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

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.

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• Identifying the topological order of quantized half-filled Landau levels through their daughter states
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• High spatial resolution charge sensing of quantum Hall states
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Universal charge conductance at Abelian--non-Abelian quantum Hall interfaces
• Fractional quantum Hall state at $\nu =1/2$ with energy gap up to 6 K, and possible transition from one- to two-component state
• Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• Interlayer exciton condensates between second Landau level orbitals in double bilayer graphene