Evidence for non-abelian spin-singlet state in graphene quantum Hall bilayer

The even-denominator fractional quantum Hall state (FQHE) at 5/2 filling is believed to host Ising-type non-abelian anyons - exotic excitations that are thought to enable a subset of operations in topological quantum computation (TQC). It has been proposed that in a spinful system, a non-abelian spin singlet (NASS) state could host Fibonacci anyons, a more robust kind of non-abelian whose braiding properties are theoretically capable of realizing the entire set of operation in TQC. The 2/3 FQHE state has been identified as a candidate for these more exotic non-abelians but, experimental evidence is lacking. Here we discuss measurements of the 4/3 state In double-layer graphene, consisting of two graphene monolayers separated by an interlay dielectric, where the layer degree of freedom plays the role of pseudo spin. Using a combination of Corbino parallel flow and counterflow, together with Hall bar drag measurements, we identify evidence for existence of the k=2 NASS state. The implication of our results on the search for Fibonnacci anyons will be discussed.