Valley-controlled even-denominator fractional quantum Hall effect in bilayer graphene

In a magnetic field, strong electron-electron interaction leads to the celebrated fractional quantum Hall(FQH) effect. FQH states with even-denominators are particularly interesting as they are predicted to host non-Abelian excitations that are foundations of topological quantum computing. Bernal-stacked bilayer graphene has been shown to support even-denominator FQH states at large perpendicular displacement field D at filling factors ν = -5/2, -1/2, 3/2, and 7/2. Here we report the observation of a new even-denominator state at filling factor ν = 5/2 in bilayer graphene. Thanks to higher device quality, we are able to access the regime of very small D-field and probe the gap of the 5/2 state Δ_5/2 in the limit of vanishing valley splitting E_V. We find that Δ_5/2 increases with increasing D and extrapolates to a finite value in the limit of E_V = 0. This result indicates the spontaneous valley polarization of the 5/2 state and provides support for the Moore-Read Pfaffian/anti-Pfaffian wave functions. The exquisite control we have in manipulating the valley pseudospin opens the door to exciting valley-coherent many-body phenomena.