Even denominator fractional quantum Hall states in higher Landau levels of graphene

An important development in the field of the fractional quantum Hall effect has been the proposal that the 5/2 state observed in the Landau level with orbital index $n = 1$ of two dimensional electrons in a GaAs quantum well originates from a chiral $p$-wave paired state of composite fermions which are topological bound states of electrons and quantized vortices. This state is theoretically described by a "Pfaffian" wave function or its hole partner called the anti-Pfaffian, whose excitations are neither fermions nor bosons but Majorana quasiparticles obeying non-Abelian braid statistics. This has inspired ideas on fault-tolerant topological quantum computation and has also instigated a search for other states with exotic quasiparticles. Here we report experiments on monolayer graphene that show clear evidence for unexpected even-denominator fractional quantum Hall physics in the $n=3$ Landau level. We numerically investigate the known candidate states for the even-denominator fractional quantum Hall effect, including the Pfaffian, the particle-hole symmetric Pfaffian, and the 221-parton states, and conclude that, among these, the 221-parton appears a potentially suitable candidate to describe the experimentally observed state. Like the Pfaffian, this state is believed to harbour quasi-particles with non-Abelian braid statistics