Non-Abelian Chern band in rhombohedral multilayer graphene

We demonstrate the emergence of a non-Abelian Chern band at integer filling ν = 2 in rhombohedral multilayer graphene, where a doubly spin degenerate band carries a total Chern number of C = -1 [1]. This counterintuitive result, defying the expectation that topological contributions from degenerate bands cancel out, originates from the non-Abelian structure of the Berry curvature. Using self-consistent Hartree-Fock calculations, we construct phase diagrams for rhombohedral 3-, 4-, and 5-layer graphene under varying perpendicular displacement fields and electronic periodicities. These reveal the stabilization of the non-Abelian state over a finite parameter regime, with a characteristic spin texture exhibiting magnetic winding number +2.

Recent advances in rhombohedral graphene/hBN moiré systems have uncovered a wide range of topological phases, including those at both integer and fractional filling factors [2,3]. While rhombohedral graphene has been recognized as a promising platform due to its flat bands and strong correlations, correlated states at integer fillings beyond ν = 1 remain less understood. Our results clarify the nature of the ν = 2 state and show that the non-Abelian state is energetically favored over the previously known quantum spin Hall [4] and metallic states, both with and without hBN. We further present an explicit expression for the Fock term that gives rise to the nontrivial topology.