Low-temperature magnetic penetration depth in d-wave superconductors: Zero-energy bound state and impurity effects

Abstract

We report a theoretical study on the deviations of the Meissner penetration depth $\ensuremath{\lambda}(T)$ from its London value in d-wave superconductors at low temperatures. The difference arises from low-energy surface Andreev bound states. The temperature dependent penetration depth is shown to go through a minimum at the temperature ${T}_{m0}\ensuremath{\sim}\sqrt{{\ensuremath{\xi}}_{0}/{\ensuremath{\lambda}}_{0}}{T}_{c}$ if the broadening of the bound states is small. The minimum will straighten out when the broadening reaches ${T}_{m0}.$ The impurity scattering sets up the low-temperature anomalies of the penetration depth and destroys them when the mean free path is not sufficiently large. A phase transition to a state with a spontaneous surface supercurrent is investigated and its critical temperature determined in the absence of a subdominant channel activated at low temperatures near the surface. Nonlinear corrections from Andreev low-energy bound states to the penetration length are obtained and shown, on account of their broadening, to be small in the Meissner state of strong type-II superconductors.