Is the nonlinear Meissner effect unobservable?

TL;DR

This paper investigates the nonlinear Meissner effect in d-wave superconductors, finding it to be generally unobservable due to a quadratic field dependence and a crossover scale, except in special orientations.

Contribution

It demonstrates that nonlocal electrodynamics causes the nonlinear Meissner effect to be unobservable in most cases, with a detailed analysis of geometry and orientation effects.

Findings

Nonlocal effects lead to quadratic field dependence of penetration depth.

The crossover scale H* is often larger than Hc1, suppressing observability.

Special orientations may still exhibit the nonlinear Meissner effect.

Abstract

We examine the effects of nonlocal electrodynamics for a d-wave superconductor on the field dependence of the magnetic penetration depth. The linear field dependence predicted in the local limit, commonly known as the nonlinear Meissner effect, is instead found to be quadratic, $\delta\lambda\sim H^2$ for fields below a crossover scale $H^*$. This crossover is shown to be geometry dependent and for most orientations of the screening currents is of the same order as or greater than $H_{c1}$, implying that the nonlinear Meissner effect can not be observed. For special orientations where the current flows along the nodal directions, however, the nonlinear Meissner effect may be recovered.