Landau level broadening in graphene with long-range disorder -- Robustness of the n=0 level

TL;DR

This study numerically investigates how long-range correlated disorder affects Landau level broadening in graphene, revealing the exceptional robustness and sharpness of the n=0 Landau level due to chiral symmetry preservation.

Contribution

It demonstrates that correlated disorder preserves the sharpness of the n=0 Landau level in graphene, highlighting a universal anomaly linked to chiral symmetry.

Findings

The n=0 Landau level remains sharply defined under correlated disorder.

Hall transition exhibits fixed-point-like criticality for the n=0 level.

Anomalous behavior occurs in correlated magnetic fields, indicating a generic phenomenon.

Abstract

Broadening of the Landau levels in graphene and the associated quantum Hall plateau-to-plateau transition are investigated numerically. For correlated bond disorder, the graphene-specific n=0 Landau level of the Dirac fermions becomes anomalously sharp accompanied by the Hall transition exhibiting a fixed-point-like criticality. Similarly anomalous behavior for the n=0 Landau level is also shown to occur in correlated random magnetic fields, which suggests that the anomaly is generic to disorders that preserve the chiral symmetry.