Low temperature superfluid stiffness of d-wave superconductor in a magnetic field

The temperature and field dependence of the superfluid density $\rho_s$ in the vortex state of a d-wave superconductor are calculated using a microscopic model in the quasiclassical approximation. We show that at temperatures below T^{*} \varpropto \sqrt{H}$, the linear T dependence of rho_s crosses over to a T^2 dependence differently from the behavior of the effective penetration depth, lambda_eff^{-2}(T). We point out that the expected dependences could be probed by a mutual-inductance technique experiment.