Incompressible Even Denominator Fractional Quantum Hall States in the Zeroth Landau Level of Monolayer Graphene

TL;DR

This paper investigates the nature of even denominator fractional quantum Hall states in monolayer graphene using a Chern-Simons framework, proposing unified explanations and experimental tests for these exotic states.

Contribution

It introduces a flux attachment scheme that unifies odd and even denominator fractions and links them to symmetry-breaking orders in composite Dirac fermions.

Findings

Experimental fractions can be explained within the same flux attachment scheme.

Proposes variational wavefunctions for these states.

Suggests symmetry-breaking orders as the origin of observed fractions.

Abstract

Incompressible even denominator fractional quantum Hall states at fillings $\nu = \pm \frac{1}{2}$ and $\nu = \pm \frac{1}{4}$ have been recently observed in monolayer graphene. We use a Chern-Simons description of multi-component fractional quantum Hall states in graphene to investigate the properties of these states and suggest variational wavefunctions that may describe them. We find that the experimentally observed even denominator fractions and standard odd fractions (such as $\nu=1/3, 2/5$, etc.) can be accommodated within the same flux attachment scheme and argue that they may arise from sublattice or chiral symmetry breaking orders (such as charge-density-wave and antiferromagnetism) of composite Dirac fermions, a phenomenon unifying integer and fractional quantum Hall physics for relativistic fermions. We also discuss possible experimental probes that can narrow down the candidate broken symmetry phases for the fractional quantum Hall states in the zeroth Landau level of monolayer graphene.