Odd-Integer Quantum Hall Effect in Graphene: Interaction and Disorder Effects

TL;DR

This paper investigates the interplay of interactions, disorder, and lattice effects in the integer quantum Hall effect in graphene, revealing different stability and pseudospin characteristics for the $ u=1$ and $ u=3$ states.

Contribution

It provides a detailed analysis of the stability, excitation spectrum, and pseudospin nature of IQHE states in graphene considering realistic effects.

Findings

$ u=1$ and $ u=3$ IQHE states are present in the lowest two Dirac Landau levels.

The critical disorder strength for destroying $ u=3$ IQHE is lower than for $ u=1$.

The $ u=1$ state is a Dirac valley and sublattice polarized Ising pseudospin ferromagnet.

Abstract

We study the competition between the long-range Coulomb interaction, disorder scattering, and lattice effects in the integer quantum Hall effect (IQHE) in graphene. By direct transport calculations, both $\nu=1$ and $\nu=3$ IQHE states are revealed in the lowest two Dirac Landau levels. However, the critical disorder strength above which the $\nu=3$ IQHE is destroyed is much smaller than that for the $\nu=1$ IQHE, which may explain the absence of a $\nu=3$ plateau in recent experiments. While the excitation spectrum in the IQHE phase is gapless within numerical finite-size analysis, we do find and determine a mobility gap, which characterizes the energy scale of the stability of the IQHE. Furthermore, we demonstrate that the $\nu=1$ IQHE state is a Dirac valley and sublattice polarized Ising pseudospin ferromagnet, while the $\nu=3$ state is an $xy$ plane polarized pseudospin ferromagnet.