The Nonlinear Meissner Effect in Unconventional Superconductors

TL;DR

This paper investigates how the nonlinear Meissner effect in unconventional superconductors reveals the structure of the order parameter through field-dependent penetration length and magnetic torque measurements.

Contribution

It introduces a method to detect the order parameter symmetry in anisotropic superconductors via nonlinear current response and magnetic torque analysis.

Findings

Nonlinear current-velocity relation varies with order parameter symmetry.

Effective penetration length is linear in magnetic field H.

Magnetic torque exhibits a characteristic angular dependence and scales as H^3 at low temperatures.

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 which 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 relation 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 $H^3$ for $T\rightarrow 0$ and has a characteristic angular dependence. We analyze the effects of thermal excitations, impurity scattering and geometry on the current response of a $d_{x^2-y^2}$ superconductor, and discuss our results in light of recent measurements of the low-temperature penetration length and in-plane magnetization of single-crystals of $YBa_2Cu_3O_{7-\delta}$ and $LuBa_2Cu_3O_{7-\delta}$.