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

Abstract

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, $H/H_{c2}\ll 1$ and $T/T_c\ll 1$. 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 superconductor as well; a possible candidate of the superconductivity in Sr${}_2$RuO${}_4$.

11 pages, 4 figures

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