Augmented space recursion study of the effect of disorder on superconductivity

Abstract

We present a real-space approach to study the effect of disorder on superconductivity. The method is based on augmented space formalism that goes beyond mean-field approximations for configuration averaging and effectively deals with the influence of configuration fluctuations of the neighborhood of an atom. In the regime of validity of Anderson's theorem our results for s-and d-wave dirty superconductors have excellent agreement with existing results. The formalism is extended and tested for random negative U Hubbard model. Having verified the reliability of our method we use it to study environment-dependent inhomogeneous randomness in disordered superconducting systems.

A real space approach to study the effect of off-diagonal disorder on superconductivity

“…As mentioned before, in an earlier communication [11] we have studied superconductivity in ordered systems as well as in disordered systems with uncorrelated and correlated on-site disorder.…”

“…3a that as v is varied from the negative to the positive end, D increases showing greater hopping interaction strength between similar species supports and enhances superconductivity. In our previous communication [11] we had seen that phase segregation (similar species clustering together) enhances superconductivity more than AB ordering. This is consistent with our present finding.…”

“…It has been widely used to study both s-and d-wave superconductivity in ordered systems [22,23]. We have also used it to analyze the existence of stable solutions for ordered superconductors in our previous communication [11]. We now briefly review the Hamiltonian considered in our study to introduce the notations.…”

“…The ASF is a natural generalization of the CPA and allows us not only to include effects of configuration fluctuations of the near neighbourhood of a site, but also, through the ''terminator" approximation regulate the accuracy of the numerical results. Recently we have illustrated [11] the viability of our real space approach to solve BdG equations in the presence of disorder for several models for diagonal disorder, disorder in the on-site attractive term U ii so that electrons attract each other provided they are near certain randomly placed impurity centre, and for correlated disorder i.e. alloys with short ranged order.…”

“…While DCA is restricted only to a limited number of disordered configurations, CPA is ideally suited only for models with on-site disorder. Very recently we have developed a real space technique to solve BdG equations in the presence of disorder [11]. Here the technique of disorder averaging is based on the augmented space formalism (ASF) introduced by one of us [12] and is not constrained by the above mentioned limitations of DCA and CPA.…”