Nonlinear response and scaling law in the vortex state of d-wave superconductors

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/Hc2 ≪ 1 and T/Tc ≪ 1. Both the superfluid density and the spin susceptibility exhibit the characteristic √H-field dependence, while the nuclear spin lattice relaxation rate T1−1 and the thermal conductivity are linear in field H. With increasing temperature, these quantities exhibit the scaling behavior in T/√H. The present theory applies to 2D f-wave superconductors as well; a possible candidate of the superconductivity is Sr2RuO4.