the current status of the experiment and potential applications have recently been reviewed ͑Geim and Novoselov,2007͒,in this paper we concen-trate on the theory and more technical aspects of elec-tronic properties with this exciting new material.II.ELEMENTARY ELECTRONIC PROPERTIES OF GRAPHENEA.Single layer:Tight-binding approachGraphene is made out of carbon atoms arranged in hexagonal structure,as shown in Fig.2.The structure can be seen as a triangular lattice with a basis of two atoms per unit cell.The lattice vectors can be written asa 1=a 2͑3,ͱ3͒,a 2=a2͑3,−ͱ3͒,͑1͒where a Ϸ1.42Åis the carbon-carbon distance.Thereciprocal-lattice vectors are given byb 1=2␲3a͑1,ͱ3͒,b 2=2␲3a͑1,−ͱ3͒.͑2͒Of particular importance for the physics of graphene are the two points K and K Јat the corners of the graphene Brillouin zone ͑BZ ͒.These are named Dirac points for reasons that will become clear later.Their positions in momentum space are given byK =ͩ2␲3a ,2␲3ͱ3aͪ,K Ј=ͩ2␲3a ,−2␲3ͱ3aͪ.͑3͒The three nearest-neighbor vectors in real space are given by␦1=a 2͑1,ͱ3͒␦2=a 2͑1,−ͱ3͒␦3=−a ͑1,0͒͑4͒while the six second-nearest neighbors are located at ␦1Ј=±a 1,␦2Ј=±a 2,␦3Ј=±͑a 2−a 1͒.The tight-binding Hamiltonian for electrons in graphene considering that electrons can hop to both nearest-and next-nearest-neighbor atoms has the form ͑we use units such that ប=1͒H =−t͚͗i ,j ͘,␴͑a ␴,i †b ␴,j +H.c.͒−t Ј͚͗͗i ,j ͘͘,␴͑a ␴,i †a ␴,j +b ␴,i †b ␴,j +H.c.͒,͑5͒where a i ,␴͑a i ,␴†͒annihilates ͑creates ͒an electron with spin ␴͑␴=↑,↓͒on site R i on sublattice A ͑an equiva-lent definition is used for sublattice B ͒,t ͑Ϸ2.8eV ͒is the nearest-neighbor hopping energy ͑hopping between dif-ferent sublattices ͒,and t Јis the next nearest-neighbor hopping energy 1͑hopping in the same sublattice ͒.The energy bands derived from this Hamiltonian have the form ͑Wallace,1947͒E ±͑k ͒=±t ͱ3+f ͑k ͒−t Јf ͑k ͒,1The value of t Јis not well known but ab initio calculations ͑Reich et al.,2002͒find 0.02t Շt ЈՇ0.2t depending on the tight-binding parametrization.These calculations also include the effect of a third-nearest-neighbors hopping,which has a value of around 0.07eV.A tight-binding fit to cyclotron resonance experiments ͑Deacon et al.,2007͒finds t ЈϷ0.1eV.FIG.2.͑Color online ͒Honeycomb lattice and its Brillouin zone.Left:lattice structure of graphene,made out of two in-terpenetrating triangular lattices ͑a 1and a 2are the lattice unit vectors,and ␦i ,i =1,2,3are the nearest-neighbor vectors ͒.Right:corresponding Brillouin zone.The Dirac cones are lo-cated at the K and K Јpoints.112Castro Neto et al.:The electronic properties of grapheneRev.Mod.Phys.,V ol.81,No.1,January–March 2009f ͑k ͒=2cos ͑ͱ3k y a ͒+4cosͩͱ32k y a ͪcosͩ32k x a ͪ,͑6͒where the plus sign applies to the upper ͑␲*͒and the minus sign the lower ͑␲͒band.It is clear from Eq.͑6͒that the spectrum is symmetric around zero energy if t Ј=0.For finite values of t Ј,the electron-hole symmetry is broken and the ␲and ␲*bands become asymmetric.In Fig.3,we show the full band structure of graphene with both t and t Ј.In the same figure,we also show a zoom in of the band structure close to one of the Dirac points ͑at the K or K Јpoint in the BZ ͒.This dispersion can be obtained by expanding the full band structure,Eq.͑6͒,close to the K ͑or K Ј͒vector,Eq.͑3͒,as k =K +q ,with ͉q ͉Ӷ͉K ͉͑Wallace,1947͒,E ±͑q ͒Ϸ±vF ͉q ͉+O ͓͑q /K ͒2͔,͑7͒where q is the momentum measured relatively to the Dirac points and v F is the Fermi velocity,given by v F =3ta /2,with a value v F Ӎ1ϫ106m/s.This result was first obtained by Wallace ͑1947͒.The most striking difference between this result and the usual case,⑀͑q ͒=q 2/͑2m ͒,where m is the electron mass,is that the Fermi velocity in Eq.͑7͒does not de-pend on the energy or momentum:in the usual case we have v =k /m =ͱ2E /m and hence the velocity changes substantially with energy.The expansion of the spectrum around the Dirac point including t Јup to second order in q /K is given byE ±͑q ͒Ӎ3t Ј±vF ͉q ͉−ͩ9t Јa 24±3ta 28sin ͑3␪q ͉͒ͪq ͉2,͑8͒where␪q =arctanͩq x q yͪ͑9͒is the angle in momentum space.Hence,the presence of t Јshifts in energy the position of the Dirac point and breaks electron-hole symmetry.Note that up to order ͑q /K ͒2the dispersion depends on the direction in mo-mentum space and has a threefold symmetry.This is the so-called trigonal warping of the electronic spectrum ͑Ando et al.,1998,Dresselhaus and Dresselhaus,2002͒.1.Cyclotron massThe energy dispersion ͑7͒resembles the energy of ul-trarelativistic particles;these particles are quantum me-chanically described by the massless Dirac equation ͑see Sec.II.B for more on this analogy ͒.An immediate con-sequence of this massless Dirac-like dispersion is a cy-clotron mass that depends on the electronic density as its square root ͑Novoselov,Geim,Morozov,et al.,2005;Zhang et al.,2005͒.The cyclotron mass is defined,within the semiclassical approximation ͑Ashcroft and Mermin,1976͒,asm *=12␲ͫץA ͑E ͒ץEͬE =E F,͑10͒with A ͑E ͒the area in k space enclosed by the orbit andgiven byA ͑E ͒=␲q ͑E ͒2=␲E 2v F2.͑11͒Using Eq.͑11͒in Eq.͑10͒,one obtainsm *=E Fv F2=k Fv F.͑12͒The electronic density n is related to the Fermi momen-tum k F as k F2/␲=n ͑with contributions from the two Dirac points K and K Јand spin included ͒,which leads tom *=ͱ␲v Fͱn .͑13͒Fitting Eq.͑13͒to the experimental data ͑see Fig.4͒provides an estimation for the Fermi velocity andtheFIG.3.͑Color online ͒Electronic dispersion in the honeycomb lattice.Left:energy spectrum ͑in units of t ͒for finite values of t and t Ј,with t =2.7eV and t Ј=−0.2t .Right:zoom in of the energy bands close to one of the Diracpoints.FIG.4.͑Color online ͒Cyclotron mass of charge carriers in graphene as a function of their concentration n .Positive and negative n correspond to electrons and holes,respectively.Symbols are the experimental data extracted from the tem-perature dependence of the SdH oscillations;solid curves are the best fit by Eq.͑13͒.m 0is the free-electron mass.Adapted from Novoselov,Geim,Morozov,et al.,2005.113Castro Neto et al.:The electronic properties of grapheneRev.Mod.Phys.,V ol.81,No.1,January–March 2009hopping parameter as v F Ϸ106ms −1and t Ϸ3eV,respec-tively.Experimental observation of the ͱn dependence on the cyclotron mass provides evidence for the exis-tence of massless Dirac quasiparticles in graphene ͑No-voselov,Geim,Morozov,et al.,2005;Zhang et al.,2005;Deacon et al.,2007;Jiang,Henriksen,Tung,et al.,2007͒—the usual parabolic ͑Schrödinger ͒dispersion im-plies a constant cyclotron mass.2.Density of statesThe density of states per unit cell,derived from Eq.͑5͒,is given in Fig.5for both t Ј=0and t Ј 0,showing in both cases semimetallic behavior ͑Wallace,1947;Bena and Kivelson,2005͒.For t Ј=0,it is possible to derive an analytical expression for the density of states per unit cell,which has the form ͑Hobson and Nierenberg,1953͒␳͑E ͒=4␲2͉E ͉t 21ͱZ 0F ͩ␲2,ͱZ 1Z 0ͪ,Z 0=Άͩ1+ͯE t ͯͪ2−͓͑E /t ͒2−1͔24,−t ഛE ഛt4ͯE t ͯ,−3t ഛE ഛ−t ∨t ഛE ഛ3t ,Z 1=Ά4ͯE t ͯ,−t ഛE ഛtͩ1+ͯE tͯͪ2−͓͑E /t ͒2−1͔24,−3t ഛE ഛ−t ∨t ഛE ഛ3t ,͑14͒where F ͑␲/2,x ͒is the complete elliptic integral of thefirst kind.Close to the Dirac point,the dispersion is ap-proximated by Eq.͑7͒and the density of states per unit cell is given by ͑with a degeneracy of 4included ͒␳͑E ͒=2A c ␲͉E ͉v F2,͑15͒where A c is the unit cell area given by A c =3ͱ3a 2/2.It is worth noting that the density of states for graphene is different from the density of states of carbon nanotubes ͑Saito et al.,1992a ,1992b ͒.The latter shows 1/ͱE singu-larities due to the 1D nature of their electronic spec-trum,which occurs due to the quantization of the mo-mentum in the direction perpendicular to the tube axis.From this perspective,graphene nanoribbons,which also have momentum quantization perpendicular to the ribbon length,have properties similar to carbon nano-tubes.B.Dirac fermionsWe consider the Hamiltonian ͑5͒with t Ј=0and theFourier transform of the electron operators,a n =1ͱN c͚ke −i k ·R na ͑k ͒,͑16͒where N c is the number of unit ing this transfor-mation,we write the field a n as a sum of two terms,coming from expanding the Fourier sum around K Јand K .This produces an approximation for the representa-tion of the field a n as a sum of two new fields,written asa n Ӎe −i K ·R n a 1,n +e −i K Ј·R n a 2,n ,b n Ӎe −i K ·R n b 1,n +e −i K Ј·R n b 2,n ,͑17͒ρ(ε)ε/tρ(ε)ε/tFIG.5.Density of states per unit cell as a function of energy ͑in units of t ͒computed from the energy dispersion ͑5͒,t Ј=0.2t ͑top ͒and t Ј=0͑bottom ͒.Also shown is a zoom-in of the density of states close to the neutrality point of one electron per site.For the case t Ј=0,the electron-hole nature of the spectrum is apparent and the density of states close to the neutrality point can be approximated by ␳͑⑀͒ϰ͉⑀͉.114Castro Neto et al.:The electronic properties of grapheneRev.Mod.Phys.,V ol.81,No.1,January–March 2009where the index i =1͑i =2͒refers to the K ͑K Ј͒point.These new fields,a i ,n and b i ,n ,are assumed to vary slowly over the unit cell.The procedure for deriving a theory that is valid close to the Dirac point con-sists in using this representation in the tight-binding Hamiltonian and expanding the opera-tors up to a linear order in ␦.In the derivation,one uses the fact that ͚␦e ±i K ·␦=͚␦e ±i K Ј·␦=0.After some straightforward algebra,we arrive at ͑Semenoff,1984͒H Ӎ−t͵dxdy ⌿ˆ1†͑r ͒ͫͩ3a ͑1−i ͱ3͒/4−3a ͑1+i ͱ3͒/4ͪץx +ͩ3a ͑−i −ͱ3͒/4−3a ͑i −ͱ3͒/4ͪץy ͬ⌿ˆ1͑r ͒+⌿ˆ2†͑r ͒ͫͩ3a ͑1+i ͱ3͒/4−3a ͑1−i ͱ3͒/4ͪץx +ͩ3a ͑i −ͱ3͒/4−3a ͑−i −ͱ3͒/4ͪץy ͬ⌿ˆ2͑r ͒=−i v F͵dxdy ͓⌿ˆ1†͑r ͒␴·ٌ⌿ˆ1͑r ͒+⌿ˆ2†͑r ͒␴*·ٌ⌿ˆ2͑r ͔͒,͑18͒with Pauli matrices ␴=͑␴x ,␴y ͒,␴*=͑␴x ,−␴y ͒,and ⌿ˆi†=͑a i †,b i †͒͑i =1,2͒.It is clear that the effective Hamil-tonian ͑18͒is made of two copies of the massless Dirac-like Hamiltonian,one holding for p around K and the other for p around K Ј.Note that,in first quantized lan-guage,the two-component electron wave function ␺͑r ͒,close to the K point,obeys the 2D Dirac equation,−i v F ␴·ٌ␺͑r ͒=E ␺͑r ͒.͑19͒The wave function,in momentum space,for the mo-mentum around K has the form␺±,K ͑k ͒=1ͱ2ͩe −i ␪k /2±e i ␪k /2ͪ͑20͒for H K =v F ␴·k ,where the Ϯsigns correspond to the eigenenergies E =±v F k ,that is,for the ␲*and ␲bands,respectively,and ␪k is given by Eq.͑9͒.The wave func-tion for the momentum around K Јhas the form␺±,K Ј͑k ͒=1ͱ2ͩe i ␪k /2±e −i ␪k /2ͪ͑21͒for H K Ј=v F ␴*·k .Note that the wave functions at K and K Јare related by time-reversal symmetry:if we set the origin of coordinates in momentum space in the M point of the BZ ͑see Fig.2͒,time reversal becomes equivalent to a reflection along the k x axis,that is,͑k x ,k y ͒→͑k x ,−k y ͒.Also note that if the phase ␪is rotated by 2␲,the wave function changes sign indicating a phase of ␲͑in the literature this is commonly called a Berry’s phase ͒.This change of phase by ␲under rotation is char-acteristic of spinors.In fact,the wave function is a two-component spinor.A relevant quantity used to characterize the eigen-functions is their helicity defined as the projection of the momentum operator along the ͑pseudo ͒spin direction.The quantum-mechanical operator for the helicity has the formhˆ=12␴·p ͉p ͉.͑22͒It is clear from the definition of h ˆthat the states ␺K͑r ͒and ␺K Ј͑r ͒are also eigenstates of h ˆ,h ˆ␺K ͑r ͒=±12␺K͑r ͒,͑23͒and an equivalent equation for ␺K Ј͑r ͒with inverted sign.Therefore,electrons ͑holes ͒have a positive ͑negative ͒helicity.Equation ͑23͒implies that ␴has its two eigen-values either in the direction of ͑⇑͒or against ͑⇓͒the momentum p .This property says that the states of the system close to the Dirac point have well defined chiral-ity or helicity.Note that chirality is not defined in regard to the real spin of the electron ͑that has not yet ap-peared in the problem ͒but to a pseudospin variable as-sociated with the two components of the wave function.The helicity values are good quantum numbers as long as the Hamiltonian ͑18͒is valid.Therefore,the existence of helicity quantum numbers holds only as an asymptotic property,which is well defined close to the Dirac points K and K Ј.Either at larger energies or due to the presence of a finite t Ј,the helicity stops being a good quantum number.1.Chiral tunneling and Klein paradoxIn this section,we address the scattering of chiral elec-trons in two dimensions by a square barrier ͑Katsnelson et al.,2006;Katsnelson,2007b ͒.The one-dimensional scattering of chiral electrons was discussed earlier in the context on nanotubes ͑Ando et al.,1998;McEuen et al.,1999͒.We start by noting that by a gauge transformation the wave function ͑20͒can be written as115Castro Neto et al.:The electronic properties of grapheneRev.Mod.Phys.,V ol.81,No.1,January–March 2009。

Third Edition (© 2001 McGraw-Hill) Chapter 88.1 Inductance of a long solenoid Consider the very long (ideally infinitely long) solenoid shown in Figure 8.69. If r is the radius of the core and is the length of the solenoid, then >> r. The total number of turns is N and the number of turns per unit length is n = N/ . The current through the coil wires is I. Apply Ampere's law around C, which is the rectangular circuit PQRS,and show thatB≈μoμr nIFurther, show that the inductance isL≈μoμr n2V core Inductance of long solenoid where V core is the volume of the core. How would you increase the inductance of a long solenoid?Figure 8.69What is the approximate inductance of an air-cored solenoid with a diameter of 1 cm, length of 20 cm, and 500 turns? What is the magnetic field inside the solenoid and the energy stored in the whole solenoid when the current is 1 A? What happens to these values if the core medium has a relative permeability μr of 600? SolutionWe use Ampere's law in Equation 8.15. Consider Figure 8.9. If H is the field along a small length d along a closed path C, then around C, ⎰Hd= total threaded current = I total = NI.Figure 8.9:Ampere’s circuital lawAssume that the solenoid is infinitely long. The rectangular loop PQRS has n (PQ ) number of turns where n is the number of turns per unit length or n = N / (See Figure 8.69). The field is only inside the solenoid and only along the PQ direction (long solenoid assumption) and therefore the field along QR , RS and SP is zero. Assume that the field H is uniform across the solenoid core cross section. Then the path integral of the magnetic field intensity H around PQRS is simply is H = H (PQ ). Ampere's law ⎰ Hd = I total is then H (PQ ) = I (nPQ ) i.e.H = nIThe dimensions of the solenoid are such that length >> diameter. We can assume that H field isrelatively uniform at all points inside the solenoid. Note: The approximate equality sign in the text (equation for B ) is due to the fact that we assumed H is uniform across the core and, further, along the whole length of the solenoid from one end to the other. The ends of the solenoid will have different fields (lower). Let A be the cross-sectional area of the solenoid. The magnetic field B , the flux Φ and hence the inductance L are B = μo μr H ≈ μo μr nI∴ Φ = BA ≈ μo μr nAI = μo μr (N / )AIand L = (N Φ)/I = N [μo μr (N / )AI ]/I = μo μr (N 2/ )A = μo μr n 2( A ) ∴L = μo μr n 2V corewhere V core is the volume of the core. Inductance depends on n 2, where n is the number of turns per unit length, on the relative permeability μr and on the volume of the core containing the magnetic flux. For a given volume inductor, L can be increased by using a higher μr material or increasing n , e.g. thinner wire to get more turns per unit length (not so thin that the skin effect diminishes the Q -factor, quality factor; see §2.8). The theoretical inductance of the coil is L = (4π ⨯ 10-7 H/m)(1)[(500)/(0.2 m)]2(0.2 m)(π)[(0.01 m)/(2)]2 ∴ L = 1.23 ⨯ 10-4 H or 0.123 mHB ≈ (4π ⨯ 10-7 Wb A -1 m -1)(1)[(500)/(0.2 m)](1 A) = 3.14 ⨯ 10-3 T The energy per unit volume is,E vol = B 2/(2μo ) = (3.14 ⨯ 10-3 T)2/[2(4π ⨯ 10-7 Wb A -1 m -1)] ∴E vol = 3.92 J / m 3The total energy stored is then,()()()J 61.6tot μm 2.02m 01.0J/m 92.3Area Length 23vol =⎪⎭⎫ ⎝⎛=⨯=πE E Suppose that μr = 600 and suppose that the core does not saturate (an ideal ferromagnetic material) then, ()()H 0.0738=⨯≈-600H 1023.14L()()T 1.88=⨯≈-600T 1014.33Band()()()372vol J/m 2344600m Wb/A 1042T 88.1=⋅⨯≈-πEso that E tot = (E vol )(Volume) = 36.8 mJThis is a dramatic increase and shows the virtue of using a magnetic core material for increasing theinductance and the stored magnetic energy.8.2 Magnetization Consider a long solenoid with a core that is an iron alloy (see Problem 8.1 for therelevant formulas). Suppose that the diameter of the solenoid is 2 cm and the length of the solenoid is 20 cm. The number of turns on the solenoid is 200. The current is increased until the core is magnetized to saturation at about I = 2 A and the saturated magnetic field is 1.5 T.a . What is the magnetic field intensity at the center of the solenoid and the applied magnetic field, μo H , forsaturation? b . What is the saturation magnetization M sat of this iron alloy?c . What is the total magnetization current on the surface of the magnetized iron alloy specimen?d . If we were to remove the iron-alloy core and attempt to obtain the same magnetic field of 1.5 T inside thesolenoid, how much current would we need? Is there a practical way of doing this?Solutiona. Applying Ampere’s law or H = NI we have,()()m2.0A 2200==NI H Since I = 2 A gives saturation, corresponding magnetizing field is H sat ≈ 2000 A/mSuppose the applied magnetic field is the magnetic field in the toroid core in the absence of material. ThenB ap p =μo H sat =4π⨯10-7 Wb A -1 m -1()2000 A/m () ∴ B app = 2.51 ⨯ 10-3 Tb. Apply()sat sat sat H M B o +=μ∴ A/m 2000mA Wb 104T5.11-1-7sat satsat -⨯=-=-πμH B M o∴ M sat ≈ 1.19 ⨯ 106 A/m c. Since M is the magnetization current per unit length,I m = M sat ≈ 1.19 ⨯ 106 A/mThen I surf ace = Total circulating surface current:∴I surface =I m =1.19⨯106 A/m ()0.2 m ()=2.38⨯105 ANote that the actual current in the wires, 2 A is negligible compared with I surf ace . d. Apply, B ≈μo nI (for air)()⎪⎭⎫⎝⎛⨯≈-m 2.0200m A Wb 104T5.11-1-7πI = 1194 ANot very practical in every day life! Perhaps this current (thus field B = 1.5 T) could be achieved byusing a superconducting solenoid.8.3 Paramagnetic and diamagnetic materials Consider bismuth with χm = -16.6×10-5 andaluminum with χm = 2.3×10-5. Suppose that we subject each sample to an applied magnetic field B o of 1 T applied in the +x direction. What is the magnetization M and the equivalent magnetic field μo M in each sample? Which is paramagnetic and which is diamagnetic?SolutionBismuth: χm = -16.6×10-5 χm is negative and small. Bismuth is a diamagnetic material.M = χm H = χm B o /μo∴M = (-16.6×10-5) (1 Wb m -2)/(4π×10-7 Wb m -1 A -1) = -132.1 A m -1Negative sign indicate – x direction.Magnetic field = B o + μo M = B o + χm B o = B o (1 + χm ) = (1 - 16.6×10-5)(1 T) = 0.999834 TAluminum: χm = 2.3×10-5 χm is positive and small. Aluminum is paramagnetic material.M = χm H = χm B o /μo∴M = (2.3×10-5) (1 Wb m -2)/(4π×10-7 Wb m -1 A -1) = 18.3 A m -1Positive sign indicates + x direction.Magnetic field = B o + μo M = B o + χm B o = B o (1 + χm ) = (1 +2.3×10-5)(1 T) = 1.000023 T Author's Note: Both effects are quite small.8.4 Mass and molar susceptibilities Sometimes magnetic susceptibilities are reported as molar ormass susceptibilities. Mass susceptibility (in m 3 kg -1) is χm /ρ where ρ is the density. Molar susceptibility (inm 3 mol -1) is χm (M at /ρ) where M at is the atomic mass. Terbium (Tb) has a magnetic molar susceptibility of 2 cm 3 mol -1. Tb has a density of 8.2 g cm -3 and an atomic mass of 158.93 g mol -1. What is its susceptibility, masssusceptibility and relative permeability? What is the magnetization in the sample in an applied magnetic field of 2 T?Solutionχm = Molar susceptibility (ρ/M at ) = (2 cm 3 mol -1) (8.2 g cm -3)/(158.93 g mol -1) = 0.1032 μr = 1 + χm = 1 + 0.1032 = 1. 1032 M = χm H = χm B o /μo∴M = (0.1032)(2 Wb m -2)/(4π×10-7 Wb m -1 A -1) = 1.642×105 A m -1Note: The magnetic field in the sample iso r o r B H B μμμ===1.1032( 2 T) = 2.206 T.8.5 Pauli spin paramagnetism Paramagnetism in metals depends on the number of conductionelectrons that can flip their spins and align with the applied magnetic field. These electrons are near the Fermilevel E F , and their number is determined by the density of states g (E F ) at E F . Since each electron has a spin magnetic moment of β, paramagnetic susceptibility can be shown to be given byχpara ≈ μo β 2 g (E F )Pauli spin paramagnetismwhere the density of states is given by Equation 4.10. The Fermi energy of calcium, E F , is 4.68 eV. Evaluate the paramagnetic susceptibility of calcium and compare with the experimental value of 1.9 ⨯ 10-5.SolutionApply,()()E h m E e 23228⎪⎭⎫⎝⎛=πg(Equation 4.10)so that ()()()()()J/eV 10602.1eV 68.4s J 10626.6kg 10109.928192323431---⨯⎪⎪⎭⎫⎝⎛⋅⨯⨯=πF E g∴g E F ()=9.197⨯1046 J -1 m -3Then, χpara ≈ μo β 2 g (E F )()()()314622241-1-7para m J 10199.9m A 10273.9m A Wb 104----⨯⨯⨯≈πχ∴χpara ≈ 0.994 ⨯ 10-5This is in reasonable agreement within an order of magnitude with the experimental value of 1.9 ⨯ 10-5.8.6 Ferromagnetism and the exchange interaction Consider dysprosium (Dy), which is arare earth metal with a density of 8.54 g cm -3 and atomic mass of 162.50 g mol -1. The isolated atom has theelectron structure [Xe] 4f 106s 2. What is the spin magnetic moment in the isolated atom in terms of number of Bohr magnetons? If the saturation magnetization of Dy near absolute zero of temperature is 2.4 MA m -1, whatis the effective number of spins per atom in the ferromagnetic state? How does this compare with the number of spins in the isolated atom? What is the order of magnitude for the exchange interaction in eV per atom in Dy if the Curie temperature is 85 K?SolutionIn an isolated Dy atom, the valence shells will fill in accordance with the exchange interaction:4f 106s 2Obviously, there are 4 unpaired electrons. Therefore for an isolated Dy atom, the spin magnetic moment = 4β.Atomic concentration in dysprosium (Dy) solid is (where ρ is the density, N A is Avogadro’s number and M at is the atomic mass):()()3283-12333m 10165.3kg/mol1050.162mol 10022.6kg/m 1054.8--⨯=⨯⨯⨯==atAat M N n ρSuppose that each atom contributes x Bohr magnetons, then βx n M at =sat()()2243286sat mA 10273.9m 10165.3A/m104.2--⨯⨯⨯==βat n M x = 8.18 This is almost twice the net magnetic moment in the isolated atom. Suppose that the Dy atom in the solid loses all the 4 electrons that are paired into the "electron gas" in the solid. This would make Dy +4 have 8 unpaired electrons and a net spin magnetic moment of 8β (this is an oversimplified view).Exchange interaction ~ kT C =8.617⨯10-5 eV/K ()85 K ()=0.00732 eV The order of magnitude of exchange interaction ~ 10-2 eV/atom for Dy (small).8.7 Magnetic domain wall energy and thickness The energy of a Bloch wall depends on twomain factors: the exchange energy E ex (J /atom) and magnetocrystalline energy K (J m -3). If a is the interatomicdistance, δ is the wall thickness, then it can be shown that the potential energy per unit area of the wall isδδπK a E U +=2ex2wall Potential energy of a Bloch wallShow that the minimum energy occurs when the wall has the thickness2/1ex 22⎪⎪⎭⎫ ⎝⎛='aK E πδBloch wall thicknessand show that when δ = δ', the exchange and anisotropy energy contributions are equal . Using reasonable values for various parameters, estimate the Bloch energy and wall thickness for Ni. (See Example 8.4)SolutionδδπK a E U +=2ex2wall∴K a E d dU +-=2ex2wall 2δπδ Minimum energy occurs, when 0wall=δd dU ∴ 022ex 2=+'-K a E δπ ∴2/1ex 22⎪⎪⎭⎫ ⎝⎛='aK E πδAt δδ'=δδδδπ'=''='=K K a E U 2ex 2exchange 2Andexchange anisotropy U K U ='=δFor Ni, T C = 631 K and K = 5 mJ cm -3 = 5×103 J m -3 E ex = kT C = (1.38×10-23 J K -1) (631 K) = 8.71×10-21 J ∴⎥⎦⎤⎢⎣⎡⨯⨯⨯=⎪⎪⎭⎫ ⎝⎛='---)m J 10(5 m)103.0(2)J 1071.8(23392122/1ex 2ππδaK E = 1.69×10-7m or 169 nm And m)10(1.69)m J 105(m)10m)(1.69103.0(2 J) 108.71(27-337-9-212ex 2wall ⨯⨯+⨯⨯⨯='+'=--πδδπK a E U= 1.69×10-3 J m -2 or 1.69 mJ m -2.*8.8 Toroidal inductor and radio engineers toroidal inductance equationa . Consider a toroidal coil (Figure 8.10) whose mean circumference is and has N tightly wound turnsaround it. Suppose that the diameter of the core is 2a and >> a . By applying Ampere's law, show that if the current through the coil is I , then the magnetic field in the core isNIB r o μμ=[8.30]where μr is the relative permeability of the medium. Why do you need >> a for this to be valid? Doesthis equation remain valid if the core cross section is not circular but rectangular, a ⨯ b , and >> a and b ? b . Show that the inductance of the toroidal coil isAN L r o 2μμ=Toroidal coil inductance [8.31]where A is the cross-sectional area of the core.c . Consider a toroidal inductor used in electronics that has a ferrite core size FT-37, that is, round but with arectangular cross section. The outer diameter is 0.375 in (9.52 mm), the inner diameter is 0.187 in (4.75 mm), and the height of the core is 0.125 in (3.175 mm). The initial relative permeability of the ferrite core is 2000, which corresponds to a ferrite called the 77 Mix. If the inductor has 50 turns, then using Equation 8.31, calculate the approximate inductance of the coil. d . Radio engineers use the following equation to calculate the inductances of toroidal coils,6210)mH (N A L L =Radio engineers inductance equation [8.32]where L is the inductance in millihenries (mH) and A L is an inductance parameter, called an inductance index , that characterizes the core of the inductor. A L is supplied by the manufacturers of ferrite cores and is typically quoted as millihenries (mH) per 1000 turns. In using Equation 8.32, one simply substitutes the numerical value of A L to find L in millihenries. For the FT-37 ferrite toroid with the 77 Mix as the ferrite core, A L is specified as 884 mH/1000 turns. What is the inductance of the toroidal inductor in part (c ) from the radio engineers equation in Equation 8.32? What is the percentage difference in values calculated by Equations 8.32 and 8.31? What is your conclusion? (Comment : The agreement is not always this close).SolutionFigure 8.10: A toroidal coil with N turns.a. As in Figure 8.10, if we choose a closed path C that runs along the geometric center of the core and if I is the current, N is the number of turns and = mean circumference, then: NIH d H Ct ==⎰ or H = (NI )/∴NIH B r o r o μμμμ==This particular derivation only applies in the special case of >> radius (a ); that is, for a very long, narrow core. If the core is very long and narrow, it may be safely assumed that the magnetic flux density B is uniform across the entire width (2a ) of the core. If B was not uniform, then applying Ampere’s Law to different (concentric) closed paths would yield different results.This above derivation for B is valid for a rectangular cross-sectioned core of area a ⨯ b , provided that >> a and >> b . The magnetic field is then,B =μo μrNIb. The inductance by definition is given by,A N I NAI N I BA N I N L r o r o 2)(μμμμ=⎪⎭⎫ ⎝⎛==Φ=c.Figure 8Q8-1: Toroidal core with rectangular cross section.Given, outer radius = r outer = 0.00476 m, inner radius = r inner = 0.002375 m and height = H = 0.003175 m.We take the mean circumference through the geometric center of the core so that the mean radius is: mm 5675.32inner innerouter =+-=r r r r ∴()()m 1042.22m 105675.32233--⨯=⨯==ππ rWidth = W = r outer - r inner = 0.002385 mA = Cross sectional area = W ⨯ H = (0.002385 m)(0.003175 m) = 7.572 ⨯ 10-6 m 2. Since >> a and >> b (at least approximately) we can calculate L as follows:AN L r o 2μμ=∴ ()()()()m1042.22m 10572.7502000H/m 10432627---⨯⨯⨯=πL ∴L = 0.00212 H or 2.12 mH (2)d. Using the radio engineer’s equation,()()()mH 2.21mH ===62621050mH 88410N A L L (3)so that 4.07%=⨯-=%100mH21.2mH12.2mH 21.2difference %Equations 2 and 3 differ only by 4.1% in this case. This is a good agreement.*8.9 A toroidal inductora . Equations 8.31 and 8.32 allow the inductance of a toroidal coil in electronics to be calculated. Equation8.32 is the equation that is used in practice. Consider a toroidal inductor used in electronics that has a ferrite core of size FT-23 that is round but with a rectangular cross section. The outer diameter is 0.230 in (5.842 mm), the inner diameter is 0.120 in (3.05 mm), and the height of the core is 0.06 in (1.5 mm). The ferrite core is a 43-Mix that has an initial relative permeability of 850 and a maximum relative permeability of 3000. The inductance index for this 43-Mix ferrite core of size FT-23 is A L =188 (mH/1000 turns). If the inductor has 25 turns, then using Equations 8.31 and 8.32, calculate the inductance of the coil under small-signal conditions and comment on the two values. b . The saturation field, B sat , of the 43-mix ferrite is 0.2750 T. What will be typical dc currents that willsaturate the ferrite core (an estimate calculation is required)? It is not unusual to find such an inductor in an electronic circuit also carrying a dc current? Will your calculation of the inductance remain valid in these circumstances? c . Suppose that the above toroidal inductor discussed in parts (a) and (b) is in the vicinity of a very strongmagnet that saturates the magnetic field inside the ferrite core. What will be the inductance of the coil?Solutiona. Provided that the mean circumference is much greater than any long cross sectional dimension (e.g. >> diameter or >> a and >> b ), then we can use,AN L r o 2μμ≈Note that μr is the initial permeability. We need the mean circumference which can be calculated from the mean radius r ,mm 97.132 that so mm 223.22inner innerouter ===+-=r r r r r π Width = W = r outer - r inner = 0.001396 m and Height = H = 0.0015 m.A = Cross sectional area = W ⨯ HSince >> a and >> b (at least approximately) we can calculate L as follows:)(2WH N L r o μμ≈()()()()()m1097.13m105.1m 10396.125850H/m 10433327----⨯⨯⨯⨯≈πLL ≈ 0.10 mHAnd, the radio engineer’s equation, Equation 8.32, (radio engineers toroidal inductance equation, pg. 6.25 and data pg. 24.7 in The ARRL Handbook 1995)()()mH 0.118===62621025mH 18810N A L L There is a 15% difference between the two inductances; limitations of the approximation are apparent. b. To estimate H sat , we’ll take the maximum relative permeability μr max = 3000 as an estimate in order to findH sat (see Figure 8Q9-1). We know that sat max sat and H B NIH o r μμ==∴satmax sat NI B r o μμ=∴ ()()()m1097.13253000m A Wb 104T 2750.03sat-1-17--⨯⨯=I π∴I sat = 40.8 mAwill saturate the core.Figure 8Q9-1: B versus H curve for 43 - Mix ferrite .If the core is saturated, the calculation of inductance is of course no longer valid as it used the initialpermeability. The inductance now will be much reduced. Since under saturation ∆B = μ0∆H , effectively μr = 1. The use of an initial permeability such as μr = 850 implies that we have small changes (and also reversible changes) near around H = 0 or I = 0.When an inductor carries a dc current in addition to an ac current, the core will operate “centered” at a different part of the material’s B -H curve, depending on the magnitude of the dc current inasmuch as H ∝ I . Thus, a dc current I 1 imposes a constant H 1 and shifts the operation of the inductor to around H 1. μr will depend on the magnitude of the dc current.c. The same effect as passing a large dc current and saturating the core. When the core is saturated, theincrease in the magnetic field B in the core is that due to free space, i.e. ∆B = μo ∆H . This means we can use μ = 1 in Equation 8.31 to find the inductance under saturation. It will be about 0.10 mH / 850 or 0.12 μH , very small.Author’s Note: Static inductance can be defined as L = Flux linked per unit dc current or L = N Φ/I . It applies under dc conditions and I = dc current. For ac signals, the current i will be changing harmonically (or following some other time dependence) and we use the definition⎪⎭⎫ ⎝⎛⎪⎭⎫ ⎝⎛Φ=Φ=dt di dt d N i N L δδ Further, by Faraday’s law, since v is the induced voltage across the inductor by the changing total flux Nd Φ/dt , we can also define L by,⎪⎭⎫ ⎝⎛=dt di L vMoreover, since L = N δΦ/δi we see that the ac L is proportional to the slope of the B versus H behavior.*8.10 The transformera . Consider the transformer shown in Figure 8.70a whose primary is excited by an ac (sinusoidal) voltage offrequency ƒ. The current flowing into the primary coil sets up a magnetic flux in the transformer core. By virtue of Faraday's law of induction and Lenz's law, the flux generated in the core is the flux necessary to induce a voltage nearly equal and opposite to the applied voltage. Thus,dtNAdBdt d ==)linked f lux Total (υwhere A is the cross-sectional area, assumed constant, and N is the number of turns in the primary.Show that if V rms is the rms voltage at the primary (V max = V rms √2) and B m is the maximum magnetic field in the core, thenV rms = 4.44 NAƒB mTransformer equation[8.33]Transformers are typically operated with B m at the "knee" of the B -H curve, which corresponds roughly to maximum permeability. For transformer irons, B m ≈ 1.2 T. Taking V rms = 120 V and a transformer core with A = 10 cm ⨯ 10 cm, what should N be for the primary winding? If the secondary winding is to generate 240 V, what should be the number of turns for the secondary coil?b . The transformer core will exhibit hysteresis and eddy current losses. The hysteresis loss per unitsecond, as power loss in watts, is given byP h = KƒB m n V coreHysteresis loss[8.34]where K = 150.7, ƒ is the ac frequency (Hz), B m is the maximum magnetic field (T) in the core (assumed to be in the range 0.2 - 1.5 T), n = 1.6 and, V core is the volume of the core. The eddy current losses are reduced by laminating the transformer core as shown in Figure 8.70b. The eddy current loss is given bycore 22265.1V d B f P me ⎪⎪⎭⎫⎝⎛=ρEddy current loss [8.35]where d is the thickness of the laminated iron sheet in meters (8.70b) and ρ is its resistivity (Ω m). Suppose that the transformer core has a volume of 0.0108 m 3 (corresponds to a mean circumference of 1.08 m). If the core is laminated into sheets of thickness 1 mm and the resistivity of the transformer iron is 6 ⨯ 10-7 Ω m, calculate both the hysteresis and eddy current losses at f = 60 Hz, and comment on theirrelative magnitudes. How would you achieve this?Figure 8.70(a) A transformer with N turns in the primary. (b) Laminated core reduces eddy current losses.Solutiona. The induced voltage either at the primary or the secondary is given by Faraday’s law of induction (the negative sign indicates an induced voltage opposite to the applied voltage), that is,dtdB NA-=υ Suppose we apply this to the primary winding. Then υ = V m sin(2πft ) where f = 60 Hz and V m is the maximum voltage, that is V m = V rms (√2). ThendtdB NAft V m -=π)2sin( It is clear that B is also a sinusoidal waveform. Integrating this equation we find,)2cos()2(ft f NA V B mππ=which can be written asB = B m cos(2πft )so that the maximum B is B m given byfNAV fNA V B m m ππ222rms==where we used V m = V rms (√2). Thus,V rms =4.44NAfB mLet N P = Primary winding turns and assume f = 60 Hz, then()()()()T 2.1Hz 60m 1.044.4V12044.42rms ==m AfB V P N = 38 turns on primary Secondary winding turns are()()()()T 2.1Hz 60m 1.044.4V2402=S N = 75 turns on secondary b. Part a gives B m = 1.2 T. Then the hysteresis loss isP h =KfB m nV co reB m = 1.2 T()()()()36.1m 0108.0T 2.1Hz 607.150=h P = 131 WEddy current loss iscore 22265.1V d B f P me ⎪⎪⎭⎫ ⎝⎛=ρB m = 1.2 T()()()()W 154=⎪⎪⎭⎫ ⎝⎛Ω⨯=-37222m 0108.0m 106m 001.0T 2.1Hz 6065.1e P With 1 mm lamination and at this low frequency (60 Hz) hysteresis loss seems to dominate the eddycurrent loss. Eddy current loss can be reduced with thinner laminations or higher resistivity core materials (e.g. ferrites at the expense of B max ). Hysteresis loss can be reduced by using different core material but that changes B . Eqn. 8.34 is valid for only silicon steel cores only which have the required typical B m for power applications.8.11 Losses in a magnetic recording head Consider eddy current losses in a permalloymagnetic head for audio recording up to 10 kHz. We will use Equation 8.35 for the eddy current losses.Consider a magnetic head weighing 30 g and made from a permalloy with density 8.8 g cm -3 and resistivity 6 ⨯ 10-7 Ω m. The head is to operate at B m of 0.5 T. If the eddy current losses are not to exceed 1 mW, estimate the thickness of laminations needed. How would you achieve this?SolutionWe will apply the eddy current loss equation in this problem though this equation has a number of assumptions so that answer is only an estimate . The eddy current loss iscore 22265.1V d B f P me ⎪⎪⎭⎫⎝⎛=ρwhere the core volume is3633core m 10409.3 or cm 409.3g/cm8.8g30Density Mass -⨯===V Then,core22265.1V B f P d m e ρ=∴ ()()()()()()362273m10409.3T 5.0Hz 000,1065.1mW 106W 101---⨯⨯⨯=d ∴d = 2.07 μmVery thin (a page of a textbook is typically about 50 - 100 μm).*8.12 Design of a ferrite antenna for an AM receiver We consider an AM radio receiverthat is to operate over the frequency range 530 - 1600 kHz. Suppose that the receiving antenna is to be a coil with a ferrite rod as core, as depicted in Figure 8.71. The coil has N turns, its length is , and the cross-sectional area is A . The inductance, L , of this coil is tuned with a variable capacitor C . The maximum value of C is 265 pF, which with L should correspond to tuning in the lowest frequency at 530 kHz. The coil with the ferrite core receives the EM waves, and the magnetic field of the EM wave permeates the ferrite core and induces a voltage across the coil. This voltage is detected by a sensitive amplifier, and in subsequent electronics it is suitably demodulated. The coil with the ferrite core therefore acts as the antenna of the receiver (ferrite antenna). We will try to find a suitable design for the ferrite coil by carrying out approximate calculations - in practice some trial and error experimentation would also be necessary. We will assume that the inductance of a finite solenoid is2AN L o ri μγμ=Inductance of a solenoid [8.36]where A is the cross-sectional area of the core, is the coil length, N is the number of turns, and γ is a geometric factor that accounts for the solenoid coil being of finite length. Assume γ ≈ 0.75. The resonant frequency f of an LC circuit is given by()2/121LC f π=[8.37]a . If d is the diameter of the enameled wire to be used as the coil winding, then the length ≈ Nd . If we usean enameled wire of diameter 1 mm, what is the number of coil turns, N , we need for a ferrite rod given its diameter is 1 cm and its initial relative permeability is 100? b . Suppose that the magnetic field intensity H of the signal in free space is varying sinusoidally, that isH = H m sin(2πƒt )[8.38]where H m is the maximum magnetic field intensity. H is related to the electric field E at a point by H = E /Z space where Z space is the impedance of free space given by 377 Ω.. Show that the induced voltage at the antenna coil is2ππ377CfdE V m m =Induced voltage across a ferrite antenna [8.39]。

超导电力技术的发展与超导电力装置的性能检测胡　毅1,唐跃进2,任　丽2,蔡　炜1,陈轩恕1,石　晶2,陈　磊2,张翌晖2,郭　芳2(1.国网武汉高压研究院,武汉430074;2.华中科技大学超导电力研究中心,武汉430074)摘　要:充分利用国内各种优势资源开展超导电力技术的研究与开发,对于提高我国电力设备行业在国际市场上的竞争力及电力系统的技术经济性能均有重大的意义。

基于对国内外超导电力技术及超导电力装置的充分调研,概括了超导电力技术的研究现状,归纳了超导电力技术中的关键课题,即超导电力装置;超导电力系统的协调运行与系统理论研究;超导电力系统中的在线监测与控制策略;超导电力相关学科的基础研究。

指出了未来超导电力装置的研究重点,并给出了具有代表性的超导电力装置的试验、检测内容和性能检测方法,迈出了超导电力装置性能检测方法与规程研究的第一步。

关键词:超导电力技术;电力系统;超导电缆;超导磁储能系统;超导变压器;超导限流器中图分类号:TM26文献标志码:A 文章编号:100326520(2007)0720001208基金资助项目:国网武汉高压研究院科研基金(062SH080)。

Project Supported by Scientific Research Foundation of Wuhan High Voltage Research Institute of SGCC (062SH080).Development of Superconducting Pow er T echnology and Performance T estof Superconducting Pow er DeviceHU Y i 1,TAN G Yue 2jin 2,REN Li 2,CA I Wei 1,CH EN Xuan 2shu 1,SH I Jing 2,CH EN Lei 2,ZHAN G Yi 2hui 2,GUO Fang 2(1.Wuhan High Voltage Research Instit ute of SGCC ,Wuhan 430074,China ;2.R &D Center of Applied Superconductivity ,Huazhong Univercity of Science and Technology ,Wuhan 430074,China )Abstract :Application of superconducting power technology to conventional power industry is the inevitable step in the development of power industry.The development strategy of superconducting power technology ,f ull utilization of domestic dominant resource and establishment of superconducting power experiment and research base ,that has considerable significance in the continual development of national economy ,were reviewed.The present research state and key subjects in superconducting power technology were summarized.And ,the focal research points in fu 2ture superconducting power areas was presented.Finally ,the test items of some typical superconducting power de 2vices was discussed as the first step of the research for performance test and standard of superconducting power de 2vices.K ey w ords :superconducting power technology ;power system ;superconducting cable ;SM ES ;superconducting transformer ;SFCL0　引　言随着电力系统容量的增大、系统结构复杂化以及电力用户对供电品质要求的提高,电力系统已突显出了若干技术难题,如电力安全、高密度供电、高品质供电、高效率输送电等[1]。

超导合金英文作文Superconducting alloys are a fascinating area of research in the field of materials science. These alloys possess unique properties that make them highly desirablefor various applications. For instance, they exhibit zero electrical resistance at low temperatures, allowing for efficient transmission of electricity. This remarkable characteristic has the potential to revolutionize power generation and distribution systems.Moreover, superconducting alloys also have the abilityto generate intense magnetic fields. This property opens up possibilities for their use in magnetic resonance imaging (MRI) machines, particle accelerators, and even levitating trains. Imagine a world where trains float above the tracks, eliminating friction and enabling high-speed transportation!In addition to their electrical and magnetic properties, superconducting alloys are also known for their incredible strength. This strength, combined with their ability towithstand extreme temperatures, makes them ideal for applications in aerospace and defense industries. These alloys can be used to build lightweight yet sturdystructures for aircraft and spacecraft, enhancing their performance and durability.Furthermore, superconducting alloys have shown promisein the field of energy storage. By utilizing their abilityto store large amounts of electrical energy, these alloys can be used to develop more efficient and compact batteries. This could revolutionize the way we store and utilize energy, leading to a more sustainable and environmentally friendly future.Additionally, superconducting alloys have the potential to revolutionize the field of quantum computing. Their unique properties allow for the creation of qubits, the basic building blocks of quantum computers. These qubitscan store and process information in a way that is exponentially faster than traditional computers. This could lead to breakthroughs in fields such as cryptography, drug discovery, and optimization problems.In conclusion, superconducting alloys are a fascinating area of research with immense potential. Their unique properties make them highly desirable for various applications, ranging from power generation and transportation to aerospace and quantum computing. Continued research and development in this field will undoubtedly lead to exciting advancements that will shape the future of technology.。

Development prospect of smart grid姓名：赵海洋班级：电气二班学号：1304815081指导老师：刘增磊专业：电气工程及其自动化Development prospect of smart gridAbstractPower supply in twenty-first Century is facing major challenges such as environmental pressure, purchasing power, safe, reliable and efficient use. With the United States and the European Union as the representative of different countries and organizations are not about to build a flexible, clean, safe, economical and friendly smart grid, smart grid as the future development direction of the power grid. Smart grid has become a hot topic at home and abroad in recent years, the development trend of the future power grid.The smart grid is based on advanced computer, electronic equipment and advanced components such as, by introducing the communication, automatic control and other information technology, from the realization of the transformation of the electric power network to power network more economical, reliable, safe, environmental protection this ultimate goal. This paper mainly analyzes the research background of smart grid, and analyzes the necessity of the development of smart grid, smart grid concept, characteristics at home and abroad. Finally, the prospects for the development of smart grid are discussed, and summarized its advantages and problems. In science and technology leading the era of social change, the smart grid will show its strong vitality.Key words:Smart grid ; Electronic equipment ; Internet ; Grid system1 curriculum backgroundIn the 20th century, large power grid domain engineering as one of the greatest achievements of embodies the strategic layout of the energy industry, to achieve a variety of energy conversion into electrical energy after supplementing each other, complement each other's quick, flexible and highly efficient and energy distribution channels. However, the world's energy system is facing a choice, the current global energy supply and consumption trends from the environmental,economic, social and other aspects of the view is not sustainable. In the current world energy shortage crisis is increasingly serious, the scale of the power system continues to grow, the impact of climate change and other factors, the power supply in twenty-first Century is facing a series of new challenges. Therefore, in the EU, the United States and China, government, universities and research institutions and enterprises to participate in together, in order to ensure energy supply in the 21st century is facing technical problems, the technical difficulties and the technical route to carry out in-depth study proposed the concept of smart grid. At present, these countries and regions will increase the smart grid to the height of the national strategy, the development of smart grid is regarded as an important measure of national security, economic development and environmental protection. Smart grid is an effective way to solve the problem of power supply in 2l century.In China with the rapid advancement of Jiangsu coastal development, Yancheng area of wind power, solar power and other new energy industry development rapidly, the access and the normal operation of power grid has become increasingly apparent, the grid is facing a tremendous challenges and opportunities. On the one hand, the grid needs to cope with the increasingly serious pressure on resources and the environment, a wide range of resources to achieve the optimal configuration, improve the ability of all-weather operation, meet the needs of the adjustment of energy structure, adapt to the electric power system reform; on the other hand, transmission and distribution, power, information technology, digital and other technology progress to solve a series of problems provide a solid technical support [2]. From this smart grid has become the direction of the development of modern power industry. 2009, held at the International Conference on UHV transmission technology, by 2020, China will be fully integrated into a unified strong smart grid.2 Smart GridSmart grid (smart power grids), is the power grid intelligent, intelligent smart grid is the power grid, also known as the "2 power", which is based on high-speed bidirectional communication network integration, through the control method of advanced sensing andmeasurement technology, advanced equipment, advanced technology and the application of advanced decision support system, to achieve grid reliability, security, economic, efficient, environmental friendly and safe target, its main features include self-healing, incentive and resist the attacks, including users, in twenty-first Century to meet the user demand for power quality, allowing various forms of power generation, power and market access start asset optimization and efficient operation. The smart grid includes a smart meter infrastructure for all power flow recording system. Through smart meters, it will be used to monitor the power status. Smart grid including superconducting transmission line to reduce the transmission power loss, also has the integration of new energy, such as wind energy, solar energy and other capabilities. The modern power network has been considered by many governments to reduce energy dependence and slow down the global warming effect. Intelligent metering as part of the smart grid, but it itself can not be referred to as a smart grid. From the angle of technology development and application, all countries in the world, the domain experts, scholars generally agree that the following points of view: smart grid is the advanced sensing technology, information and communication technology, analysis decision technology, automatic control.The comprehensive utilization of resources and renewable energy and resources, such as solar power, wind power generation, combined heat and power, biogas utilization, etc.. The distribution of electric power technology and energy technology, a new modern power grid and power grid infrastructure and highly integrated form. The research and development of smart grid is still in the initial stage, the national conditions and resource distribution, direction and focus of development are not the same, the international has not reached a unified and clear definition. According to the current research situation, the smart grid is the grid into new technologies, including advanced communication technology, computer technology, information technology, automatic control technology and power engineering technology, thus giving Grid some kind of artificial intelligence, which has strong adaptability, become a fully automated power supply network.3 development status of smart grid3.1 current research situation in foreign countriesIn the United States, the Obama administration's economic stimulus plan, there are about $4 billion 500 million loan for smart grid investment and regional demonstration projects. Smart grid uses digital technology to collect, exchange and process data to improve the efficiency and reliability of power system. Smart grid advocates to make customers believe that smart grid will help customers to reduce the cost of electricity. In addition, the solar energy distribution of renewable energy, plug and pull electric vehicles will also create a large number of indirect work opportunities, smart grid will bring millions of green jobs".Three AC transmission network nationwide in the United States, due to the lack of investment, technological obsolescence, United States in smart grid construction pay more attention to the electric power network infrastructure upgrades, in order to improve the level and reliability of power grid operation. At the same time, to maximize use of information technology, intelligent system of artificial replacement of the. Its focus on the development of smart grid distribution and power side, focusing on promoting the development of renewable energy, focusing on business model innovation and customer service upgrade.European countries for the development of smart grid is mainly promote and meet the needs of the rapid development of wind, solar and biomass and other renewable energy, renewable energy, distributed power pickup and carbon zero emissions and other environmental problems as the focus. Japan to build smart grid based on new energy. Japan will be based on its own national conditions, mainly around the large-scale development of solar energy and other new energy sources, to ensure the stability of power grid system to build smart grid. After the Japanese government plans to consult with the power company, began to build a large-scale smart grid test.3.2 domestic research progressTo carry out the research of the smart grid system though slightly late, but in the field of smart grid technology carried out a lot of research and practice, in the field of power transmission, a number of research application reached the international advanced level, in the distribution of electric field, the researches and applications of intelligent system is also actively exploring. China'ssmart grid and Western countries are different, is established in the UHV construction on the basis of strong smart grid, China smart grid will in UHV power network as the backbone network using advanced communication and information and control technology, with information technology, digitization, dynamic, interactive for the characteristics of independent innovation, the world's leading smart grid construction. Its features will include the realization of information technology, digital, automation and interaction, while the management to achieve the group, intensive lean, standardization.In February 2, 2009, China energy expert Wu Jiandong in "comprehensive push the revolution to promote economic innovation and transformation of" interactive grid, clearly Chinese grid must implement the "interactive grid" revolutionary transformation. In 2008 5 held at the end of the UHV International Conference, Vice Premier Zhang Dejiang said, China from reality and actively explore the road of smart grid development in line with the national conditions of Chinese. This is the first time our country leaders on the expression of smart grid in public attitude. The meeting, the China State Grid Corp announced, will be divided into three stages to promote the construction of strong smart grid: from 2009 to 2010 for the planning of the pilot phase, focusing on the development planning of strong smart grid ", to develop technical and management standards, the development of key technologies and equipment research and development, and all aspects of the pilot work; from 2011 to 2015 for the comprehensive construction stage speed up, UHV power grid and the urban and rural distribution network construction, the initial formation of intelligent power grid operation control and interactive service system, a major breakthrough and wide application of key technologies and equipment; from 2016 to 2020 as the leading phase of ascension, the completion of a comprehensive unified strong smart grid technology and equipment, all reached the international advanced level. The grand blueprint for many power equipment and automation enterprise excited, and have invested in human, material and financial resources of the smart grid of technology research, hope can in this round with technology of the revolutionary nature of the industry reshuffle topped. China's western region power grid construction level is lower than the eastern region, while in the west is the large amount of wind power, solar and other clean energy waiting for access to the grid. Therefore, it is expected thatthe pickup of clean energy in China will in the west to carry out a pilot.4 the importance of power gridRemember that the second half of the last century, the United States at least three large-scale blackout, destruction of large, the impact is deep, than previously expected, especially New York 1977 blackout, once caused the city to looting and arson, blackouts will some people pushed to the edge of antisocial, a direct threat to national security.In the last century, the United States, the major power outages, basically quickly identify the cause. Such as in 1965 led to large-scale power outage causes the northeastern United States is relay station fault, 1996 resulted in Oregon, and California and other western states blackout the culprit is lead to short-circuit transmission line fall into the bushes. The 1977 New York blackouts reason is very simple, lightning destroyed the suburb of New York City, somewhere in the grid, immediately triggered the whole city power network paralysis.1977 blackout caused by social chaos or to the United States military to provide inspiration, a magic weapon is to attack the enemy's power grid, leading to the enemy communications, electricity, production, transportation and paralysis. The US military developed a weapon called "graphite bomb", which is called "power bomb" ". It installed in the cluster weapons bullet head, shaped like a tin, is equipped with a large number of thinner than a human hair graphite fiber, graphite bomb, those countless graphite filaments, forming a waterfall, from the sky floating down, winding in the high-voltage lines, causing a short circuit, burned power equipment.American during the Kosovo war and the Iraq war use graphite bombs, destroying Yugoslavia Belgrade power supplies and in Baghdad, Iraq grid, even in 2009 at the beginning of the new year when the outbreak of war between Hamas and Israel, the Israeli air force to the Hamas controlled Gaza City put graphite bombs and the entire Gaza City into the city of fear.The path of social development often forms paradox. People are increasingly aware of the importance of the safe operation of the power grid to the national security, but the degree of people's reliance on the power is more and more serious. The development of science and technology does not give full guarantee to the security of the power grid, but it is this side of the defect to overcome, the other side of the loophole and the emergence of. Now the power, in against lightning, floods, physical short-circuit, technology is increasing day by day, but after the traditional threat, a new threat again, as some of the major power plant near, always set of military airdefense missile group, to destroy the invading enemy missiles.The more modern things, the more show its vulnerable side. Terrorist attacks, but also aimed at the relationship between the country's lifeblood of the power grid facilities. Now a new threat is constantly being mentioned, that is, hackers".This century is only ten years, but with the world's most advanced and mature technology of the United States, has suffered several major power outages. 2003 power outage, extended from Michigan to New York and even Canada, 50 million people did not have the power supply. 2008, Florida, another major power outage, 3 million people did not have the power supply.Confusing is that, with the last century after the last half of the power cut, the official organization of several major power outage cause investigation, check to check, still not a unified conclusion. However, the conclusion of a non official but in the media on a wide range of communication: lead to the Great North American blackout of 2003 and 2008 Florida blackout "murderer" is Chinese military hackers. The first release of this speculation is the United States "have an ulterior motive" National Journal magazine.Although United States of Wired magazine after the National Journal magazine soon published refutations, refers to "Chinese hacker attacks on" false news, Blackout "not surprising" is caused by manual operation errors, rather than the so-called "hacker attacks, but the story about" Chinese hacker "in the United States has a market. False news that much has become true news.But, on the other hand, it is a necessary method for the contemporary information age to reflect on the security of the power grid from the perspective of "hacker". Highly intelligent power grid, the power grid is becoming more and more dependent on network technology, to improve the efficiency of the power grid at the same time, also to the enemy through the network war destroyed each other grid opportunities.US military in June 23rd formally announced the establishment of cyber warfare command, the United States has become the first public network to form a war agency. Chinese hacker threat theory to mobilize the generosity of the U.S. taxpayer support the government, Congress soon passed the relevant budget and funding, the United States in the fight for the right to make network in the upper hand.Recall the United States blackout, the United States can be seen in each round after blackout of collective reflection and decisive actions. "A power outage, even for a few seconds, is no less than a great earthquake". Americans on the big power cut across a regular perspective, to promote its innovative breakthrough.5 challenges encountered in power gridAccording to the world economic forum recently a report, the smart grid mainly exists six challenges: Party Supervision incentive mechanism to a standstill, this policy environment factors hinder the smart grid create persuasive business application cases; future legislation is not clear direction, in the value chain of the utility 2081.272,92.40,4.65%, risks and benefits is difficult to adjust and distribute; data privacy, network security, interactivity and standard is still facing challenges; goal conflicts still exist; pilot projects in terms of customer interaction also encountered challenges, including how efficient communication with clients such as.The composition of smart grid includes several aspects such as data acquisition, data transmission, information integration, analysis and optimization, information display, etc.. Smart grid greatly expands the supervisory control and data acquisition system (supervisorycontrol and data acquisition, SCADA) data acquisition range and quantity, acquisition is involved in power grid operation, equipment status and measure customer, including a variety of real-time data. Power grid company will these real-time data and other data management, etc. through more advanced means of communication transmission, integration and optimization analysis, and then through analysis and optimization of the processing of information is presented to the users with customized portal and the instrument panel.From the view of the current pilot experience, in the process of the realization of the smart grid, technology relatively is not a problem, a greater degree should concern related mechanism, and overall environment for the development of smart grid.In the mechanism of the change, it may gradually change people's behavior. But still, there may be a lot of new mechanisms (such as price mechanism) is not sensitive to the people. So, in addition to the higher degree of automation of electricity meter terminal control directly, more important is the change in consumer behavior is not sensitive to the user through education, training and other means. Moreover, people's consumption behavior of the continuous development of the new pricing mechanism based on the mode also need to improve.6 concept and characteristics of smart gridThe so-called smart grid that to physical grid based, modern advanced sensor technology, communication technology, information technology, computer technology and control technology with the physical power highly integrated and the formation of new grid. It in order to fully meet the user of electricity demand and optimize the allocation of resources, ensure power supply safety, reliability and economy, to meet the environmental constraints and ensure power quality and adapt to power market development for the purpose, implementation of users a reliable, economical, clean and interactive power supply and value-added services.In accordance with the description of China's well-known energy expert Wu Jiandong Mr., smart grid is known as the interactive smart grid or grid interactive, interactive grid is defined in the model on the basis of open and interconnected information, through the loading system digital equipment and upgrading the grid network management system, to achieve generation, transmission, power supply, electricity, customers the sale of electricity, power grid level scheduling, comprehensive service etc. the electric power industry in the whole process of intelligence, information, classification of interactive management, is a collection of the industrial revolution, technical revolution and management revolution of comprehensive efficiency change. The core content of smart grid is to realize grid information technology, digitization, automation and interaction, referred to as "strong smart grid". Smart grid concept of time, though not long, but the enthusiasm of the change is extremely high, the fundamental reason is, smart grid strategy not only for global energy transformation provides an important opportunity, but also provide unlimited business opportunities and the rare development opportunity for the electrical equipment industry.The smart grid is an inevitable choice for the new energy of power supply and demand balance, pickup, power grid reliability and information security challenges facing mankind. It represents the a vision of the future evolution of the grid, combined with the advanced automation technology, information technology and controllable power equipment, from power generation to use electricity for the entire power supply chain optimization management support, especially for the new energy of the pickup and power grid safe operation. The smart grid in thesafe operation of power grid can provide users with high quality and reliable power under the premise of improving energy efficiency, reduce the impact on the environment, at the same time can form a new industrial base to promote employment.In general, the smart grid has the following features1) Stable and reliable self healing. Self healing is to achieve the main function of the safe and reliable operation of the power grid, one that does not need or only need a small amount of human intervention, the electric power network in existence issue of components in isolation or to restore the normal operation and minimize or avoid the interruption of power supply for the customers.2) Security against attacks. Regardless of the physical system or computer by external attack, smart grid can effectively resist the resulting to the power system itself attack damage and the formation of the other areas of damage, the event of a disruption, also can quickly restore operation.3) Compatible power generation resources. Traditional power network is mainly for remote centralized power generation by introducing similar to computer "plug and play" technology, especially the distributed generation resources), the grid can accommodate contains centralized power generation, a variety of different types of power and energy storage device in the field of power interconnection.4) Interactive power users. Grid in the run in with the user equipment and behavior interact will be regarded as the integrity of the power system part of, can promote power users play an active role and achieve power operation and environmental protection benefits.5) Coordination - electricity market. And wholesale electricity markets and retail electricity market to achieve a seamless and effective market design can improve the power system planning, operation and reliability management level, enhance the management ability of power system to promote the improvement of the efficiency of electricity market competition.6) Efficient asset optimization. Introducing the most advanced information and control technology to optimize the efficiency in the use of equipment and resources can improve individual assets utilization efficiency, optimizes the network operation and expansion as a wholeand reduce its running maintenance cost and investment.7) High quality electric energy quality. In the digital, high-tech dominant economic model, the power quality of the power users can be effectively guaranteed, and the power quality of the differential pricing.8) Integrated information system. Implementation, including monitoring, control, maintenance, energy management system (EMS) and distribution management (DMS), market operation (MOS), enterprise resource planning (ERP) and all kinds of other information system between integrated and implemented on the basis of business integration.7 development prospects of smart gridChina's vast geographical, resource and demand distribution is uneven, especially the large-scale renewable energy mainly concentrated in the western region, the need for smart grid has a large capacity of the transmission channel. And in dense areas of Eastern load, the development of renewable energy tend to be small and close to the load and need to smart grid can be compatible with distributed utilization at the same time different from has been in power demand saturation period in Europe and the United States and other developed countries. China's rapid economic development, power demand to maintain high growth every year, the need for smart grid to meet this growth and to ensure the safety of electricity, reliable supply and continuously improve the user requirements from. I look at the current situation of the development of electric power, China is currently building a special high-voltage power grid. To effectively build the future of strong smart grid transmission grid, North China, East China and other regional power grid has been carried out digital substation and dispatching integrated a number of work, so that our country has possessed good smart grid operation control based. But in the distribution network, China's vast territory, uneven development, most areas are still weak electricity, away from the smart power distribution and intelligent power with a large gap. At the same time, due to the superconducting, energy storage and other technologies are still to mature development, distributed energy has not been into large-scale use, smart grid in these areas is still a lack of certain external conditions. Smart grid construction is a long-term strategy, the smart gridinvestment is huge but due to the system to reduce the energy consumption and blocking and improve the energy efficiency, obtained the higher power quality and power supply reliability, low system operation and maintenance costs. Reduce the assets of the power generation and transmission and distribution, and so on. According to the United States is expected to bring revenue will be more than 400%.Smart grid can realize power grid operation reliable, safe, economical, efficient, environmentally friendly and safe use, full support and promote nationwide resource optimization configuration and way of development of new energy and new energy utilization progress. This can also lead to the IT as a feature of other related industries and services of the great development. It will be an inevitable trend of development at the same time, the smart grid is a huge systematic project. It needs not only participate in electric power industry equipment manufacturing, construction, power generation, operation, research and other almost all professional units, also need more industry, multi-disciplinary, multi field of the cross, the need for more government guidance and policy support. This shows that the development and construction of smart grid will be the continuous application of cutting-edge technology and set, the long-term process of continuous change of the power grid operation.As one of the key technologies of smart grid, digital substation technology will be a long-term process, and the maturity of the technology needs to be combined with the engineering application. The technology of digital substation is based on the technology of integrated automatic substation, which can achieve the stable development of application and the breakthrough of key technologies.At present, distributed energy in China only accounted for a smaller proportion, but it is expected within the next few years, distributed power supply can not only as a centralized power is a kind of important supplement, will also in the comprehensive utilization of energy occupies very important position, therefore, whether it is to solve the city's power supply, solving the remote and rural areas of electricity, has a huge potential market, once solved the main bottleneck, distributed energy system will get rapid development.。

a r X i v :0808.4093v 1 [c o n d -m a t .s t r -e l ] 29 A u g 2008Where can we find the highest T c in SmO 1−x F x FeAs superconductor?Xiuqing Huang 1,2∗1Department of Physics and National Laboratory of Solid State Microstructure,Nanjing University,Nanjing 210093,China2Department of Telecommunications Engineering ICE,PLAUST,Nanjing 210016,China(Dated:August 29,2008)We report on doping dependencies of superconducting transition temperatures in SmO 1−x F x FeAs superconductor using the newly developed real space spin-parallel theory of superconductivity.Based on the experimental lattice constants (a and c )and the relation c/a ≈3,it is shown an-alytically that the highest superconducting transition temperature T c can potentially be observed in the following eight doped samples of x =2/27,1/12,1/8,1/6,1/5,1/3,1/2and 2/3.By intro-ducing the concept of optimal mixed-phase,we provide a qualitative interpretation of the causes of various high-T c phases reported for SmO 1−x F x FeAs;for instance,x =0.1and T c =55K [Chin.Phys.Lett.25,2215(2008)],x =0.15and T c =43K [Nature 453,761(2008)],x =0.2and T c =54K [Phys.Rev.Lett.101,087001(2008)],x =0.3and T c =54.6K [arXiv:0806.2839],x =0.35of T c =52K [arXiv:0806.2451],x =0.4of T c =53K [arXiv:0808.3666].PACS numbers:74.20.-z,74.25.QtThe recent discovery of superconductivity with a su-perconducting transition temperature (T c )of 26K in the iron-based LaO 1−x F x FeAs superconductor [1]has gen-erated a great deal of interest.Through elemental sub-stitution,T c has rapidly raised from 26K to 55K in the ReO 1−x F x FeAs family [2,3].Obviously,such a high T c cannot be explained by the conventional BCS the-ory.It is worth emphasis that BCS theory even doesn’t work for low-temperature superconductivity.In other words,this famous theory is entirely incorrect [4].Some researchers believed that the new FeAs superconductors reveal the need for fresh mechanism and theoretical mod-els.However,our viewpoint is somewhat different from the mainstream’s idea of superconductivity.In our opin-ion,if there exists only a few superconductors in nature,it may be reasonable to expect different superconducting materials have different reasons.As more and more ma-terials (several thousands)with superconductivity have been discovered,it becomes more clear that any elec-tronic pairing and superconducting phenomena should share exactly the same physical mechanism.Thus,the discovery of FeAs family further demonstrates that we need a unified theory for the description of different su-perconductors [4].More importantly,this unified theory should be built on the most common and reliable elec-tromagnetic interactions,and any artificial quasiparticles should be excluded from the suggested theory.In the iron-based layered superconductors,SmO 1−x F x FeAs has been studied extensively be-cause of the highest T c among this class of materials.We think that the most unconventional behavior in SmO 1−x F x FeAs lies in the optimal doping problem.As we know,the superconducting transition for five SmO 1−x F x FeAs samples of doping level x =0.1[2],0.2[5],0.3[6],0.35[7]and 0.4[8]with almost the same temperature T c =55K,54K,54.6K,52K and 53K have been reported by different authors,respectively.This raises one basic question:Why can the maximum T c for the superconducting SmO 1−x F x FeAs occur over a rather wide range of carrier concentration?or among these high T c superconducting phases,which one is the real optimal doped sample?To the best of our knowledge,this question has so far not been noted and discussed anywhere.Undoubtedly,the existing theory of superconductors could not explain these experiments.In the present paper,based on the newly developed theory of superconductivity [4,9,10,11,12,13],we try to provide an explanation for these observations.Our theory can be explicitly illustrated in Fig. 1.Fig.1(a)shows a real-space quasi-zero-dimensional lo-calized Cooper pair.In a previous paper [9],it has been shown that there are two special positions where the lo-calized Cooper pair will be in its minimum energy states.To maintain a stable superconducting phase (minimum energy),first the Cooper pairs of Fig.1(a)must con-dense themselves into a real-space quasi-one-dimensional dimerized vortex line (a charge-Peierls dimerized transi-tion),or a Cooper pairs’s charge river,as shown in Fig.1(b).And second,in order to further minimize the system energy,the vortex lines must self-organize into four pos-sible quasi-two-dimensional vortex lattices where a uni-form distribution of vortex lines is formed in the plane perpendicular to the stripes,as shown in Figs.1(c)-(f).Thus,the analytical doping level x is given byx =p (h,k,l )=2×1k ×1FIG.1:The principle in FeAs superconductors.(a)(b)a quasi-one-dimensional dimerized vortex lattices with a uniform distribution of in XZ plane,(d) LTT2(h,k,l),the and(f)are the simple hexagonal(SH)phasesreal-space low-energycrystals).Accordingbe tuned directly bycharge carrierwords,for a giventimal matchingand charge carrierperconductingductor.Table I.shows the experimental values of T c,lat-tice constants(a and c)and c/a for SmO1−x F x FeAs superconductor[2,3,5,6,7,8].Note that the ratio of c/a is very close to3for all samples.This in turn leads to some minimum-energy superconducting vortex phases of Fig.1with the highest superconducting transi-tion temperatures of the corresponding superconductors. By utilizing the Fig.1-ground theory and the relationcandidates of op-superconductor,are LTT1(9,1,3),,1,2),SH2(10,1,1),constants(a and c)and c/a ratio for SmO1−x F x FeAs superconductor,where a (=a0/√0.1543K2.7868.4963.049X.H.Chen et al.[3]0.3054.6K2.7778.4823.054Yanwei Ma et al.[6]0.4053K2.7788.4763.051Lei Wang et al.[8]FIG.2:The schematic plot of eight analytical superconducting vortex lattices for SmO 1−x F x FeAs superconductor based on arelationship of the lattice constants c/a ≈3.LTT2(6,1,1),SH1(4,1,1)and LTT1(3,1,1)phases with the doping level x =2/27≈0.07407,1/12≈0.0833,1/8=0.125,1/6≈0.1667,1/5=0.2,1/3≈0.3333,1/2=0.5and 2/3≈0.6667,respectively.A new struc-tural parameter δintroduced for evaluating the vortex lattice deformation is given byδ=|A/C −(A/C )0|×1004111.332/√6112.0021/3LTT203a√10113.332√38121.332/√12122.0021/12LTT206a √9131.0012/27LTT109alowest doped superconducting SmO 1−x F x FeAs sample,in favor of the most recent experimental result that su-perconductivity emerges at x ∼0.07in SmO 1−x F x FeAs superconductor [5].Theoretically,we can obtain accurate superconducting vortex phases (see Fig.2)from the data of lattice con-stants of the superconductor.Experimentally,the real superconducting phases are probably some mixture of the vortex phases of Fig.2.We therefore find it instructive to construct some mixed vortex phases for SmO 1−x F x FeAs with a required doping level x .For the simplest situa-4TABLE III:The theoretical prediction of two-phases mixed superconducting vortex lattices for several experimental SmO1−x F x FeAs samples.x Mixed vortex phases x1x2ααLTT2(12,1,2)+(1−α)LTT1(6,1,2)1/121/60.80αLTT1(6,1,2)+(1−α)LTT2(12,1,2)1/61/120.80 0.3αLTT2(6,1,1)+(1−α)SH2(10,1,1)1/31/50.75 0.35αLTT2(6,1,1)+(1−α)SH1(4,1,1)1/31/20.90x1−x2,(2)where x1and x2are the doping levels of the pure vortex lattices of Fig.2,andαis the weight factor.The combination of Eq.2and Fig.2may explain the experimental observations of various high-T c phases reported for SmO1−x F x FeAs[2,3,5,6,7,8],as shown in Table III.It is no doubt that to have a correct un-derstanding of the relation between the vortex lattices and superconducting transition temperature T c of the su-perconductors,we need to do more detailed qualitative research.Brief summary and discussions:the optimal doping problem in the new iron-based SmO1−x F x FeAs super-conductor has been studied by using the newly devel-oped unified theory of superconductivity.Based on the relation of the experimental lattice constants c/a≈3, it is shown analytically that the highest superconduct-ing transition temperature T c may be observed in eight doped samples of x=2/27,1/12,1/8,1/6,1/5,1/3, 1/2and2/3.By introducing the new concept of op-timal mixed-phase,we provide a qualitative interpreta-tion of the causes of various high-T c phases reported for SmO1−x F x FeAs superconductor.To further enhance su-perconducting transition temperature of the iron-based superconductors,high-quality single crystal samples with one of the above doping levels of Fig.2must be precisely grown.Finally,a challenge question:Can room temper-ature superconductors be achieved from iron-based ma-terial?Disappointedly,our theory predicts that,for any iron-based superconductors,their superconducting tran-sition temperature is difficult to break through T c=60 K.This research is in progress.∗Electronic address:xqhuang@[1]Y.Kamihara et al.,J.Am.Chem.Soc.130,3296(2008).[2]Ren Zhi-An et al.,Chin.Phys.Lett.25,2215(2008).[3]X.H.Chen,T.Wu,G.Wu,R.H.Liu,H.Chen and D.F.Fang,Nature453,761(2008).[4]Xiuqing Huang,arXiv:0804.1615.[5]R.H.Liu et al.,Phys.Rev.Lett.101,087001(2008).[6]Yanwei Ma,Zhaoshun Gao,Lei Wang,Yanpeng Qi,Dongliang Wang,Xianping Zhang,arXiv:0806.2839.[7]Zhaoshun Gao et al.,arXiv:0806.2451.[8]Lei Wang,Zhaoshun Gao,Yanpeng Qi,Xianping Zhang,Dongliang Wang,Yanwei Ma,arXiv:0808.3666.[9]Xiuqing Huang,arXiv:0806.3125.[10]Xiuqing Huang,cond-mat/0606177v5.[11]Xiuqing Huang,arXiv:0805.0355.[12]Xiuqing Huang,arXiv:0805.3977.[13]Xiuqing Huang,arXiv:0807.0899.。

New Electron-Doped Superconducting Cuprate Li x Sr2CuO2Br2Tetsuya Kajita1, Masatsune Kato1*, Takashi Suzuki1, Takashi Itoh2, Takashi Noji1 and Yoji Koike1*E-mail address: kato@teion.apph.tohoku.ac.jp1Department of Applied Physics, Graduate School of Engineering, Tohoku University, 6-6-05 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan2Center for Interdisciplinary Research, Tohoku University, 6-3 Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan(Received )A new electron-doped superconductor Li x Sr2CuO2Br2 with x = 0.15 has successfully been synthesized by an electrochemical Li-intercalation technique. The magnetic susceptibility shows superconductivity of bulk with the superconducting transition temperature T c = 8 K. This compound is the first electron-doped superconducting cuprate with the K2NiF4 structure.KEYWORDS: superconductivity, Li-intercalation, layered perovskite, cuprate, electron-dopingSince the discovery of high-T c superconductivity1), a large number of superconducting cuprates have been synthesized. Most of them are hole-doped superconductors, including (La, Sr)2CuO42) and YBa2Cu3O7.3)On the other hand, only two families of electron-doped superconducting cuprates are known: one is T'-(Ln, Ce)2CuO4 (Ln : lanthanide)4) and the other is the so-called infinite-layer compounds (Sr, Ln)CuO2.5)As shown in Fig. 1, Sr2CuO2Br2 is a layered perovskite with the K2NiF4 structure and essentially isostructural to the well-known hole-doped high-T c superconductor (La, Sr)2CuO4. The Sr2CuO2Br2 contains CuO2 planes as in the case of (La, Sr)2CuO4, but the out-of-plane oxygen ions at the apices of the CuO6 octahedron are replaced by Br- ions, and (La, Sr) by Sr. In the rock-salt layer of Sr and Br, Sr2+ ions shift a little towards the nearest CuO2 plane and Br-ions away from the CuO2 plane, which is due to the larger radius of Br- than of O2- and the smaller Coulomb attraction between Cu2+ and Br- than between Cu2+ and O2-. This leads to the formation of the Br-- Br- double layers. Accordingly, Li+ ions are expected to be readily intercalated between the electronegative Br- layers, which are weakly bound through the van der Waals force, as in the case of Li x FeOCl 6) and the superconducting Li x HfNCl (the superconducting transition temperature T c = 25.5 K). 7)In this paper, we report the synthesis and superconductivity of a new electron-doped superconducting cuprate, namely, the Li-intercalated layered perovskite Li x Sr2CuO2Br2.Polycrystalline host samples of Sr2CuO2Br2 were synthesized as follows. First, polycrystals of SrCuO2 were prepared from stoichiometric amounts of SrCO3 and CuO powders. The powders were mixed, ground and heated in air at 925 °C for 10 h. The products were then pulverized, pressed into pellets and sintered for 20 h at 950 °C. Next, the obtained single-phase samples of SrCuO2 were mixed with a stoichiometric amount of SrBr2, pressed into pellets and then sintered for 24 h at 825 °C. Finally, the obtained samples of Sr2CuO2Br2 were mixed with naphthalene of 30 weight %, pelletized with the dimensions of 7 mm in diameter and 1.5 mm in thickness and then sintered again for 6 h at 600 °C to obtain porous samples of Sr2CuO2Br2 which were suitable for the homogeneous intercalation of Li. The electrochemical Li-intercalation was carried out at room temperature in an argon-filled glove box. A three-electrode cell was set up as Sr2CuO2Br2|1.0 M LiClO4/PC|Li. The working electrode was a pellet of Sr2CuO2Br2 which was put between Ni meshes. The counter electrode was a sheet of Li. As an electrolyte, 1.0 M LiClO4 dissolved in propylene carbonate (PC) was used. A sheet of Li was used also as a reference electrode. The Li-intercalation was performed under a constant potential of 0.5 V (vs Li/Li+) using a potentiostat. The total amount of Li intercalated intoSr2CuO2Br2 was estimated to be 0.15 according to the simple Faraday law and also the ICP analysis. All products were characterized by powder x-ray diffraction using Cu Kαradiation to be of the single phase. Since the products were unstable in air, they were mixed with grease in order to avoid the exposure to the moisture in the atmosphere during the measurements. The magnetic susceptibility was measured using a SQUID magnetometer in a magnetic field of 3 Oe.Figure 2 shows the powder x-ray diffraction pattern of Li0.15Sr2CuO2Br2. The pattern is the same as that of the host sample. All the peaks can be indexed on the basis of the tetragonal symmetry, indicating no formation of byproducts. Moreover, no change of the lattice parameters through the Li-intercalation is observed within our experimental accuracy.Figure 3 displays the temperature dependence of the magnetic susceptibility of Li0.15Sr2CuO2Br2. A single-step diamagnetic response due to the Meissner effect is observed below 8 K. The superconducting volume fraction estimated at 2 K on field cooling is about 6 %, indicating that the superconductivity is of bulk. The small value may suggest the presence of a pristine region of Sr2CuO2Br2 in the sample. At present, we have not yet succeeded in the electrical resistivity measurement because the porous Li-intercalated samples are too brittle for us to make electrically good contact.The present compound Li x Sr2CuO2Br2 is the first electron-doped superconducting cuprate with apical anions. So far, it has been believed that hole carriers cannot be introduced into the CuO2 plane with no apical anion and that electron carriers neither into the CuO2 plane with apical anions. In the A2CuO2X2 system (A = alkaline earth metal; X = halogen) with apical halogen ions of X, actually, both Sr2CuO2F2+x (T c = 46 K)8) and (Ca, Na)2CuO2Cl2 (T c = 26K)9) are hole-doped superconductors. The noticeable difference in the carrier type is considered to come from the difference in the length of the a-axis. The a-axis length a = 3.99 Å in the present compound is much larger than those of Sr2CuO2F2 (a = 3.81 Å) and Ca2CuO2Cl2 (a = 3.84 Å). The increase in the a-axis length, namely, the increase in the Cu-O bond length in the CuO2 plane decreases the Madelung potential at the Cu site, so that electronegative electron carriers tend to be readily introduced into the CuO2 plane. According to the empirical rule of the carrier-doping into the CuO2 plane, the critical length of the Cu-O bond in the CuO2 plane at which the carrier type changes from hole-like to electron-like is 1.94 Å, namely, a = 3.88 Å. 10)The present result is consistent with this rule.In conclusion, we have successfully synthesized a new superconductor Li0.15Sr2CuO2Br2 with T c = 8 K, which is the third family of electron-doped superconducting cuprates, using the electrochemical Li-intercalation technique. Thiscompound is the first electron-doped superconducting cuprate with apical anions. It has been found that the value of the a-axis length is crucial to the carrier type in the superconducting cuprates with the CuO2 plane.This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan.References1) J. G. Bednorz and K. A. Muller: Z. Phys. B 64 (1986) 189.2) K. Kishio, K. Kitazawa, S. Kanbe, I. Yasuda, N. Sugii, H. Takagi, S. Uchida, K.Fueki, S. Tanaka: Chem. Lett. (1987) 429.3) M. K. Wu, J. R. Ashburn, C. J. Torng, P. H. Hor, R. L. Meng, L. Gao, Z. J. Huang,Y. Q. Wang and C. W. Chu: Phys. Rev. B 58 (1987) 908.4) Y. Tokura, H. Takagi and S. Uchida: Nature 337 (1989) 345.5) M. G. Smith, A. Manthiram, J. Zhou, J. B. Goodenough, J. T. Markert: Nature 351(1991) 549.6) P. Palvadeau, L. Coic, J. Rouxel and J. Portier: Mat. Res. Bull. 13 (1978) 221.7) S. Yamanaka, K. Hotehama and H. Kawaji: Nature 392 (1998) 580.8) M. Al-Mamouri, P. P. Edwards, C. Greaves and M. Slaski: Nature 369 (1994) 382.9) Z. Hiroi, N. Kobayashi and M. Takano: Nature 371 (1994) 139.10) Y. Tokura: Physica C 185-189 (1992) 174.Figure CaptionsFig. 1 Crystal structure of Sr2CuO2Br2.Fig. 2 Powder x-ray diffraction pattern of Li0.15Sr2CuO2Br2 at room temperature. The hump around 20° is due to grease mixed with the powdered sample in order toavoid the exposure to the moisture in the atmosphere.Fig. 3 Temperature dependence of the magnetic susceptibility of Li0.15Sr2CuO2Br2 measured in a magnetic field of 3 Oe on warming after zero-field cooling andthen on cooling in a field. The inset shows the onset of the superconductingtransition on an expanded scale.SrOCuBr Fig. 101011020304050607020020041030611011407010215110208θ(deg.)05Li 0.15Sr 2CuO 2Br 2　2000012217Fig. 2Fig. 3。