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    188宝金博页面版: RMP2011_Electronic properties of graphene in a strong magnetic field

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    内容提示： Electronic properties of graphene in a strong magnetic fieldM.O. GoerbigLaboratoire de Physique des Solides, Universite ? Paris-Sud,CNRS UMR 8502, F-91405 Orsay, France(published 3 November 2011)The basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strongperpendicular magnetic field are reviewed. One of its most salient features is the relativisticquantum Hall effect, the observation of which has been the experimental breakthrough inidentifying pseudorelativistic massless char...

    文档格式：PDF | 页数：51 | 浏览次数：82 | 上传日期：2015-01-01 15:58:40 | 文档星级：
    Electronic properties of graphene in a strong magnetic fieldM.O. GoerbigLaboratoire de Physique des Solides, Universite ´ Paris-Sud,CNRS UMR 8502, F-91405 Orsay, France(published 3 November 2011)The basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strongperpendicular magnetic field are reviewed. One of its most salient features is the relativisticquantum Hall effect, the observation of which has been the experimental breakthrough inidentifying pseudorelativistic massless charge carriers as the low-energy excitations in gra-phene. The effect may be understood in terms of Landau quantization for massless Diracfermions, which is also the theoretical basis for the understanding of more involved phenomenadue to electronic interactions. The role of electron-electron interactions both in the weak-coupling limit, where the electron-hole excitations are determined by collective modes, and inthe strong-coupling regime of partially filled relativistic Landau levels are presented. In thelatter limit, exotic ferromagnetic phases and incompressible quantum liquids are expected to beat the origin of recently observed (fractional) quantum Hall states. Furthermore, the electron-phonon coupling in a strong magnetic field is discussed. Although the present review has adominant theoretical character, a close connection with available experimental observation isintended.DOI: 10.1103/RevModPhys.83.1193PACS numbers: 81.05.ue, 73.43.Lp, 73.22.PrCONTENTSI. Introduction to grapheneA. The carbon atom and its hybridizationsB. Crystal structure of grapheneC. Electronic band structure of graphene1. Tight-binding model for electrons on thehoneycomb lattice2. Continuum limitD. Deformed graphene1. Dirac point motion2. Tilted Dirac conesII. Dirac equation in a magnetic field and therelativistic quantum Hall effectA. Massless 2D fermions in a strong magnetic field1. Quantum-mechanical treatment2. Relativistic Landau levelsB. Limits of the Dirac equation in the descriptionof graphene Landau levelsC. Landau level spectrum in the presence of anin-plane electric fieldD. Landau levels in deformed graphene1. The generalized Weyl Hamiltonian in amagnetic field2. Tilted Dirac cones in crossed magneticand electric fieldIII. Electronic interactions in graphene: Integer quantumHall regimeA. Decomposition of the Coulomb interactionin the two-spinor basis1. SU(2) valley symmetry2. SU(4) spin-valley-symmetric interactionHamiltonianB. Particle-hole excitation spectrum1. Graphene particle-hole excitation spectrumat B¼01194119411951196119611991202120312031204120412051205120812091210121012111211121212131214121412142. Polarizability for B?03. Electron-electron interactions in therandom-phase approximation: Upper hybridmode and linear magnetoplasmons4. Dielectric function and static screeningIV. Magnetophonon resonance in grapheneA. Electron-phonon coupling1. Coupling Hamiltonian2. Hamiltonian in terms of magnetoexcitonoperatorsB. Phonon renormalization and Raman spectroscopy1. Nonresonant coupling and Kohn anomaly2. Resonant couplingV. Electronic correlations in partially filled landau levelsA. Electrons in a single relativistic Landau level1. SU(4)-symmetric model2. Symmetry-breaking long-range terms3. Qualitative expectations for correlatedelectron phases4. External spin-valley symmetry-breakingterms5. Hierarchy of relevant energy scalesB. SU(4) Quantum Hall ferromagnetism in graphene1. Ferromagnetic ground state andGoldstone modes2. Skyrmions and entanglement3. Comparison with magnetic catalysis4. The quantum Hall effect at ?¼?1 and ?¼0C. Fractional quantum Hall effect in graphene1. Generalized Halperin wave functions2. The use of generalized Halperin wave functionsin graphene3. Experiments on the graphene FQHEVI. Conclusions and outlookAppendix: Matrix elements of the density operators1216121812181220122012211221122212221222122412241225122612261227122812291229123012321233123512351236123812381239REVIEWS OF MODERN PHYSICS, VOLUME 83, OCTOBER–DECEMBER 20110034-6861=2011=83(4)=1193()1193? 2011 American Physical Society

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