The three fractional quantum Hall states at filling factor ν = 7/5 in bilayer graphene

The celebrated fractional quantum Hall (FQH) effect takes on new twists in Bernal-stacked bilayer graphene due to its orbital and valley degrees of freedom. In our previous work, we made ultra-high-quality dual-gated devices and observed a new even-denominator state at ν = 5/2 and demonstrated the ability to select the orbital wave function (N=0 vs N=1) for a given Landau level (LL) using a perpendicular electric displacement field D (Huang et al., Phys. Rev. X 12, 031019 (2022)). In this talk, we examine the phase diagram of filling factor ν = 7/5 in a wide range of displacement and magnetic fields. Three FQH states are found. The 7/5 state riding on the N=0 LL exhibits the familiar properties of Jain FQH states. The state riding on the N=1 LL of bilayer graphene, which contains a small component of the N=0 wave function, exhibits an intriguing evolution with increasing magnetic field. Remarkably, the state with the largest energy gap occurs at the crossing of |+1>(|-1>) and |-0> (|+0>) levels, suggesting possible valley orbital coherence. We report on the gap energies of the three FQH states and discuss their possible origins.