Quantum Hall Effect of Dirac Fermions in Graphene: Disorder Effect and Phase Diagram

TL;DR

This study numerically explores the quantum Hall effect in graphene, revealing two regimes with distinct robustness to disorder, a phase diagram for the unconventional effect, and predicting a new insulating phase near zero gate voltage.

Contribution

It provides a detailed phase diagram for the disorder effects on the quantum Hall states in graphene, highlighting the robustness of the unconventional half-integer QHE and predicting a new insulating phase.

Findings

Unconventional half-integer QHE near band center is more robust against disorder.

Disorder causes float-up of extended levels, destroying Hall plateaus.

A new insulating phase is predicted between b1 2 QHE states.

Abstract

We numerically study the interplay of band structure, topological invariant and disorder effect in two-dimensional electron system of graphene in a magnetic field. Two \emph{distinct} quantum Hall effect (QHE) regimes exist in the energy band with the unconventional "half-integer" QHE appearing near the band center, consistent with the experimental observation. The latter is more robust against disorder scattering than the conventional QHE states near the band edges. The phase diagram for the unconventional QHE is obtained where the destruction of the Hall plateaus at strong disorder is through the float-up of extended levels toward band center and higher plateaus always disappear first. We further predict a new insulating phase between $\nu =\pm 2$ QHE states at the band center, which may explain the experimentally observed resistance discontinuity near zero gate voltage.