Quantum Hall Effect in Graphene with Interface-Induced Spin-Orbit Coupling

TL;DR

This paper models the quantum Hall effect in graphene with interface-induced spin-orbit coupling, analyzing its dependence on magnetic field, gate voltage, and disorder, providing insights for experimental characterization.

Contribution

It introduces a comprehensive effective model for graphene with spin-orbit coupling and investigates the robustness of the quantum Hall effect under disorder using combined first-principles and transport calculations.

Findings

Different scaling laws for spin-splitting of quantum Hall states.

Quantum Hall conductivity's robustness to hydrogen impurity disorder.

A graphene-only Hamiltonian model for impurity effects.

Abstract

We consider an effective model for graphene with interface-induced spin-orbit coupling and calculate the quantum Hall effect in the low-energy limit. We perform a systematic analysis of the contribution of the different terms of the effective Hamiltonian to the quantum Hall effect (QHE). By analysing the spin-splitting of the quantum Hall states as a function of magnetic field and gate-voltage, we obtain different scaling laws that can be used to characterise the spin-orbit coupling in experiments. Furthermore, we employ a real-space quantum transport approach to calculate the quantum Hall conductivity and investigate the robustness of the QHE to disorder introduced by hydrogen impurities. For that purpose, we combine first-principles calculations and a genetic algorithm strategy to obtain a graphene-only Hamiltonian that models the impurity.