Splitting of the Zero-Energy Landau Level and Universal Dissipative Conductivity at Critical Points in Disordered Graphene

TL;DR

This paper investigates the robustness of the zero-energy Landau level's conductivity in disordered graphene under varying magnetic fields, revealing universal critical conductivities and the effects of sublattice symmetry breaking.

Contribution

It provides a theoretical analysis of the Landau level splitting and conductivity behavior in disordered graphene, highlighting universal critical values and the impact of symmetry breaking.

Findings

Critical conductivity $\sigma_{xx} hickapprox 1.4 e^{2}/h$ is robust under disorder and magnetic field variations.

Breaking sublattice symmetry causes $\sigma_{xx}$ to vanish at the Dirac point due to localization.

Pseudospin-split states exhibit a universal critical conductivity of $\sigma_{xx} hickapprox e^{2}/h$ regardless of disorder or magnetic strength.

Abstract

We report on robust features of the longitudinal conductivity ($\sigma_{xx}$) of the graphene zero-energy Landau level in presence of disorder and varying magnetic fields. By mixing an Anderson disorder potential with a low density of sublattice impurities, the transition from metallic to insulating states is theoretically explored as a function of Landau-level splitting, using highly efficient real-space methods to compute the Kubo conductivities (both $\sigma_{xx}$ and Hall $\sigma_{xy}$). As long as valley-degeneracy is maintained, the obtained critical conductivity $\sigma_{xx}\simeq 1.4 e^{2}/h$ is robust upon disorder increase (by almost one order of magnitude) and magnetic fields ranging from about 2 to 200 Tesla. When the sublattice symmetry is broken, $\sigma_{xx}$ eventually vanishes at the Dirac point owing to localization effects, whereas the critical conductivities of pseudospin-split states (dictating the width of a $\sigma_{xy}=0$ plateau) change to $\sigma_{xx}\simeq e^{2}/h$, regardless of the splitting strength, superimposed disorder, or magnetic strength. These findings point towards the non dissipative nature of the quantum Hall effect in disordered graphene in presence of Landau level splitting.