Even denominator fractional quantum Hall physics in higher order 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 innovative ideas for computation and has also instigated a quest 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 investigated the known candidate states for even-denominator fractional quantum Hall effect, including the Pfaffian, the particle-hole symmetric Pfaffian, the 221-parton, and several valley/spin singlet states. We conclude that, among these, the 221-parton state is a possible candidate to explain the experimentally observed state and that this incompressible ground state is distinct from the 5/2 state in GaAs . Like the Pfaffian, this state is also believed to harbour quasi-particles with non-Abelian braid statistics.

This work has been carried out with Youngwook Kim, Ajit Balram, Takashi Taniguchi, Kenji Watanabe and Jainendra Jain.