Nonlinear Meissner effect in unconventional superconductors

Abstract

We examine the long-wavelength current response in anisotropic superconductors and show how the field dependence of the Meissner penetration length can be used to detect the structure of the order parameter. Nodes in the excitation gap lead to a nonlinear current-velocity constitutive equation at low temperatures that is distinct for each symmetry class of the order parameter. The effective Meissner penetration length is linear in H and exhibits a characteristic anisotropy for fields in the ab plane that is determined by the positions of the nodes in momentum space. The nonlinear current-velocity realtion also leads to an intrinsic magnetic torque for in-plane fields that are not parallel to a nodal or antinodal direction. The torque scales as ${\mathit{H}}^3$ for T→0 and has a characteristic angular dependence. We analyze the effects of thermal excitations, impurity scattering and geometry on the current response of a ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ superconductor, and discuss our results in light of recent measurements of the low-temperature penetration length and in-plane magnetization of single-crystals of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ and ${\mathrm{LuBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$.