Assouline Alexandre, Wang Taige, Zhou Haoxin, Cohen Liam A, Yang Fangyuan, Zhang Ruining, Taniguchi Takashi, Watanabe Kenji, Mong Roger S K, Zaletel Michael P, Young Andrea F
Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA.
Department of Physics, University of California, Berkeley, California 94720, USA.
Phys Rev Lett. 2024 Jan 26;132(4):046603. doi: 10.1103/PhysRevLett.132.046603.
Bernal bilayer graphene hosts even-denominator fractional quantum Hall states thought to be described by a Pfaffian wave function with non-Abelian 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 5.1 K at B=12 T 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 11.6 K is smaller than theoretical expectations for the clean limit by approximately a factor of 2. 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.
伯纳尔双层石墨烯中存在偶数分母的分数量子霍尔态，人们认为这些态由具有非阿贝尔准粒子激发的Pfaffian波函数描述。在此，我们报告了利用热激活输运和化学势的直接测量对双层石墨烯中分数量子霍尔能隙进行的定量测定。我们发现，对于半填充的N = 1朗道能级，在B = 12 T时输运激活能隙为5.1 K，这与Pfaffian态的密度矩阵重整化群计算结果一致。然而，测得的11.6 K的热力学能隙比清洁极限下的理论预期小约2倍。我们在具有长波长无序的分数准粒子维格纳晶体的简化模型内分析了分数填充附近的化学势数据，解释了这种差异。我们的结果定量地确立了双层石墨烯作为一个强大的平台，用于探测预期作为偶数分母态基本激发而出现的非阿贝尔任意子。
