Pair correlations and the survival of superconductivity in and around a superconducting impurity

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Abstract

The problem of the survival of superconductivity in a small superconducting grain placed in a metal substrate is addressed. For this aim the pair correlations and superconducting gap around and inside a negative- U impurity in one and two dimensions are calculated in a discrete tight-binding model and a continuous model. Using a mean-field decomposition, it is shown that finite pairing in the grain develops when the system has a degeneracy between a successive number of electron pairs, and thus may oscillate as a function of the chemical potential. For finite pairing in the island, pair correlations in the normal part exhibit a crossover from being long ranged to exponentially decaying, depending on the strength of interaction in the grain. It is shown analytically that there is a minimal island size under which pairing vanishes, which is different from that given by Anderson's criterion, and that it scales as a power law with island size, rather than exponentially as in isolated grains.

Original languageEnglish
Article number094510
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume75
Issue number9
DOIs
StatePublished - 28 Mar 2007

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