Influence of Landau-level mixing on Wigner crystallization in graphene

TL;DR

This study examines how Landau level mixing affects Wigner crystallization in graphene, finding that mixing remains minimal and does not significantly alter the phase diagram, supporting the validity of the single Landau level approximation.

Contribution

It demonstrates that Landau level mixing has a negligible impact on Wigner crystal states in graphene, validating the single Landau level approximation across high Landau levels.

Findings

Landau level mixing oscillates around 2% and remains below 4%.

The phase diagram is not qualitatively affected by Landau level mixing.

Single Landau level approximation is valid even at high Landau levels.

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.