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

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.