Hall and Spin Hall Viscosity in 2d Topological Systems

International audienceWe study linear responses to metric perturbation in two-dimensional topological systems based on the Dirac fermion formalism. We introduce a novel quantity, Hall viscosity to particle density ratio, which is analogous to the viscosity to entropy ratio suggested by AdS/CFT correspondence. This quantity corresponds to the filling fraction which characterizes the quantum Hall states, and hence it could be discussed in Haldane’s zero-field quantum Hall system. We also consider dissipationless viscosity in the time reversal invariant quantum spin Hall system, which is a spin analog of the Hall viscosity