Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene

The current proposals for producing non-Abelian anyons and Majorana particles, which are neither fermions nor bosons, are primarily based on the realization of topological superconductivity in two dimensions. We show theoretically that the unique Landau level structure of bilayer graphene provides a new possible avenue for achieving such exotic particles. Specifically, we demonstrate the feasibility of a "parton" fractional quantum Hall (FQH) state, which supports non-Abelian particles without the usual topological superconductivity. Furthermore, we advance this state as the fundamental explanation of the puzzling $1/2$ FQH effect observed in bilayer graphene [Kim {\em et al.}, Nano Lett. {\bf 15}, 7445 (2015)], and predict that it will also occur in trilayer graphene. We indicate experimental signatures that differentiate the parton state from other candidate non-Abelian FQH states and predict that a transverse electric field can induce a topological quantum phase transition between two distinct non-Abelian FQH states.