Integer Quantum Hall Effect in a Lattice Model Revisited: Kubo Formalism

TL;DR

This paper numerically studies the integer quantum Hall effect in a 2D lattice with disorder and magnetic field, using Kubo formalism to analyze conductivities, providing insights into lattice-based IQHE.

Contribution

It revisits IQHE in lattice models with a numerical approach using Kubo formalism, highlighting the effects of disorder and magnetic fields.

Findings

Quantitative analysis of longitudinal and transverse conductivities.

Insights into the interplay between magnetic field and disorder.

Methodology applicable to various lattice models.

Abstract

We investigate numerically the integer quantum Hall effect (IQHE) in a two-dimensional square lattice with non-interacting electrons subjected to disorder and uniform magnetic field in a direction perpendicular to the lattice plane. We employ nearest-neighbor tight-binding Hamiltonian to describe the system and obtain the longitudinal and transverse conductivities by using Kubo formalism. The interplay between the magnetic field and disorder is also discussed. Our analysis may be helpful in studying IQHE in any discrete lattice model.