Charged two-dimensional magnetoexciton and two-mode squeezed vacuum states

Two-Dimensional Gas of Massless Dirac Fermions in Graphene K.S. Novoselov1, A.K. Geim1, S.V. Morozov2, D. Jiang1, M.I. Katsnelson3, I.V. Grigorieva1, S.V. Dubonos2, A.A. Firsov21Manchester Centre for Mesoscience and Nanotechnology, University of Manchester, Manchester, M13 9PL, UK2Institute for Microelectronics Technology, 142432, Chernogolovka, Russia3Institute for Molecules and Materials, Radboud University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, the NetherlandsElectronic properties of materials are commonly described by quasiparticles that behave as nonrelativistic electrons with a finite mass and obey the Schrödinger equation. Here we report a condensed matter system where electron transport is essentially governed by the Dirac equation and charge carriers mimic relativistic particles with zero mass and an effective “speed of light” c∗ ≈106m/s. Our studies of graphene – a single atomic layer of carbon – have revealed a variety of unusual phenomena characteristic of two-dimensional (2D) Dirac fermions. In particular, we have observed that a) the integer quantum Hall effect in graphene is anomalous in that it occurs at halfinteger filling factors; b) graphene’s conductivity never falls below a minimum value corresponding to the conductance quantum e2/h, even when carrier concentrations tend to zero; c) the cyclotron mass mc of massless carriers with energy E in graphene is described by equation E =mcc∗2; and d) Shubnikov-de Haas oscillations in graphene exhibit a phase shift of π due to Berry’s phase.Graphene is a monolayer of carbon atoms packed into a dense honeycomb crystal structure that can be viewed as either an individual atomic plane extracted from graphite or unrolled single-wall carbon nanotubes or as a giant flat fullerene molecule. This material was not studied experimentally before and, until recently [1,2], presumed not to exist. To obtain graphene samples, we used the original procedures described in [1], which involve micromechanical cleavage of graphite followed by identification and selection of monolayers using a combination of optical, scanning-electron and atomic-force microscopies. The selected graphene films were further processed into multi-terminal devices such as the one shown in Fig. 1, following standard microfabrication procedures [2]. Despite being only one atom thick and unprotected from the environment, our graphene devices remain stable under ambient conditions and exhibit high mobility of charge carriers. Below we focus on the physics of “ideal” (single-layer) graphene which has a different electronic structure and exhibits properties qualitatively different from those characteristic of either ultra-thin graphite films (which are semimetals and whose material properties were studied recently [2-5]) or even of our other devices consisting of just two layers of graphene (see further). Figure 1 shows the electric field effect [2-4] in graphene. Its conductivity σ increases linearly with increasing gate voltage Vg for both polarities and the Hall effect changes its sign at Vg ≈0. This behaviour shows that substantial concentrations of electrons (holes) are induced by positive (negative) gate voltages. Away from the transition region Vg ≈0, Hall coefficient RH = 1/ne varies as 1/Vg where n is the concentration of electrons or holes and e the electron charge. The linear dependence 1/RH ∝Vg yields n =α·Vg with α ≈7.3·1010cm-2/V, in agreement with the theoretical estimate n/Vg ≈7.2·1010cm-2/V for the surface charge density induced by the field effect (see Fig. 1’s caption). The agreement indicates that all the induced carriers are mobile and there are no trapped charges in graphene. From the linear dependence σ(Vg) we found carrier mobilities µ =σ/ne, whichreached up to 5,000 cm2/Vs for both electrons and holes, were independent of temperature T between 10 and 100K and probably still limited by defects in parent graphite. To characterise graphene further, we studied Shubnikov-de Haas oscillations (SdHO). Figure 2 shows examples of these oscillations for different magnetic fields B, gate voltages and temperatures. Unlike ultra-thin graphite [2], graphene exhibits only one set of SdHO for both electrons and holes. By using standard fan diagrams [2,3], we have determined the fundamental SdHO frequency BF for various Vg. The resulting dependence of BF as a function of n is plotted in Fig. 3a. Both carriers exhibit the same linear dependence BF = β·n with β ≈1.04·10-15 T·m2 (±2%). Theoretically, for any 2D system β is defined only by its degeneracy f so that BF =φ0n/f, where φ0 =4.14·10-15 T·m2 is the flux quantum. Comparison with the experiment yields f =4, in agreement with the double-spin and double-valley degeneracy expected for graphene [6,7] (cf. caption of Fig. 2). Note however an anomalous feature of SdHO in graphene, which is their phase. In contrast to conventional metals, graphene’s longitudinal resistance ρxx(B) exhibits maxima rather than minima at integer values of the Landau filling factor ν (Fig. 2a). Fig. 3b emphasizes this fact by comparing the phase of SdHO in graphene with that in a thin graphite film [2]. The origin of the “odd” phase is explained below. Another unusual feature of 2D transport in graphene clearly reveals itself in the T-dependence of SdHO (Fig. 2b). Indeed, with increasing T the oscillations at high Vg (high n) decay more rapidly. One can see that the last oscillation (Vg ≈100V) becomes practically invisible already at 80K whereas the first one (Vg <10V) clearly survives at 140K and, in fact, remains notable even at room temperature. To quantify this behaviour we measured the T-dependence of SdHO’s amplitude at various gate voltages and magnetic fields. The results could be fitted accurately (Fig. 3c) by the standard expression T/sinh(2π2kBTmc/heB), which yielded mc varying between ≈ 0.02 and 0.07m0 (m0 is the free electron mass). Changes in mc are well described by a square-root dependence mc ∝n1/2 (Fig. 3d). To explain the observed behaviour of mc, we refer to the semiclassical expressions BF = (h/2πe)S(E) and mc =(h2/2π)∂S(E)/∂E where S(E) =πk2 is the area in k-space of the orbits at the Fermi energy E(k) [8]. Combining these expressions with the experimentally-found dependences mc ∝n1/2 and BF =(h/4e)n it is straightforward to show that S must be proportional to E2 which yields E ∝k. Hence, the data in Fig. 3 unambiguously prove the linear dispersion E =hkc∗ for both electrons and holes with a common origin at E =0 [6,7]. Furthermore, the above equations also imply mc =E/c∗2 =(h2n/4πc∗2)1/2 and the best fit to our data yields c∗ ≈1⋅106 m/s, in agreement with band structure calculations [6,7]. The employed semiclassical model is fully justified by a recent theory for graphene [9], which shows that SdHO’s amplitude can indeed be described by the above expression T/sinh(2π2kBTmc/heB) with mc =E/c∗2. Note that, even though the linear spectrum of fermions in graphene (Fig. 3e) implies zero rest mass, their cyclotron mass is not zero. The unusual response of massless fermions to magnetic field is highlighted further by their behaviour in the high-field limit where SdHO evolve into the quantum Hall effect (QHE). Figure 4 shows Hall conductivity σxy of graphene plotted as a function of electron and hole concentrations in a constant field B. Pronounced QHE plateaux are clearly seen but, surprisingly, they do not occur in the expected sequence σxy =(4e2/h)N where N is integer. On the contrary, the plateaux correspond to half-integer ν so that the first plateau occurs at 2e2/h and the sequence is (4e2/h)(N + ½). Note that the transition from the lowest hole (ν =–½) to lowest electron (ν =+½) Landau level (LL) in graphene requires the same number of carriers (∆n =4B/φ0 ≈1.2·1012cm-2) as the transition between other nearest levels (cf. distances between minima in ρxx). This results in a ladder of equidistant steps in σxy which are not interrupted when passing through zero. To emphasize this highly unusual behaviour, Fig. 4 also shows σxy for a graphite film consisting of only two graphene layers where the sequence of plateaux returns to normal and the first plateau is at 4e2/h, as in the conventional QHE. We attribute this qualitative transition between graphene and its two-layer counterpart to the fact that fermions in the latter exhibit a finite mass near n ≈0 (as found experimentally; to be published elsewhere) and can no longer be described as massless Dirac particles. 2The half-integer QHE in graphene has recently been suggested by two theory groups [10,11], stimulated by our work on thin graphite films [2] but unaware of the present experiment. The effect is single-particle and intimately related to subtle properties of massless Dirac fermions, in particular, to the existence of both electron- and hole-like Landau states at exactly zero energy [912]. The latter can be viewed as a direct consequence of the Atiyah-Singer index theorem that plays an important role in quantum field theory and the theory of superstrings [13,14]. For the case of 2D massless Dirac fermions, the theorem guarantees the existence of Landau states at E=0 by relating the difference in the number of such states with opposite chiralities to the total flux through the system (note that magnetic field can also be inhomogeneous). To explain the half-integer QHE qualitatively, we invoke the formal expression [9-12] for the energy of massless relativistic fermions in quantized fields, EN =[2ehc∗2B(N +½ ±½)]1/2. In QED, sign ± describes two spins whereas in the case of graphene it refers to “pseudospins”. The latter have nothing to do with the real spin but are “built in” the Dirac-like spectrum of graphene, and their origin can be traced to the presence of two carbon sublattices. The above formula shows that the lowest LL (N =0) appears at E =0 (in agreement with the index theorem) and accommodates fermions with only one (minus) projection of the pseudospin. All other levels N ≥1 are occupied by fermions with both (±) pseudospins. This implies that for N =0 the degeneracy is half of that for any other N. Alternatively, one can say that all LL have the same “compound” degeneracy but zeroenergy LL is shared equally by electrons and holes. As a result the first Hall plateau occurs at half the normal filling and, oddly, both ν = –½ and +½ correspond to the same LL (N =0). All other levels have normal degeneracy 4B/φ0 and, therefore, remain shifted by the same ½ from the standard sequence. This explains the QHE at ν =N + ½ and, at the same time, the “odd” phase of SdHO (minima in ρxx correspond to plateaux in ρxy and, hence, occur at half-integer ν; see Figs. 2&3), in agreement with theory [9-12]. Note however that from another perspective the phase shift can be viewed as the direct manifestation of Berry’s phase acquired by Dirac fermions moving in magnetic field [15,16]. Finally, we return to zero-field behaviour and discuss another feature related to graphene’s relativistic-like spectrum. The spectrum implies vanishing concentrations of both carriers near the Dirac point E =0 (Fig. 3e), which suggests that low-T resistivity of the zero-gap semiconductor should diverge at Vg ≈0. However, neither of our devices showed such behaviour. On the contrary, in the transition region between holes and electrons graphene’s conductivity never falls below a well-defined value, practically independent of T between 4 and 100K. Fig. 1c plots values of the maximum resistivity ρmax(B =0) found in 15 different devices, which within an experimental error of ≈15% all exhibit ρmax ≈6.5kΩ, independent of their mobility that varies by a factor of 10. Given the quadruple degeneracy f, it is obvious to associate ρmax with h/fe2 =6.45kΩ where h/e2 is the resistance quantum. We emphasize that it is the resistivity (or conductivity) rather than resistance (or conductance), which is quantized in graphene (i.e., resistance R measured experimentally was not quantized but scaled in the usual manner as R =ρL/w with changing length L and width w of our devices). Thus, the effect is completely different from the conductance quantization observed previously in quantum transport experiments. However surprising, the minimum conductivity is an intrinsic property of electronic systems described by the Dirac equation [17-20]. It is due to the fact that, in the presence of disorder, localization effects in such systems are strongly suppressed and emerge only at exponentially large length scales. Assuming the absence of localization, the observed minimum conductivity can be explained qualitatively by invoking Mott’s argument [21] that mean-free-path l of charge carriers in a metal can never be shorter that their wavelength λF. Then, σ =neµ can be re-written as σ = (e2/h)kFl and, hence, σ cannot be smaller than ≈e2/h per each type of carriers. This argument is known to have failed for 2D systems with a parabolic spectrum where disorder leads to localization and eventually to insulating behaviour [17,18]. For the case of 2D Dirac fermions, no localization is expected [17-20] and, accordingly, Mott’s argument can be used. Although there is a broad theoretical consensus [18-23,10,11] that a 2D gas of Dirac fermions should exhibit a minimum 3conductivity of about e2/h, this quantization was not expected to be accurate and most theories suggest a value of ≈e2/πh, in disagreement with the experiment. In conclusion, graphene exhibits electronic properties distinctive for a 2D gas of particles described by the Dirac rather than Schrödinger equation. This 2D system is not only interesting in itself but also allows one to access – in a condensed matter experiment – the subtle and rich physics of quantum electrodynamics [24-27] and provides a bench-top setting for studies of phenomena relevant to cosmology and astrophysics [27,28].1. Novoselov, K.S. et al. PNAS 102, 10451 (2005). 2. Novoselov, K.S. et al. Science 306, 666 (2004); cond-mat/0505319. 3. Zhang, Y., Small, J.P., Amori, M.E.S. & Kim, P. Phys. Rev. Lett. 94, 176803 (2005). 4. Berger, C. et al. J. Phys. Chem. B, 108, 19912 (2004). 5. Bunch, J.S., Yaish, Y., Brink, M., Bolotin, K. & McEuen, P.L. Nanoletters 5, 287 (2005). 6. Dresselhaus, M.S. & Dresselhaus, G. Adv. Phys. 51, 1 (2002). 7. Brandt, N.B., Chudinov, S.M. & Ponomarev, Y.G. Semimetals 1: Graphite and Its Compounds (North-Holland, Amsterdam, 1988). 8. Vonsovsky, S.V. and Katsnelson, M.I. Quantum Solid State Physics (Springer, New York, 1989). 9. Gusynin, V.P. & Sharapov, S.G. Phys. Rev. B 71, 125124 (2005). 10. Gusynin, V.P. & Sharapov, S.G. cond-mat/0506575. 11. Peres, N.M.R., Guinea, F. & Castro Neto, A.H. cond-mat/0506709. 12. Zheng, Y. & Ando, T. Phys. Rev. B 65, 245420 (2002). 13. Kaku, M. Introduction to Superstrings (Springer, New York, 1988). 14. Nakahara, M. Geometry, Topology and Physics (IOP Publishing, Bristol, 1990). 15. Mikitik, G. P. & Sharlai, Yu.V. Phys. Rev. Lett. 82, 2147 (1999). 16. Luk’yanchuk, I.A. & Kopelevich, Y. Phys. Rev. Lett. 93, 166402 (2004). 17. Abrahams, E., Anderson, P.W., Licciardello, D.C. & Ramakrishnan, T.V. Phys. Rev. Lett. 42, 673 (1979). 18. Fradkin, E. Phys. Rev. B 33, 3263 (1986). 19. Lee, P.A. Phys. Rev. Lett. 71, 1887 (1993). 20. Ziegler, K. Phys. Rev. Lett. 80, 3113 (1998). 21. Mott, N.F. & Davis, E.A. Electron Processes in Non-Crystalline Materials (Clarendon Press, Oxford, 1979). 22. Morita, Y. & Hatsugai, Y. Phys. Rev. Lett. 79, 3728 (1997). 23. Nersesyan, A.A., Tsvelik, A.M. & Wenger, F. Phys. Rev. Lett. 72, 2628 (1997). 24. Rose, M.E. Relativistic Electron Theory (John Wiley, New York, 1961). 25. Berestetskii, V.B., Lifshitz, E.M. & Pitaevskii, L.P. Relativistic Quantum Theory (Pergamon Press, Oxford, 1971). 26. Lai, D. Rev. Mod. Phys. 73, 629 (2001). 27. Fradkin, E. Field Theories of Condensed Matter Systems (Westview Press, Oxford, 1997). 28. Volovik, G.E. The Universe in a Helium Droplet (Clarendon Press, Oxford, 2003).Acknowledgements This research was supported by the EPSRC (UK). We are most grateful to L. Glazman, V. Falko, S. Sharapov and A. Castro Netto for helpful discussions. K.S.N. was supported by Leverhulme Trust. S.V.M., S.V.D. and A.A.F. acknowledge support from the Russian Academy of Science and INTAS.43µ (m2/Vs)0.8c4P0.4 22 σ (1/kΩ)10K0 0 1/RH(T/kΩ) 1 2ρmax (h/4e2)1-5010 Vg (V) 50 -10ab 0 -100-500 Vg (V)50100Figure 1. Electric field effect in graphene. a, Scanning electron microscope image of one of our experimental devices (width of the central wire is 0.2µm). False colours are chosen to match real colours as seen in an optical microscope for larger areas of the same materials. Changes in graphene’s conductivity σ (main panel) and Hall coefficient RH (b) as a function of gate voltage Vg. σ and RH were measured in magnetic fields B =0 and 2T, respectively. The induced carrier concentrations n are described by [2] n/Vg =ε0ε/te where ε0 and ε are permittivities of free space and SiO2, respectively, and t ≈300 nm is the thickness of SiO2 on top of the Si wafer used as a substrate. RH = 1/ne is inverted to emphasize the linear dependence n ∝Vg. 1/RH diverges at small n because the Hall effect changes its sign around Vg =0 indicating a transition between electrons and holes. Note that the transition region (RH ≈ 0) was often shifted from zero Vg due to chemical doping [2] but annealing of our devices in vacuum normally allowed us to eliminate the shift. The extrapolation of the linear slopes σ(Vg) for electrons and holes results in their intersection at a value of σ indistinguishable from zero. c, Maximum values of resistivity ρ =1/σ (circles) exhibited by devices with different mobilites µ (left y-axis). The histogram (orange background) shows the number P of devices exhibiting ρmax within 10% intervals around the average value of ≈h/4e2. Several of the devices shown were made from 2 or 3 layers of graphene indicating that the quantized minimum conductivity is a robust effect and does not require “ideal” graphene.ρxx (kΩ)0.60 aVg = -60V4B (T)810K12∆σxx (1/kΩ)0.4 1ν=4 140K 80K B =12T0 b 0 25 50 Vg (V) 7520K100Figure 2. Quantum oscillations in graphene. SdHO at constant gate voltage Vg as a function of magnetic field B (a) and at constant B as a function of Vg (b). Because µ does not change much with Vg, the constant-B measurements (at a constant ωcτ =µB) were found more informative. Panel b illustrates that SdHO in graphene are more sensitive to T at high carrier concentrations. The ∆σxx-curves were obtained by subtracting a smooth (nearly linear) increase in σ with increasing Vg and are shifted for clarity. SdHO periodicity ∆Vg in a constant B is determined by the density of states at each Landau level (α∆Vg = fB/φ0) which for the observed periodicity of ≈15.8V at B =12T yields a quadruple degeneracy. Arrows in a indicate integer ν (e.g., ν =4 corresponds to 10.9T) as found from SdHO frequency BF ≈43.5T. Note the absence of any significant contribution of universal conductance fluctuations (see also Fig. 1) and weak localization magnetoresistance, which are normally intrinsic for 2D materials with so high resistivity.75 BF (T) 500.2 0.11/B (1/T)b5 10 N 1/2025 a 0 0.061dmc /m00.04∆0.02 0c0 0 T (K) 150n =0e-6-3036Figure 3. Dirac fermions of graphene. a, Dependence of BF on carrier concentration n (positive n correspond to electrons; negative to holes). b, Examples of fan diagrams used in our analysis [2] to find BF. N is the number associated with different minima of oscillations. Lower and upper curves are for graphene (sample of Fig. 2a) and a 5-nm-thick film of graphite with a similar value of BF, respectively. Note that the curves extrapolate to different origins; namely, to N = ½ and 0. In graphene, curves for all n extrapolate to N = ½ (cf. [2]). This indicates a phase shift of π with respect to the conventional Landau quantization in metals. The shift is due to Berry’s phase [9,15]. c, Examples of the behaviour of SdHO amplitude ∆ (symbols) as a function of T for mc ≈0.069 and 0.023m0; solid curves are best fits. d, Cyclotron mass mc of electrons and holes as a function of their concentration. Symbols are experimental data, solid curves the best fit to theory. e, Electronic spectrum of graphene, as inferred experimentally and in agreement with theory. This is the spectrum of a zero-gap 2D semiconductor that describes massless Dirac fermions with c∗ 300 times less than the speed of light.n (1012 cm-2)σxy (4e2/h)4 3 2 -2 1 -1 -2 -3 2 44Kn7/ 5/ 3/ 1/2 2 2 210 ρxx (kΩ)-4σxy (4e2/h)0-1/2 -3/2 -5/2514T0-7/2 -4 -2 0 2 4 n (1012 cm-2)Figure 4. Quantum Hall effect for massless Dirac fermions. Hall conductivity σxy and longitudinal resistivity ρxx of graphene as a function of their concentration at B =14T. σxy =(4e2/h)ν is calculated from the measured dependences of ρxy(Vg) and ρxx(Vg) as σxy = ρxy/(ρxy + ρxx)2. The behaviour of 1/ρxy is similar but exhibits a discontinuity at Vg ≈0, which is avoided by plotting σxy. Inset: σxy in “two-layer graphene” where the quantization sequence is normal and occurs at integer ν. The latter shows that the half-integer QHE is exclusive to “ideal” graphene.。

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ARTICLEReceived1Apr2014|Accepted9Jan2015|Published24Feb2015Observation of long-lived interlayer excitonsin monolayer MoSe2–WSe2heterostructuresPasqual Rivera1,John R.Schaibley1,Aaron M.Jones1,Jason S.Ross2,Sanfeng Wu1,Grant Aivazian1,Philip Klement1,Kyle Seyler1,Genevieve Clark2,Nirmal J.Ghimire3,4,Jiaqiang Yan4,5,D.G.Mandrus3,4,5, Wang Yao6&Xiaodong Xu1,2Van der Waals bound heterostructures constructed with two-dimensional materials,such asgraphene,boron nitride and transition metal dichalcogenides,have sparked wide interest indevice physics and technologies at the two-dimensional limit.One highly coveted hetero-structure is that of differing monolayer transition metal dichalcogenides with type-II bandalignment,with bound electrons and holes localized in individual monolayers,that is,interlayer excitons.Here,we report the observation of interlayer excitons in monolayerMoSe2–WSe2heterostructures by photoluminescence and photoluminescence excitationspectroscopy.Wefind that their energy and luminescence intensity are highly tunable by anapplied vertical gate voltage.Moreover,we measure an interlayer exciton lifetime of B1.8ns,an order of magnitude longer than intralayer excitons in monolayers.Our work demonstratesoptical pumping of interlayer electric polarization,which may provoke further explorationof interlayer exciton condensation,as well as new applications in two-dimensional lasers,light-emitting diodes and photovoltaic devices.1Department of Physics,University of Washington,Seattle,Washington98195,USA.2Department of Materials Science and Engineering,University of Washington,Seattle,Washington98195,USA.3Department of Physics and Astronomy,University of T ennessee,Knoxville,T ennessee37996,USA.4Materials Science and T echnology Division,Oak Ridge National Laboratory,Oak Ridge,T ennessee37831,USA.5Department of Materials Science and Engineering,University of T ennessee,Knoxville,T ennessee37996,USA.6Department of Physics and Center of Theoretical and Computational Physics, University of Hong Kong,Hong Kong,China.Correspondence and requests for materials should be addressed to P.R.(email:pasqual@)or to X.X. (email:xuxd@).T he recently developed ability to vertically assemble different two-dimensional(2D)materials heralds a newrealm of device physics based on van der Waals heterostructures(HSs)1.The most successful example to date is the vertical integration of graphene on boron nitride.Such novel HSs not only markedly enhance graphene’s electronic properties2, but also give rise to superlattice structures demonstrating exotic physical phenomena3–5.A fascinating counterpart to gapless graphene is a class of monolayer direct bandgap semiconductors, namely transition metal dichalcogenides(TMDs)6–8.Due to the large binding energy in these2D semiconductors,excitons dominate the optical response,exhibiting strong light–matter interactions that are electrically tunable9,10.The discovery of excitonic valley physics11–15and strongly coupled spin and pseudospin physics16,17in2D TMDs opens up new possibilities for device concepts not possible in other material systems. Monolayer TMDs have the chemical formula MX2where the M is tungsten(W)or molybdenum(Mo),and the X is sulfur(S) or selenium(Se).Although these TMDs share the same crystalline structure,their physical properties,such as bandgap,exciton resonance and spin–orbit coupling strength,can vary signifi-cantly.Therefore,an intriguing possibility is to stack different TMD monolayers on top of one another to form2D HSs.First-principle calculations show that heterojunctions formed between monolayer tungsten and molybdenum dichalcogenides have type-II band alignment18–20.Recently,this has been confirmed by X-ray photoelectron spectroscopy and scanning tunnelling spectroscopy21.Since the Coulomb binding energy in2D TMDs is much stronger than in conventional semiconductors, it is possible to realize interlayer excitonic states in van der Waals bound heterobilayers,that is,bound electrons and holes that are localized in different layers.Such interlayer excitons have been intensely pursued in bilayer graphene for possible exciton condensation22,but direct optical observation demonstrating the existence of such excitons is challenging owing to the lack of a sizable bandgap in graphene.Monolayer TMDs with bandgaps in the visible range provide the opportunity to optically pump interlayer excitons,which can be directly observed through photoluminescence(PL)measurements.In this report,we present direct observation of interlayer excitons in vertically stacked monolayer MoSe2–WSe2HSs.We show that interlayer exciton PL is enhanced under optical excitation resonant with the intralayer excitons in isolated monolayers,consistent with the interlayer charge transfer resulting from the underlying type-II band structure.We demonstrate the tuning of the interlayer exciton energy by applying a vertical gate voltage,which is consistent with the permanent out-of-plane electric dipole nature of interlayer excitons.Moreover,wefind a blue shift in PL energy at increasing excitation power,a hallmark of repulsive dipole–dipole interac-tions between spatially indirect excitons.Finally,time-resolved PL measurements yield a lifetime of1.8ns,which is at least an order of magnitude longer than that of intralayer excitons.Our work shows that monolayer semiconducting HSs are a promising platform for exploring new optoelectronic phenomena.ResultsMoSe2–WSe2HS photoluminescence.HSs are prepared by standard polymethyl methacrylate(PMMA)transfer techniques using mechanically exfoliated monolayers of WSe2and MoSe2(see Methods).Since there is no effort made to match the crystal lattices of the two monolayers,the obtained HSs are considered incom-mensurate.An idealized depiction of the vertical MoSe2–WSe2HS is shown in Fig.1a.We have fabricated six devices that all show similar results as those reported below.The data presented here are from two independent MoSe2–WSe2HSs,labelled device1and device2.Figure1b shows an optical micrograph of device1,which has individual monolayers,as well as a large area of vertically stacked HS.This device architecture allows for the comparison of the excitonic spectrum of individual monolayers with that of the HS region,allowing for a controlled identification of spectral changes resulting from interlayer coupling.We characterize the MoSe2–WSe2monolayers and HS using PL measurements.Inspection of the PL from the HS at room temperature reveals three dominant spectral features(Fig.1c). The emission at1.65and1.57eV corresponds to the excitonic states from monolayer WSe2and MoSe2(refs10,15),respectively. PL from the HS region,outlined by the dashed white line in Fig.1a,reveals a distinct spectral feature at1.35eV(X I).Two-dimensional mapping of the spectrally integrated PL from X I shows that it is isolated entirely to the HS region(inset,Fig.1c), with highly uniform peak intensity and spectral position (Supplementary Materials1).Low-temperature characterization of the HS is performed with 1.88eV laser excitation at20K.PL from individual monolayer WSe2(top),MoSe2(bottom)and the HS area(middle)are shown with the same scale in Fig.1d.At low temperature,the intralayer neutral(X M o)and charged(X MÀ)excitons are resolved10,15,where M labels either W or parison of the three spectra shows that both intralayer X M o and X MÀexist in the HS with emission at the same energy as from isolated monolayers,demonstrating the preservation of intralayer excitons in the HS region.PL from X I becomes more pronounced and is comparable to the intralayer excitons at low temperature.We note that the X I energy position has variation across the pool of HS samples we have studied (Supplementary Fig.1),which we attribute to differences in the interlayer separation,possibly due to imperfect transfer and a different twisting angle between monolayers.We further perform PL excitation(PLE)spectroscopy to investigate the correlation between X I and intralayer excitons.A narrow bandwidth(o50kHz)frequency tunable laser is swept across the energy resonances of intralayer excitons(from1.6to 1.75eV)while monitoring X I PL response.Figure2a shows an intensity plot of X I emission as a function of photoexcitation energy from device2.We clearly observe the enhancement of X I emission when the excitation energy is resonant with intralayer exciton states(Fig.2b).Now we discuss the origin of X I.Since X I has never been observed in our exfoliated monolayer and bilayer samples,if its origin were related to defects,they must be introduced by the fabrication process.This would result in sample-dependent X I properties with non-uniform spatial dependence.However,our data show that key physical properties of X I,such as the resonance energy and intensity,are spatially uniform and isolated to the HS region(inset of Fig.1c and Supplementary Fig.2).In addition,X I has not been observed in WSe2–WSe2homo-structures constructed from exfoliated or physical vapor deposi-tion(PVD)grown monolayers(Supplementary Fig.3).All these facts suggest that X I is not a defect-related exciton.Instead,the experimental results support the observation of an interlayer exciton.Due to the type-II band alignment of the MoSe2–WSe2HS18–20,as shown in Fig.2c,photoexcited electrons and holes will relax(dashed lines)to the conduction band edge of MoSe2and the valence band edge of WSe2,respectively.The Coulomb attraction between electrons in the MoSe2and holes in the WSe2gives rise to an interlayer exciton,X I,analogous to spatially indirect excitons in coupled quantum wells.The interlayer coupling yields the lowest energy bright exciton in the HS,which is consistent with the temperature dependence of X I PL,that is,it increases as temperature decreases (Supplementary Fig.4).From the intralayer and interlayer exciton spectral positions,we can infer the band offsets between the WSe 2and MoSe 2monolayers (Fig.2c).The energy difference between X W and X I at room temperature is 310meV.Considering the smaller binding energy of interlayer than intralayer excitons,this sets a lower bound on the conduction band offset.The energy difference between X M and X I then provides a lower bound on the valence band offset of 230meV.This value is consistent with the valence band offset of 228meV found in MoS 2–WSe 2HSs by micro X-ray photoelectron spectroscopy and scanning tunnelling spectro-scopy measurements 21.This experimental evidence strongly corroborates X I as an interlayer exciton.The observation of bright interlayer excitons in monolayer semiconducting HSs is of central importance,and the remainder of this paper will focus on their physical properties resulting from their spatially indirect nature and the underlying type-II band alignment.WSe 2HSMoSe 2W M SeIn te n s i t y (a .u .)1.31.51.7Energy (eV)MoSe 2HeterostructureWSe 2W0WX X X X −0MoMo−e hehe h1.3 1.41.51.6 1.7I n t e n s i t y (a .u .)Energy (eV)5μm 0123×104Y (μm )246X (μm)0246Figure 1|Intralayer and interlayer excitons of a monolayer MoSe 2–WSe 2vertical heterostructure.(a )Cartoon depiction of a MoSe 2–WSe 2heterostructure (HS).(b )Microscope image of a MoSe 2–WSe 2HS (device 1)with a white dashed line outlining the HS region.(c )Room-temperature photoluminescence of the heterostructure under 20m W laser excitation at 2.33eV.Inset:spatial map of integrated PL intensity from the low-energy peak (1.273–1.400eV),which is only appreciable in the heterostructure area,outlined by the dashed black line.(d )Photoluminescence of individual monolayers and the HS at 20K under 20m W excitation at 1.88eV (plotted on the samescale).Energy (eV)WSe MoSe PL energy (eV)E x c i t a t i o n e n e r g y (e V )1.28 1.3 1.32 1.34 1.36 1.381.61.651.71.754,0006,0008,00010,000IntensityFigure 2|Photoluminescence excitation spectroscopy of the interlayer exciton at 20K.(a )PLE intensity plot of the heterostructure region with an excitation power of 30m W and 5s charge-coupled device CCD integration time.(b )Spectrally integrated PLE response (red dots)overlaid on PL (black line)with 100m W excitation at 1.88eV.(c )Type-II semiconductor band alignment diagram for the 2D MoSe 2–WSe 2heterojunction.interlayer exciton .Applying vertical energy of Figure 3a contact stacked insu-Electrostatic contact shows the 100to about analogue of reversed,varied expected for from reduces device 2,conduction 3b,c.of the in the on top band-offset at X I PL energy of basis of would should have X I PL This effect,intensity.further Power dependence and lifetime of interlayer exciton PL .The interlayer exciton PLE spectrum as a function of laser power with excitation energy in resonance with X W o reveals several properties of the X I .Inspection of the normalized PLE intensity (Fig.4a)shows the evolution of a doublet in the interlayer excitonspectrum,highlighted by the red and Both peaks of the doublet display a consistent increased laser intensity,shown by the dashed which are included as a guide to the eye.intensity of X I also exhibits a strong saturation laser power,as shown in Fig.4b (absolute Supplementary Fig.6).The sublinear power excitation powers above 0.5m W is distinctly the intralayer excitons in isolated monolayers,saturation power threshold of about Fig.7).The low power saturation of X I PL lifetime than that of intralayer excitons.the intralayer exciton is substantially reduced interlayer charge hopping 23,which is quenching of intralayer exciton PL (Fig.Fig.8).Moreover,the lifetime of the interlayer because it is the lowest energy configuration indirect nature leads to a reduced optical long lifetime is confirmed by time-resolved Fig.4c.A fit to a single exponential decay exciton lifetime of 1.8±0.3ns.This timescale the intralayer exciton lifetime,which is ps 24–27.By modelling the saturation behaviour three-level diagram,the calculated saturation interlayer exciton is about 180times (Supplementary Fig.7;Supplementary with our observation of low saturation intensity DiscussionWe attribute the observed doublet feature splitting of the monolayer MoSe 2conduction assignment is mainly based on the fact difference between the doublet is B 25with MoSe 2conduction band splitting predicted calculations 28.This explanation is also supported by the evolution of the relative strength of the two peaks with increasing excitation power,as shown in Fig.4a (similar results in device 1with 1.88eV excitation shown in Supplementary Fig.9).At low power,the lowest energy configuration of interlayer excitons,with the electron in the lower spin-split band of MoSe 2,is populated first.Due to phase space filling effects,the interlayer excitonSiO 2n + Si2MoSe 2e –h +e –h +P Ee –h +V g < 0WSe 2MoSe 2WSe 2MoSe 2h ωV g = 0Photon energy (eV)1.321.361.41.444080e –h +h +PL intensity (a.u.) -hω’-the interlayer exciton and band alignment.(a )Device 2geometry.The interlayer exciton has a out-of-plane electric polarization.(b )Electrostatic control of the band alignment and the interlayer exciton photoluminescence as a function of applied gate voltage under 70m W excitation at 1.744eV,1s integrationconfiguration with the electron in the higher energy spin-split band starts to be filled at higher laser power.Consequently,the higher energy peak of the doublet becomes more prominent at higher excitation powers.The observed blue shift of X I as the excitation power increases,indicated by the dashed arrows in Fig.4a,is a signature of the repulsive interaction between the dipole-aligned interlayer excitons (cf.Fig.3a).This is a hallmark of spatially indirect excitons in gallium arsenide (GaAs)coupled quantum wells,which have been intensely studied for exciton Bose-Einstein condensation (BEC)phenomena 29.The observation of spatially indirect interlayer excitons in a type-II semiconducting 2D HS provides an intriguing platform to explore exciton BEC,where the observed extended lifetimes and repulsive interactions are two key ingredients towards the realization of this exotic state of matter.Moreover,the extraordinarily high binding energy for excitons in this truly 2D system may provide for degenerate exciton gases at elevated temperatures compared with other material systems 30.The long-lived interlayer exciton may also lead to new optoelectronic applications,such as photovoltaics 31–34and 2D HS nanolasers.MethodsDevice fabrication .Monolayers of MoSe 2are mechanically exfoliated onto 300nm SiO 2on heavily doped Si wafers and monolayers of WSe 2onto a layer of PMMA atop polyvinyl alcohol on Si.Both monolayers are identified with an opticalmicroscope and confirmed by their PL spectra.Polyvinyl alcohol is dissolved in H 2O and the PMMA layer is then placed on a transfer loop or thin layer of poly-dimethylsiloxane (PDMS).The top monolayer is then placed in contact with the bottom monolayer with the aid of an optical microscope and micromanipulators.The substrate is then heated to cause the PMMA layer to release from the transfer media.The PMMA is subsequently dissolved in acetone for B 30min and then rinsed with isopropyl alcohol.Low-temperature PL measurements .Low-temperature measurements are con-ducted in a temperature-controlled Janis cold finger cryostat (sample in vacuum)with a diffraction-limited excitation beam diameter of B 1m m.PL is spectrally filtered through a 0.5-m monochromator (Andor–Shamrock)and detected on a charge-coupled device (Andor—Newton).Spatial PL mapping is performed using a Mad City Labs Nano-T555nanopositioning system.For PLE measurements,a continuous wave Ti:sapphire laser (MSquared—SolsTiS)is used for excitation and filtered 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chalcogenides.Proc.Natl A111,6198–6202 (2014).AcknowledgementsThis work is mainly supported by the US DoE,BES,Materials Sciences and Engineering Division(DE-SC0008145).N.J.G.,J.Y.and D.G.M.are supported by US DoE,BES, Materials Sciences and Engineering Division.W.Y.is supported by the Research Grant Council of Hong Kong(HKU17305914P,HKU9/CRF/13G),and the Croucher Foun-dation under the Croucher Innovation Award.X.X.thanks the support of the Cottrell Scholar Award.P.R.thanks the UW GO-MAP program for their support.A.M.J.is partially supported by the NSF(DGE-0718124).J.S.R.is partially supported by the NSF (DGE-1256082).S.W.and G.C.are partially supported by the State of Washington through the UW Clean Energy Institute.Device fabrication was performed at the Washington Nanofabrication Facility and NSF-funded Nanotech User Facility. Author contributionsX.X.and P.R.conceived the experiments.P.R.and P.K.fabricated the devices,assisted by J.S.R.P.R.performed the measurements,assisted by J.R.S.,A.M.J.,J.S.R.,S.W.and G.A. P.R.and X.X.performed data analysis,with input from W.Y.N.J.G.,J.Y.and D.G.M. synthesized and characterized the bulk WSe2crystals.X.X.,P.R.,J.R.S.and W.Y.wrote the paper.All authors discussed the results.Additional informationSupplementary Information accompanies this paper at / naturecommunicationsCompetingfinancial interests:The authors declare no competingfinancial interests. Reprints and permission information is available online at / reprintsandpermissions/How to cite this article:Rivera,P.et al.Observation of long-lived interlayer excitons in monolayer MoSe2–mun.6:6242doi:10.1038/ncomms7242(2015).。

NMR中常用的英文缩写和中文名称汪茂田译注APTAttached Proton Test 质子连接实验ASISAromatic Solvent Induced Shift 芳香溶剂诱导位移BBDRBroad Band Double Resonance 宽带双共振BIRDBilinear Rotation Decoupling 双线性旋转去偶（脉冲）COLOCCorrelated Spectroscopy for Long Range Coupling 远程偶合相关谱COSY( Homonuclear chemical shift ) COrrelation SpectroscopY （同核化学位移）相关谱CPCross Polarization 交叉极化CP/MASCross Polarization / Magic Angle Spinning 交叉极化魔角自旋CSAChemical Shift Anisotropy 化学位移各向异性CSCMChemical Shift Correlation Map 化学位移相关图CWcontinuous wave 连续波DDDipole-Dipole 偶极-偶极DECSYDouble-quantum Echo Correlated Spectroscopy 双量子回波相关谱DEPTDistortionless Enhancement by Polarization Transfer 无畸变极化转移增强2DFTStwo Dimensional FT Spectroscopy 二维傅立叶变换谱DNMRDynamic NMR 动态NMRDNPDynamic Nuclear Polarization 动态核极化DQ(C)Double Quantum (Coherence) 双量子（相干）DQDDigital Quadrature Detection 数字正交检测DQFDouble Quantum Filter 双量子滤波DQF-COSYDouble Quantum Filtered COSY 双量子滤波COSYDRDSDouble Resonance Difference Spectroscopy 双共振差谱EXSYExchange Spectroscopy 交换谱FFTFast Fourier Transformation 快速傅立叶变换FIDFree Induction Decay 自由诱导衰减H,C-COSY1H,13C chemical-shift COrrelation SpectroscopY 1H,13C化学位移相关谱H,X-COSY1H,X-nucleus chemical-shift COrrelation SpectroscopY 1H,X-核化学位移相关谱HETCORHeteronuclear Correlation Spectroscopy 异核相关谱HMBCHeteronuclear Multiple-Bond Correlation 异核多键相关HMQCHeteronuclear Multiple Quantum Coherence异核多量子相干HOESYHeteronuclear Overhauser Effect Spectroscopy 异核Overhause效应谱HOHAHAHomonuclear Hartmann-Hahn spectroscopy 同核Hartmann-Hahn谱HRHigh Resolution 高分辨HSQCHeteronuclear Single Quantum Coherence 异核单量子相干INADEQUATEIncredible Natural Abundance Double Quantum Transfer Experiment 稀核双量子转移实验（简称双量子实验，或双量子谱）INDORInternuclear Double Resonance 核间双共振INEPTInsensitive Nuclei Enhanced by Polarization 非灵敏核极化转移增强INVERSEH,X correlation via 1H detection 检测1H的H,X核相关IRInversion-Recovery 反（翻）转回复JRESJ-resolved spectroscopy J-分解谱LISLanthanide (chemical shift reagent ) Induced Shift 镧系（化学位移试剂）诱导位移LSRLanthanide Shift Reagent 镧系位移试剂MASMagic-Angle Spinning 魔角自旋MQ(C)Multiple-Quantum ( Coherence ) 多量子（相干）MQFMultiple-Quantum Filter 多量子滤波MQMASMultiple-Quantum Magic-Angle Spinning 多量子魔角自旋MQSMulti Quantum Spectroscopy 多量子谱NMRNuclear Magnetic Resonance 核磁共振NOENuclear Overhauser Effect 核Overhauser效应（NOE）NOESYNuclear Overhauser Effect Spectroscopy 二维NOE谱NQRNuclear Quadrupole Resonance 核四极共振PFGPulsed Gradient Field 脉冲梯度场PGSEPulsed Gradient Spin Echo 脉冲梯度自旋回波PRFTPartially Relaxed Fourier Transform 部分弛豫傅立叶变换PSDPhase-sensitive Detection 相敏检测PWPulse Width 脉宽RCTRelayed Coherence Transfer 接力相干转移RECSYMultistep Relayed Coherence Spectroscopy 多步接力相干谱REDORRotational Echo Double Resonance 旋转回波双共振RELAYRelayed Correlation Spectroscopy 接力相关谱RFRadio Frequency 射频ROESYRotating Frame Overhauser Effect Spectroscopy 旋转坐标系NOE谱ROTOROESY-TOCSY Relay ROESY-TOCSY 接力谱SCScalar Coupling 标量偶合SDDSSpin Decoupling Difference Spectroscopy 自旋去偶差谱SESpin Echo 自旋回波SECSYSpin-Echo Correlated Spectroscopy自旋回波相关谱SEDORSpin Echo Double Resonance 自旋回波双共振SEFTSpin-Echo Fourier Transform Spectroscopy (with J modulation) （J-调制）自旋回波傅立叶变换谱SELINCORSelective Inverse Correlation 选择性反相关SELINQUATESelective INADEQUATE 选择性双量子（实验）SFORDSingle Frequency Off-Resonance Decoupling 单频偏共振去偶SNR or S/NSignal-to-noise Ratio 信/ 燥比SQFSingle-Quantum Filter 单量子滤波SRSaturation-Recovery 饱和恢复TCFTime Correlation Function 时间相关涵数TOCSYTotal Correlation Spectroscopy 全（总）相关谱TOROTOCSY-ROESY Relay TOCSY-ROESY接力TQFTriple-Quantum Filter 三量子滤波WALTZ-16A broadband decoupling sequence 宽带去偶序列WATERGATEWater suppression pulse sequence 水峰压制脉冲序列WEFTWater Eliminated Fourier Transform 水峰消除傅立叶变换ZQ(C)Zero-Quantum (Coherence) 零量子相干ZQFZero-Quantum Filter 零量子滤波T1Longitudinal (spin-lattice) relaxation time for MZ 纵向（自旋-晶格）弛豫时间T2Transverse (spin-spin) relaxation time for Mxy 横向（自旋-自旋）弛豫时间tmmixing time 混合时间τ crotational correlation time 旋转相关时间。

不可压缩等离子体的2维磁场重联模型但加坤;段书超;章征伟【期刊名称】《强激光与粒子束》【年(卷),期】2012(24)8【摘要】A modified two-dimensional magnetic reconnection model is presented which focuses on the role of electrostatic field generated by charge separation in magnetic reconnection,and the E cross B drift causing the Alfvénic outflows.This reconnection model reveals that the reconnection rate described in Sweet-Parker model is strongly dependent on the ratio of the electron mass and the ion mass,and the effective local resistivity normalized by the Spitzer resistivity is proportional to the square of the ratio of the ion skin depth to the width of the current sheet.The relativistic effect and creation of electron-positron pairs in high temperature plasmas can enhance the reconnection rate.The excitation of electromagnetic waves is necessary for dissipation of magnetic energy.%提出了一种2维磁场重联模型.磁场重联过程中的电荷分离在等离子体中产生静电场,等离子体在电场中的漂移运动可以解释阿尔芬速度量级的出流.该磁场重联模型给出如下结论:Sweet- Parker模型描述的重联率强烈地依赖于电子质量与离子质量之比;反常电阻率正比于离子惯性长度和电流片宽度比值的平方;相对论效应和高温等离子体中电子-正电子对的产生可以提高重联率;电磁波的激发对于磁能的损耗是必要的.【总页数】6页(P1901-1906)【作者】但加坤;段书超;章征伟【作者单位】中国工程物理研究院流体物理研究所,四川绵阳621900;中国工程物理研究院流体物理研究所,四川绵阳621900;中国工程物理研究院流体物理研究所,四川绵阳621900【正文语种】中文【中图分类】O532.11【相关文献】1.通量传输事件的可压缩MHD模拟及与不可压缩模型的比较 [J], 慕守凤;郝宪孝2.三维不可压缩流的12速多松弛格子Boltzmann模型 [J], 胡嘉懿; 张文欢; 柴振华; 施保昌; 汪一航3.密度依赖的不可压缩液晶模型的爆破准则 [J], 张明雪;王昌花4.不可压缩Ericksen-Leslie液晶模型局部适定性的研究 [J], 牛聪;孙建筑;唐童5.不可压缩流体中球型容器内爆理论模型研究 [J], 杜志鹏;杜俭业;李营;秦中华因版权原因，仅展示原文概要，查看原文内容请购买。

二维双量子魔角旋转核磁共振技术在功能材料研究中的应用喻志武;郑安民;王强;邓风【期刊名称】《高等学校化学学报》【年(卷),期】2011(32)3【摘要】简要介绍了二维双量子魔角旋转核磁共振(DQ-MAS NMR)新技术的基本原理,详细综述了1H,19F,29Si,31P和27 Al DQ-MAS NMR技术在各种固体功能材料中的应用,并展望了该技术的应用前景.%Solid-state NMR spectroscopy has been developed into a powerful tool for obtaining detailed information about the structure, ordering, and dynamics in various kinds of inorganic organic, and biological materials. Two-dimensional double quantum magic angle spinning(DQ-MAS) NMR experiment is a useful method for probing spatial proximities or interactions between nuclei in various solid materials. During the past decade, the DQ-MAS NMR technique has been successfully applied not only to spin I = 1/2 nuclei, such as 1H, 19F, 29Si' 31p, but also to quadrupolar nuclei system, such as 27Al, 11B and 23Na. In this paper, we briefly introduce the principle of two-dimensional DQ-MAS NMR, and review the recent applications of DQ-MAS NMRtechnique(including 1H, 19F, 29Si, 31p and 27Al DQ-MAS NMR) to various solid functional materials. In addition, a perspective for the future of DQ-MAS NMR is also given.【总页数】14页(P471-484)【作者】喻志武;郑安民;王强;邓风【作者单位】中国科学院武汉物理与数学研究所,波谱与原子分子物理国家重点实验室,武汉磁共振中心,武汉,430071;中国科学院武汉物理与数学研究所,波谱与原子分子物理国家重点实验室,武汉磁共振中心,武汉,430071;中国科学院武汉物理与数学研究所,波谱与原子分子物理国家重点实验室,武汉磁共振中心,武汉,430071;中国科学院武汉物理与数学研究所,波谱与原子分子物理国家重点实验室,武汉磁共振中心,武汉,430071【正文语种】中文【中图分类】O642【相关文献】1.高分辨魔角旋转核磁共振技术(HR/MAS)在固相合成中的应用 [J], 贺文义;姚念环;KitS;LAM;刘刚2.H-MCM-22沸石分子筛中Brφnsted/Lewis酸协同效应的1H和27Al双量子魔角旋转固体核磁共振研究 [J], 喻志武;王强;陈雷;邓风3.高分辨魔角旋转磁共振波谱分析在医学中的应用 [J], 董爱生;田建明4.高分辨魔角旋转核磁共振技术在慢性结肠炎诊断的应用探讨 [J], 李旭红5.高分辨率魔角旋转核磁共振技术的应用进展 [J], 杨扬;孙小强;谷丽丽;席海涛;陈群因版权原因，仅展示原文概要，查看原文内容请购买。