Theoretical study of even denominator fractions in graphene: Fermi sea versus paired states of composite fermions

TL;DR

This paper investigates the nature of even denominator fractional quantum Hall states in graphene, comparing Fermi sea and paired states of composite fermions, and predicts the stability of certain Fermi sea configurations based on microscopic calculations.

Contribution

It provides a theoretical analysis of composite fermion states in graphene, highlighting the stability of Fermi seas over paired states and considering the effects of pseudopotentials and degeneracy.

Findings

Paired composite fermion states are not energetically favorable.

Composite fermion Fermi seas are present in both n=0 and n=1 Landau levels.

An SU(4) singlet Fermi sea is stabilized under certain conditions.

Abstract

The physics of the state at even denominator fractional fillings of Landau levels depends on the Coulomb pseudopotentials, and produces, in different GaAs Landau levels, a composite fermion Fermi sea, a stripe phase, or, possibly, a paired composite fermion state. We consider here even denominator fractions in graphene, which has different pseudopotentials as well as a possible four fold degeneracy of each Landau level. We test various composite fermion Fermi sea wave functions (fully polarized, SU(2) singlet, SU(4) singlet) as well as the paired composite fermion states in the n=0 and $n=1$ Landau levels and predict that (i) the paired states are not favorable, (ii) CF Fermi seas occur in both Landau levels, and (iii) an SU(4) singlet composite fermion Fermi sea is stabilized in the appropriate limit. The results from detailed microscopic calculations are generally consistent with the predictions of the mean field model of composite fermions.