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 to conventional two-dimensional 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 $n\text{th}$ 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 $\ensuremath{\nu}$ in the $n\text{th}$ level. We find that the inter-Landau-level mixing, which is quantified by relative occupations of the two Landau levels, ${\ensuremath{\rho}}_{n+1}/{\ensuremath{\rho}}_{n}$, oscillates around 2% and, in general, remains small $(l4%)$ 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.