Energy gap of the even-denominator fractional quantum Hall state in bilayer graphene

TL;DR

This study measures the energy gaps of the even-denominator fractional quantum Hall state in bilayer graphene, confirming its potential for exploring non-Abelian anyons and revealing discrepancies with theoretical models.

Contribution

It provides the first quantitative measurement of fractional quantum Hall energy gaps in bilayer graphene and compares experimental results with theoretical predictions.

Findings

Transport activation gap of 5.1K at 12T

Thermodynamic gap of 11.6K, smaller than theory

Chemical potential analysis supports quasiparticle Wigner crystal model

Abstract

Bernal bilayer graphene hosts even denominator fractional quantum Hall states thought to be described by a Pfaffian wave function with nonabelian quasiparticle excitations. Here we report the quantitative determination of fractional quantum Hall energy gaps in bilayer graphene using both thermally activated transport and by direct measurement of the chemical potential. We find a transport activation gap of 5.1K at B = 12T for a half-filled N=1 Landau level, consistent with density matrix renormalization group calculations for the Pfaffian state. However, the measured thermodynamic gap of 11.6K is smaller than theoretical expectations for the clean limit by approximately a factor of two. We analyze the chemical potential data near fractional filling within a simplified model of a Wigner crystal of fractional quasiparticles with long-wavelength disorder, explaining this discrepancy. Our results quantitatively establish bilayer graphene as a robust platform for probing the non-Abelian anyons expected to arise as the elementary excitations of the even-denominator state.