We derive an analytic expression for the geometric Hall viscosity of noninteracting 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. 108, 066805 (2012)], which connects the coefficient of $q^2$ in the wave-vector expansion of the Hall conductivity ${\sigma }_{xy}\left(q\right)$ 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. We also show that, for a sufficiently large number of occupied Landau levels in the positive-energy sector, the Hall conductivity of electrons in graphene reduces to that of a Galilean-invariant 2DEG with an effective mass given by $\hslash k_F/v_F$ (cyclotron mass). Even in the most demanding case, i.e., when the chemical potential falls between the zeroth and the first Landau levels, the cyclotron mass formula gives results accurate to better than 1%. The connection between the Hall conductivity and the viscosity provides a possible avenue to measure the Hall viscosity in graphene.

• Received 29 June 2016

DOI:https://doi.org/10.1103/PhysRevB.94.125427