Quantum Hall effect in graphene: A functional determinant approach

TL;DR

This paper investigates the quantum Hall effect in graphene using a functional determinant approach, analyzing the role of the Dirac determinant phase and gauge transformations on Hall conductivity at finite temperature and density.

Contribution

It introduces a novel functional determinant method to analyze the quantum Hall effect in graphene, emphasizing the impact of determinant phase choices and gauge transformations.

Findings

Dependence of Hall conductivity on the phase of the Dirac determinant.

Behavior of the lowest Landau level contribution under gauge transformations.

Interpretation of gauge transformations as spinor rotations around magnetic fields.

Abstract

We start the paper with a brief presentation of the main characteristics of graphene, and of the Dirac theory of massless fermions in 2+1 dimensions obtained as the associated low-momentum effective theory, in the absence of external fields. We then summarize the main steps needed to obtain the Hall conductivity in the effective theory at finite temperature and density, with emphasis on its dependence on the phase of the Dirac determinant selected during the evaluation of the effective action. Finally, we discuss the behavior, under gauge transformations, of the contribution due to the lowest Landau level, and interpret gauge transformations as rotations of the corresponding spinors around the magnetic field.