Influence of Landau-level mixing on Wigner crystallization in graphene

Abstract

Graphene, with its massless linearly-dispersing carriers, in the quantum Hall regime provides an instructive comparison with conventional two-dimensional (2D) systems in which carriers have a nonzero band mass and quadratic dispersion. We investigate the influence of Landau level mixing in graphene on Wigner crystal states in the $n^{\mathrm{th}}$ Landau level obtained using single Landau level approximation. We show that the Landau level mixing does not qualitatively change the phase diagram as a function of partial filling factor $\nu$ in the $n^{\mathrm{th}}$ level. We find that the inter-Landau level mixing, quantified by relative occupations of the two Landau levels, ${\rho }_{n+1}/{\rho }_n$, oscillates around 2% and, in general, remains small ($<4$) irrespective of the Landau level index $n$. Our results show that the single Landau level approximation is applicable in high Landau levels, even though the energy gap between the adjacent Landau levels vanishes.

arXiv comment6 pages, 3 figures

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• Electronic Properties of Graphene in a Strong Magnetic Field
• Orbital and interlayer Skyrmions crystals in bilayer graphene
• Skyrme and Wigner crystals in graphene
• The effect of electron dielectric response on the quantum capacitance of graphene in a strong magnetic field
• Influence of Landau level mixing on the properties of elementary excitations in graphene in strong magnetic field
• Wigner crystal phases in bilayer graphene
• Local density of states of electron-crystal phases in graphene in the quantum Hall regime
• Electron-solid and electron-liquid phases in graphene
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Charge-density-wave states in double-layer graphene structures in a high magnetic field
• Phase diagram for quantum Hall states in graphene
• Skyrme crystal in bilayer and multilayer graphene
• Landau-level composition of bound exciton states in magnetic field
• Two-dimensional bound excitons in real space and Landau quantization space: A comparative study