Quantum Anomalous Hall Effect in Single-layer and Bilayer Graphene

TL;DR

This paper investigates the quantum anomalous Hall effect in single-layer and bilayer graphene with spin-orbit coupling and exchange fields, revealing quantized conductance and tunable topological states relevant for spintronics.

Contribution

It provides a detailed analysis of the quantum anomalous Hall effect in graphene systems with Rashba spin-orbit coupling, including the effects of gating and exchange fields, and identifies conditions for different topological phases.

Findings

Single-layer graphene exhibits quantized Hall conductivity of 2e^2/h.

Bilayer graphene's Hall conductivity doubles when gate voltage is less than exchange field.

System can transition between topological states via external gate voltage.

Abstract

The quantum anomalous Hall effect can occur in single and few layer graphene systems that have both exchange fields and spin-orbit coupling. In this paper, we present a study of the quantum anomalous Hall effect in single-layer and gated bilayer graphene systems with Rashba spin-orbit coupling. We compute Berry curvatures at each valley point and find that for single-layer graphene the Hall conductivity is quantized at $\sigma_{xy} = 2e^2/h$, with each valley contributing a unit conductance and a corresponding chiral edge state. In bilayer graphene, we find that the quantized anomalous Hall conductivity is twice that of the single-layer case when the gate voltage $U$ is smaller than the exchange field $M$, and zero otherwise. Although the Chern number vanishes when $U > M$, the system still exhibits a quantized valley Hall effect, with the edge states in opposite valleys propagating in opposite directions. The possibility of tuning between different topological states with an external gate voltage suggests possible graphene-based spintronics applications.