Integer Quantum Hall Effect of Interacting Electrons in Graphene

TL;DR

This paper investigates the integer quantum Hall effect in graphene considering electron interactions, charge and spin orderings, and symmetry breaking, explaining experimental quantization steps through a mean-field theoretical approach.

Contribution

It introduces a mean-field theory that accounts for all Landau level interactions and symmetry breaking, providing a detailed explanation of the quantized Hall conductivity steps in graphene.

Findings

Sequential filling of degenerated Landau levels explains the observed conductivity steps.

Symmetry breaking lowers the energy of filled levels, leading to quantized Hall plateaus.

A high-efficiency method for Coulomb coupling calculations is presented.

Abstract

By taking into account the charge and spin orderings and the exchange interactions between all the Landau levels, we investigate the integer quantum Hall effect of electrons in graphene using the mean-field theory. At the fillings $\nu = 4n+2$ with $n = 0, 1, \cdots$, the system is in the high-symmetry state with the Landau levels four-fold degenerated. We show that with doping the degenerated lowest empty levels can be sequentially filled one level by one level, the filled level is lower than the empty ones because of the symmetry breaking. This result explains the step $\Delta\nu$ = 1 in the integer quantized Hall conductivity of the experimental observations. We also present in the supplemental material a high efficient method for dealing with huge number of the Coulomb couplings between all the levels.