Shape of the zeroth Landau level in graphene with non-diagonal disorder

TL;DR

This paper investigates the unique shape and properties of the zeroth Landau level in graphene under non-diagonal disorder, revealing how inter-valley scattering and anisotropic bond disorder influence its structure and localization.

Contribution

The study provides an analytical expression for the density of states of the zeroth Landau level in graphene with anisotropic bond disorder, aligning well with numerical simulations and highlighting the role of valley correlations.

Findings

The zeroth Landau level remains narrow and exhibits a peculiar three-peak shape.

Inter-valley scattering significantly affects the broadening of the zeroth Landau level.

Delocalization at zero energy impacts the density of states near zero energy.

Abstract

Non-diagonal (bond) disorder in graphene broadens Landau levels (LLs) in the same way as random potential. The exception is the zeroth LL, $n=0$, which is robust to the bond disorder, since it does not mix different $n=0$ states within a given valley. The mechanism of broadening of the $n=0$ LL is the inter-valley scattering. Several numerical simulations of graphene with bond disorder had established that $n=0$ LL is not only anomalously narrow but also that its shape is very peculiar with three maxima, one at zero energy, $E=0$, and two others at finite energies $\pm E$. We study theoretically the structure of the states in $n=0$ LL in the presence of bond disorder. Adopting the assumption that the bond disorder is strongly anisotropic, namely, that one type of bonds is perturbed much stronger than other two, allowed us to get an analytic expression for the density of states which agrees with numerical simulations remarkably well. On the qualitative level, our key finding is that delocalization of $E=0$ state has a dramatic back effect on the density of states near $E=0$. The origin of this unusual behavior is the strong correlation of eigenstates in different valleys.