The Effects of Landau level mixing on the fractional quantum Hall effect in monolayer Graphene

TL;DR

This study uses exact diagonalization to analyze how Landau level mixing affects fractional quantum Hall states in graphene, finding minimal effects in the lowest Landau level and significant symmetry breaking in the first excited level.

Contribution

It provides a detailed analysis of Landau level mixing effects in graphene's fractional quantum Hall states, highlighting differences between Landau levels and the impact on particle-hole symmetry.

Findings

Landau level mixing negligible in N=0 for κ<2

N=0 fractional quantum Hall states are robust within this range

Anti-Pfaffian state predicted at half-filling of N=1 for κ~0.25-0.75

Abstract

We report results of exact diagonalization studies of the spin- and valley-polarized fractional quantum Hall effect in the $N=0$ and 1 Landau levels in graphene. We use an effective model that incorporates Landau level mixing to lowest-order in the parameter $\kappa = \frac{e^2/\epsilon\ell}{\hbar v_F/\ell}=\frac{e^2}{\epsilon v_F\hbar}$ which is magnetic field independent and can only be varied through the choice of substrate. We find Landau level mixing effects are negligible in the $N=0$ Landau level for $\kappa\lesssim 2$. In fact, the lowest Landau level projected Coulomb Hamiltonian is a better approximation to the real Hamiltonian for graphene than it is for semiconductor based quantum wells. Consequently, the principal fractional quantum Hall states are expected in the $N=0$ Landau level over this range of $\kappa$. In the $N=1$ Landau level, fractional quantum Hall states are expected for a smaller range of $\kappa$ and Landau level mixing strongly breaks particle-hole symmetry producing qualitatively different results compared to the $N=0$ Landau level. At half-filling of the $N=1$ Landau level, we predict the anti-Pfaffian state will occur for $\kappa \sim 0.25$-$0.75$.