Hall viscosity and electromagnetic response of electrons in graphene

Mohammad Sherafati, Alessandro Principi, Giovanni Vignale

Published 2016-05-09Version 1

We derive an analytic expression for the geometric Hall viscosity of non-interacting electrons in a single graphene layer in the presence of a perpendicular magnetic field. We show that a recently-derived formula in [C. Hoyos and D. T. Son, Phys. Rev. Lett. {\bf 108}, 066805 (2012)], which connects the coefficient of $q^2$ in the wave vector expansion of the Hall conductivity $\sigma_{xy}(q)$ of the two-dimensional electron gas (2DEG) to the Hall viscosity and the orbital diamagnetic susceptibility of that system, continues to hold for graphene -- in spite of the lack of Galilean invariance -- with a suitable definition of the effective mass. Finally we show that, for a sufficiently large number of occupied Landau levels, the Hall conductivity of electrons in graphene reduces to that of a Galilean-invariant 2DEG with an effective mass given by $\hbar k_F/v_F$ (cyclotron mass). This connection between the Hall conductivity and the viscosity provides a possible avenue to measure the Hall viscosity in graphene.