Nonlocal Effects on the Magnetic Penetration Depth in<i>d</i>-Wave Superconductors

Abstract

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