Unconventional fractional quantum Hall states on the N=1 Landau level in bilayer graphene

In a magnetic field, strong electron-electron interaction in 2D leads to the celebrated fractional quantum Hall (FQH) effect. FQH states riding on the n=1 orbital Landau levels (LLs) are particularly fascinating. Even-denominator states occurring at half fillings have long been suspected to be non-Abelian in nature and carry excitations that are potentially useful in topological quantum computing. States with odd denominators such as 2/5 and 3/7 are also expected to be non-Abelian, with even more complex wave functions [1][2]. In prior work, we showed the appearance of a new even-denominator FQH state at nu = 5/2 in ultra-clean Bernal-stacked bilayer graphene and the spontaneously broken particle-hole symmetry at a number of even-denominator FQH states [3]. In this talk, we discuss findings at nu = 7/5, which exhibits three distinct ground states induced by a varying perpendicular electric displacement field D that moves the state from the N=0 to the N=1 LL of bilayer graphene. We measure the gap energy of all three ground states and construct a phase diagram of  = 7/5 as a function of the D- and B-fields. Connections to theoretical predictions are made.

[1] N. Read, and E. Rezayi, Phys. Rev. B 59, 8084 (1999)

[2] W. N. Faugno et al, Phys. Rev. Res. 2, 033223 (2020).

[3] K. Huang et al, arXiv:2105.07058 (2021)