Quantum Anomalous Hall State in Bilayer Graphene
arXiv:1009.0497 · doi:10.1103/PhysRevB.82.115124
Abstract
We present a symmetry-based analysis of competition between different gapped states that have been proposed in bilayer graphene (BLG), which are all degenerate on a mean field level. We classify the states in terms of a hidden SU(4) symmetry, and distinguish symmetry protected degeneracies from accidental degeneracies. One of the states, which spontaneously breaks discrete time reversal symmetry but no continuous symmetry, is identified as a Quantum Anomalous Hall (QAH) state, which exhibits quantum Hall effect at zero magnetic field. We investigate the lifting of the accidental degeneracies by thermal and zero point fluctuations, taking account of the modes softened under RG. Working in a 'saddle point plus quadratic fluctuations' approximation, we identify two types of RG- soft modes which have competing effects. Zero point fluctuations, dominated by 'transverse' modes which are unique to BLG, favor the QAH state. Thermal fluctuations, dominated by 'longitudinal' modes, favor a SU(4) symmetry breaking multiplet of states. We discuss the phenomenology and experimental signatures of the QAH state in BLG, and also propose a way to induce the QAH state using weak external magnetic fields.
minor changes, made to match journal version
References in corpus (16)
- Quantum Spin Hall Effect in Graphene
- Landau level degeneracy and quantum Hall effect in a graphite bilayer
- Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
- Topological Mott Insulators
- Topological confinement in bilayer graphene
- Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
- Scalar spin chirality and quantum Hall effect on a triangular lattice
- Broken symmetry states and divergent resistance in suspended bilayer graphene
- Many-body instability of Coulomb interacting bilayer graphene: RG approach
- Pseudospin Magnetism in Graphene
- Electron-electron interactions and the phase diagram of a graphene bilayer
- Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets
- Dynamical Screening and Ferroelectric-type Excitonic Instability in Bilayer Graphene
- Electron-electron interactions in graphene bilayers
- Screening, Kohn anomaly, Friedel oscillation, and RKKY interaction in bilayer graphene
- Intra-Landau level Cyclotron Resonance in Bilayer Graphene
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