Models for the integer quantum Hall effect: the network model, the Dirac equation, and a tight-binding Hamiltonian

TL;DR

This paper explores different theoretical models for the integer quantum Hall effect's plateau transition, establishing connections between network models, Dirac Hamiltonians, and tight-binding Hamiltonians.

Contribution

It introduces a mapping from the network model to the Dirac Hamiltonian with disorder and relates the network model to a tight-binding Hamiltonian, advancing understanding of quantum Hall physics.

Findings

Mapping from network model to Dirac Hamiltonian with disorder

Connection between network model and tight-binding Hamiltonian

Framework for analyzing quantum Hall plateau transitions

Abstract

We consider models for the plateau transition in the integer quantum Hall effect. Starting from the network model, we construct a mapping to the Dirac Hamiltonian in two dimensions. In the general case, the Dirac Hamiltonian has randomness in the mass, the scalar potential, and the vector potential. Separately, we show that the network model can also be associated with a nearest neighbour, tight-binding Hamiltonian.