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

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)similar to root 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 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 strongtype-II superconductors.