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

Abstract

The problem of the survival of superconductivity in a small super-conducting grain placed in a metal substrate is addressed. For this aim the pair correlations and super-conducting gap around and inside a negative-U impurity in one and two dimensions is 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 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 cross-over 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 than that given by Anderson's criterion, and that it scales as a power-law with island size, rather then exponentially as in isolated grains.

Charge-Kondo effect in mesoscopic superconductors coupled to normal metals

“…Surprisingly, there have been no thorough studies of CKE in superconductors with ∆ > E c . The relevant literature is limited to some peripheral statements, 21,22 along with a tacit assumption that CKE in superconducting dots is conceptually similar to CKE in non-superconducting single-electron devices (NNN devices). Contrary to this view, our results aim to draw the attention of theorists and experimentalists alike towards the study and search of charge-Kondo correlations in NSN systems.…”

Pairing Correlations around Negative-U Centre in the Two-Band Model

“…We numerically solve the BdG equations (4), (5) on a linear or square lattice with periodic boundary conditions. Both the pair correlations f 01 , f 02 and the order parameters ∆ λλ at the impurity site appear only when states with N and N + 2 electrons are degenerate [6]. Since the parameter space of two-band model is large we shall present results for few representative sets and leave the systematic discussion to future publication.…”

“…The extent of correlations does depend on the model parameters. In one-band case [6] the correlations are short ranged for |U | larger than the band width. In a model with coupled bands the dependence is more complicated and the detailed study will be presented elsewhere.…”

“…We concentrate mainly on two-dimensional systems [6] and neglect direct s-d hybridisation t λλ i,i+δ = t λ δ λλ , for our main interest here is the effect of pair scattering (i.e. the effect of potential U 12 ) on the properties of the system studied.…”

“…It is the purpose of the present paper to extend, to the two-band case, the previous study [6] of superconducting correlations in the vicinity of single (123) impurity or small grain placed in non-superconducting host. Of particular interest is the question if the two-band scenario introduces new spatial scales into the problem and how the pair correlations induced by inter-band pair scattering will depend on the distance from impurity.…”