Quantum Hall Effect of Massless Dirac Fermions in a Vanishing Magnetic Field

TL;DR

This paper investigates how strong disorder affects the quantum Hall effect in graphene, revealing that certain Hall plateaus persist at the Dirac point even with vanishing magnetic fields, indicating a robust quantum critical state.

Contribution

It demonstrates that the quantum critical point at the Dirac point remains stable under strong disorder and proposes a way to realize this in zero magnetic field through ripples in graphene.

Findings

All Hall plateaus except at  e^2/h are destroyed by disorder.

The critical state at the Dirac point is robust and belongs to the universality class of integer quantum Hall transitions.

Breaking time-reversal symmetry via ripples can realize the quantum critical point without magnetic field.

Abstract

The effect of strong long-range disorder on the quantization of the Hall conductivity $\sigma_{xy}$ in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in $\sigma_{xy}$ except the plateaus at $\sigma_{xy}=\mp e^2/2h$ (per valley and per spin). The critical state at the charge-neutral Dirac point is robust to strong disorder and belongs to the universality class of the conventional plateau transitions in the integer quantum Hall effect. We propose that the breaking of time-reversal symmetry by ripples in graphene can realize this quantum critical point in a vanishing magnetic field.