Quarter- and half-filled quantum Hall states and their competing interactions in bilayer graphene

Bilayer graphene has emerged as a key platform for studying non-Abelian fractional quantum Hall states. Its multiple half-filled plateaus with large energy gaps combined with its tunability offer an opportunity to distill the principles that determine their topological order. Here, I will present the observation of additional plateaus at ν = -³/₂ and ν = ¹/₂ for different spin and valley, revealing an alternating pattern of non-Abelian states according to their Levin-Halperin daughter states. In the N = 0 levels, where half-filled plateaus are absent, we instead observe four unexpected incompressible quarter-filled states along with daughters. The mutual exclusion of half- and quarter-filled states indicates a robust competition between the interactions favoring either paired states of two-flux or four-flux composite fermions.