  We study responses to metric perturbation in topological insulator models. In
this paper 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
related to a spin current.
