Electron-solid and electron-liquid phases in graphene

Abstract

We investigate the competition between electron-solid and quantum-liquid phases in graphene, which arise in partially filled Landau levels. The differences in the wave function describing the electrons in the presence of a perpendicular magnetic field in graphene with respect to the conventional semiconductors, such as GaAs, can be captured in a form factor which carries the Landau level index. This leads to a quantitative difference in the electron-solid and -liquid energies. For the lowest Landau level, there is no difference in the wave function of relativistic and non-relativistic systems. We compute the cohesive energy of the solid phase analytically using a Hartree-Fock Hamiltonian. The liquid energies are computed analytically as well as numerically, using exact diagonalization. We find that the liquid phase dominates in the n=1 Landau level, whereas the Wigner crystal and electron-bubble phases become more prominent in the n=2 and n=3 Landau level.

11 pages, 7 figures

References in corpus (18)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
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• Quantum Hall Ferromagnetism in Graphene
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• Electron interactions in graphene in a strong magnetic field
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• Microscopic Theory of the Reentrant IQHE in the First and Second Excited LLs
• Wigner crystal and bubble phases in graphene in the quantum Hall regime
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• De-Pinning Transition of Bubble Phases in a High Landau Level
• Influence of Landau-level mixing on Wigner crystallization in graphene
• Nonequilibrium transport in density-modulated phases of the second Landau level
• Scaling Approach to the Phase Diagram of Quantum Hall Systems
• Magnetoroton instabilities and static susceptibilities in higher Landau levels

Cited by in corpus (6)

• Even denominator fractional quantum Hall states in higher Landau levels of graphene
• Competing Fractional Quantum Hall and Electron Solid Phases in Graphene
• Unconventional fractional quantum Hall states and Wigner crystallization in suspended Corbino graphene
• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Charge density waves and their transitions in anisotropic quantum Hall systems