Anomalous viscosity of vortex hall states in graphene

Abstract: We study temperature effect on anomalous viscosity of Graphene Hall fluid within quantum many-vortex hydrodynamics. The commonly observed filling fractions, $\nu$ in the range $0 < \nu < 2$ is considered. An expression for anomalous viscosity dependent on a geometric parameter-Hall expansion coefficient, is obtained at finite temperatures. It arises from strained induced pseudo-magnetic field in addition to an anomalous term in vortex velocity, which is responsible for re-normalization of vortex-vortex interactions. We observed that both terms greatly modify the anomalous viscosity as well as an enhancement of weakly observed v fractions. Finite values of the expansion coefficient produce a constant and an infinite viscosity at varying temperatures. The infinities are identified as energy gaps and suggest temperatures at which new stable quantum hall filling fractions could be seen. This phenomenon is used to estimate energy gaps of already measured fractional quantum Hall states in Graphene.