Fractional Quantum Hall Effect in Graphene: Quantitative Comparison between Theory and Experiment

TL;DR

This paper compares theoretical models with experimental data on fractional quantum Hall states in graphene, highlighting the limitations of linear Landau level mixing corrections and evaluating the accuracy of composite-fermion projections.

Contribution

It provides a detailed phase diagram for spin-polarized fractional quantum Hall states in graphene and assesses the impact of Landau level mixing and projection methods on theoretical predictions.

Findings

Good agreement with theory neglecting Landau level mixing

Landau level mixing corrections are insufficiently captured by linear approximation

Projection methods are accurate for $n/(2n+1)$ states but less so for $n/(2n-1)$ states

Abstract

The observation of extensive fractional quantum Hall states in graphene brings out the possibility of more accurate quantitative comparisons between theory and experiment than previously possible, because of the negligibility of finite width corrections. We obtain accurate phase diagram for differently spin-polarized fractional quantum Hall states, and also estimate the effect of Landau level mixing using the modified interaction pseudopotentials given in the literature. We find that the observed phase diagram is in good quantitative agreement with theory that neglects Landau level mixing, but the agreement becomes significantly worse when Landau level mixing is incorporated assuming that the corrections to the energies are linear in the Landau level mixing parameter $\lambda$. This implies that a first order perturbation theory in $\lambda$ is inadequate for the current experimental systems, for which $\lambda$ is typically on the order of or greater than one. We also test the accuracy of the composite-fermion theory and find that all lowest Landau level projection methods used in the literature are very accurate for the states of the form $n/(2n+1)$ but for the states at $n/(2n-1)$ the results are more sensitive to the projection method. An earlier prediction of an absence of spin transitions for the $n/(4n+1)$ states is confirmed by more rigorous calculations, and new predictions are made regarding spin physics for the $n/(4n-1)$ states.