Quantum Hall Effect in Bilayer Graphene: Disorder Effect and Quantum Phase Transition

TL;DR

This paper numerically investigates the quantum Hall effect in bilayer graphene, revealing two regimes separated by a critical region, and examines how disorder affects the stability of quantum Hall plateaus and conductance.

Contribution

It provides a detailed numerical analysis of disorder effects on QHE in bilayer graphene, identifying distinct regimes and the robustness of certain Hall plateaus.

Findings

Two distinct QHE regimes separated by a critical region.

The $ u=0$ plateau is absent, aligning with experiments.

Central Hall plateaus are most robust against disorder.

Abstract

We numerically study the quantum Hall effect (QHE) in bilayer graphene based on tight-binding model in the presence of disorder. Two distinct QHE regimes are identified in the full energy band separated by a critical region with non-quantized Hall Effect. The Hall conductivity around the band center (Dirac point) shows an anomalous quantization proportional to the valley degeneracy, but the $\nu=0$ plateau is markedly absent, which is in agreement with experimental observation. In the presence of disorder, the Hall plateaus can be destroyed through the float-up of extended levels toward the band center and higher plateaus disappear first. The central two plateaus around the band center are most robust against disorder scattering, which is separated by a small critical region in between near the Dirac point. The longitudinal conductance around the Dirac point is shown to be nearly a constant in a range of disorder strength, till the last two QHE plateaus completely collapse.