Nonlinear response and scaling law in the vortex state of

We study the field dependence of the quasi-particle density of states, the thermodynamics and the transport properties in the vortex state of d-wave superconductors when a magnetic field is applied perpendicular to the conducting plane, specially for the low field and the low temperature compared to the upper critical field and transition temperature, respectively, $H/H_\ab{c2} \ll 1$ and $T/T_\ab{c} \ll 1$. Both the superfluid density and the spin susceptibility exhibit the characteristic $\sqrt{H}$-field dependence, while the nuclear spin lattice relaxation rate $T_1^{-1}$ and the thermal conductivity are linear in field H. With increasing temperature, these quantities exhibit the scaling behavior in $T/\sqrt{H}$. The present theory applies to 2D f-wave superconductors as well; a possible candidate of the superconductivity is Sr2RuO4