Multiple scattering corrections to theT-matrix approximation: Unified theory of normal and superconducting states

Abstract

We present unified theory of both normal and superconducting states based on the fully self-consistent T-matrix approximation. We argue that the failure of the customary T-matrix approach below the critical temperature is caused by nonphysical repeated collisions. We eliminated the repeated collisions from the Galitskii-Feynman approximation. Obtained corrections are proportional to the inverse volume in the normal state and, thus, vanish in the thermodynamical limit. In the superconducting state these corrections remain finite and describe the Bardeen-Cooper-Schrieffer ͑BCS͒ gap. The T-matrix approach goes beyond mean-field BCS theory. It is, thus, well suited for studies of the systems with large fluctuations such as the BCS-Bose-Einstein-condensate crossover or size effects in small metallic grains and the nuclear matter.

Tunneling spectroscopy of superconducting nanospheres

“…The T -matrix theory which offers symmetric positions of peaks has been derived from the multiple-scattering approach [37,38]. The multiple-scattering theory is not based on the straightforward power expansion, therefore it cannot be represented by diagrams as long as one follows Feynman's rules to convert diagrams into formulas.…”