Studying the non-abelian even-denominator state in Bernal-stacked bilayer graphene by scanning tunneling microscope

Non-abelian anyons have drawn interest from physicists because of their potential application as qubits in topological quantum computation. The even-denominator fractional quantum Hall (FQH) states are candidates for achieving non-abelian anyons. In this talk, I will discuss our recent scanning tunneling microscope (STM) measurement of the FQH states in the N=1 Landau levels of bilayer graphene. By measuring thermodynamic gaps locally, we find energy gaps for the even-denominator FQH states to be around 30 K at 14 T, larger by one or two orders of magnitude than prior transport and penetration capacitance measurements in other related systems. We find supporting evidence for the even-denominator states to be non-abelian by observing its Levin-Halperin daughter states. We also measure the influence of local single-atom defects on the even-denominator state gaps and identify the intrinsic FQH gaps with sizes consistent with theoretical calculations. The large gap reported in this study makes bilayer graphene an ideal platform for the future realization of topological qubits based on non-abelian anyons.