Time-reversal odd transport in bilayer graphene: Hall conductivity and Hall viscosity

We consider the time-reversal odd dynamics of the bilayer graphene at low energies in the quantum Hall regime. A generating functional for the effective action that captures the electromagnetic response to all orders in momentum and frequency is presented and evaluated to the third order in the space-time gradient O (∂³) . In addition, we calculate the Hall viscosity and derive an explicit relationship with the q² coefficient of the Hall conductivity. It is reminiscent of the Hoyos-Son relation in Galilean invariant systems, which can be recovered in the limit of large filling factor N .