Fractional quantum Hall effect with unconventional pairing in monolayer graphene

TL;DR

This paper investigates unconventional pairing mechanisms in the fractional quantum Hall effect observed in monolayer graphene, proposing novel $f$-wave and $p$-wave pairing states of composite fermions in specific Landau levels.

Contribution

It introduces a BCS variational approach revealing potential $f$-wave and $p$-wave pairing instabilities in composite fermions within certain graphene Landau levels, connecting theory with experimental observations.

Findings

Unstable Fermi sea to $f$-wave pairing in $n=3$ Landau level.

Possible $p$-wave pairing at half filling in $n=2$ Landau level.

No pairing instability in $n=0$ and $1$ Landau levels.

Abstract

Motivated by the observation of even denominator fractional quantum Hall effect in the $n=3$ Landau level of monolayer graphene [Y. Kim $\textit{et al.}$, Nature Physics $\textbf{15}$, 154 (2019)], we consider a Bardeen-Cooper-Schrieffer variational state for composite fermions and find that the composite-fermion Fermi sea in this Landau level is unstable to an $f$-wave pairing. Analogous calculation suggests the possibility of a $p$-wave pairing of composite fermions at half filling in the $n=2$ graphene Landau level, whereas no pairing instability is found at half filling in the $n=0$ and $1$ graphene Landau levels. The relevance of these results to experiments is discussed.