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 $\lambda (T)$ 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 $T_{m0}\sim \sqrt{{\xi }_0/{\lambda }_0}{T}_c$ 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 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.

12 pages, 1 figure, slightly modified version, as it is published in Phys. Rev. B

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