Dissipation and criticality in the lowest Landau level of graphene

TL;DR

This paper investigates the effects of disorder on the electronic properties of the lowest Landau level in graphene, revealing how disorder influences conductance features and localization behavior.

Contribution

It provides a numerical analysis of disorder-induced phenomena in graphene's Landau levels, including critical exponents and conductance features, with new insights into disorder effects.

Findings

Bond disorder can create a plateau at , with nonzero longitudinal conductance.

The localization length exponent at the band edges is approximately 2.47.

The localization length exponent varies between 1.0 and 7/3 with combined disorder and mass term.

Abstract

The lowest Landau level of graphene is studied numerically by considering a tight-binding Hamiltonian with disorder. The Hall conductance $\sigma_\mathrm{xy}$ and the longitudinal conductance $\sigma_\mathrm{xx}$ are computed. We demonstrate that bond disorder can produce a plateau-like feature centered at $\nu=0$, while the longitudinal conductance is nonzero in the same region, reflecting a band of extended states between $\pm E_{c}$, whose magnitude depends on the disorder strength. The critical exponent corresponding to the localization length at the edges of this band is found to be $2.47\pm 0.04$. When both bond disorder and a finite mass term exist the localization length exponent varies continuously between $\sim 1.0$ and $\sim 7/3$.