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

Abstract: Bilayer graphene has emerged as a key platform for non-Abelian fractional quantum Hall (FQH) states, exhibiting multiple half-filled plateaus with large energy gaps. Here, we report four unexpected quarter-filled states and complete the sequence of half-filled plateaus by observing the previously missing $\nu=-\frac{3}{2}$ and $\nu=\frac{1}{2}$ states. Identifying the half-filled plateaus according to their Levin--Halperin daughter states, we reveal an alternating pattern of non-Abelian topological orders. Whenever a pair of $N=1$ Landau levels cross, anti-Pfaffian and Pfaffian develop in the lower and higher levels, respectively. Surprisingly, quarter states occur in $N=0$ levels and are also accompanied by daughters. The mutual exclusion of half- and quarter-filled states indicates a robust competition between the interactions favoring paired states of either two-flux or four-flux composite fermions. Finally, we observe several FQH states that require strong interactions between composite fermions. The systematic pattern of non-Abelian states across two generations of even denominators strengthens the identification of their topological orders and suggests a universal origin.