Investigating transverse Hall conductances using two-terminal setups

TL;DR

This paper introduces a numerical method to analyze transverse Hall conductances in two-terminal setups, applicable to various models and approaches, demonstrated through quantum spin Hall effect in disordered graphene.

Contribution

The paper presents a novel numerical approach to study Hall conductances using two-terminal setups, compatible with Green's functions and scattering matrix methods.

Findings

Method effectively investigates Hall voltage dependence on model parameters.

Applicable to non-equilibrium Green's functions and scattering matrix approaches.

Demonstrated on quantum spin Hall effect in disordered graphene.

Abstract

In this paper we present a method to numerically study transverse Hall conductances using a two-terminal setup. Using nonlinear transport concepts we find that the Hall voltage dependence on the model parameters can be investigated from the difference between the injectivities from each terminal. The method is suitable to work with non-equilibrium Green's functions as well as for scattering matrix approaches. We illustrate the proposed idea by studying the quantum spin Hall effect in graphene with disordered spin-orbit scattering centers induced by adatoms. We use two distinct models, a finite difference implementation of the Dirac Hamiltonian and a tight-binding Hamiltonian combined with the scattering matrix approach and the non-equilibrium Green's functions approach, respectively.