Nonlocal Effects on the Magnetic Penetration Depth in d-wave Superconductors

TL;DR

This paper demonstrates that nonlocal electrodynamics cause a T^2 temperature dependence in the magnetic penetration depth of clean d-wave superconductors at low temperatures, challenging previous assumptions of a linear T behavior.

Contribution

It predicts a T^2 dependence of the penetration depth due to nonlocal effects in clean d-wave superconductors, which can be observed experimentally below a specific crossover temperature.

Findings

T^2 dependence of $\lambda(T)$ due to nonlocality.

Crossover temperature $T^* \\sim 1 K$ for observing effects.

Discussion of impurities and surface effects on measurements.

Abstract

We show that, under certain conditions, the low temperature behavior of the magnetic penetration depth $\lambda(T)$ of a pure d-wave superconductor is determined by nonlocal electrodynamics and, contrary to the general belief, the deviation $\Delta\lambda(T) = \lambda(T)-\lambda(0)$ is proportional to T^2 and not T. We predict that the $\Delta\lambda(T)\propto T^2$ dependence, due to nonlocality, should be observable experimentally in nominally clean high-T_c superconductors below a crossover temperature $T^* = (\xi_o/\lambda_o)\Delta_o \sim 1 K$. Possible complications due to impurities, surface quality and crystal axes orientation are discussed.