Diagrammatic analysis of the two-state quantum Hall system with chiral invariance

TL;DR

This paper uses a diagrammatic approach to analyze the two-state quantum Hall system with chiral invariance, focusing on conductivity behavior at specific energies and the effects of randomness in Zeeman energy.

Contribution

It provides an exact calculation of conductivity at the Zeeman energy and explores the independence of conductivity from Zeeman energy variations in a two-state quantum Hall model.

Findings

Exact conductivity value at Zeeman energy $E = \Delta$

Conductivity at $E = 0$ and $E = E_1$ is independent of Zeeman energy

Analysis of Zeeman energy as a random field

Abstract

The quantum Hall system in the lowest Landau level with Zeeman term is studied by a two-state model, which has a chiral invariance. Using a diagrammatic analysis, we examine this two-state model with random impurity scattering, and find the exact value of the conductivity at the Zeeman energy $E = \Delta$. We further study the conductivity at the another extended state $E = E_1$ ($ E_1 > \Delta$). We find that the values of the conductivities at $E = 0$ and $E = E_1$ do not depend upon the value of the Zeeman energy $\Delta$. We discuss also the case where the Zeeman energy $\Delta$ becomes a random field.