Anomalous criticality in the quantum Hall transition at $n=0$ Landau level of graphene with chiral-symmetric disorders

TL;DR

This study numerically examines how chiral symmetry influences the critical behavior of quantum Hall transitions in disordered graphene, revealing an anomalous transition at the n=0 Landau level that persists despite symmetry degradation.

Contribution

It demonstrates that chiral symmetry is the key factor in the anomalous quantum Hall transition at n=0 in graphene, even when the symmetry is partially broken by next-nearest neighbor hopping.

Findings

Anomalous step-function-like transition at n=0 Landau level with chiral symmetry.

Robustness of the anomaly against next-nearest neighbor hopping.

Plateau structure in ac Hall conductivity when chiral symmetry is preserved.

Abstract

We investigate numerically whether the chiral symmetry is the sole factor dominating the criticality of the quantum Hall transitions in disordered graphene. When the disorder respects the chiral symmetry, the plateau-to-plateau transition at the $n=0$ Landau level is shown to become anomalous (i.e., step-function-like). Surprisingly, however, the anomaly is robust against the inclusion of the uniform next-nearest neighbor hopping, which degrades the chiral symmetry of the lattice models. We have also shown that the ac (optical) Hall conductivity exhibits a robust plateau structure when the disorder respects the chiral symmetry.