Renormalization formalism for superconducting phase transition with inner-Cooper-pair dynamics

TL;DR

This paper develops a renormalization formalism to extend the Ginzburg-Landau theory, accounting for the coupling between center-of-mass and inner-pair degrees of freedom of Cooper pairs near the superconducting transition.

Contribution

It introduces a novel renormalization approach to incorporate inner-pair dynamics into the Ginzburg-Landau framework for superconductivity.

Findings

Formalism captures finite energy transfer effects

Enables study of inner-pair time-retarded physics

Provides insights into unconventional superconducting transitions

Abstract

As charge carrier of the macroscopic superconductivity, the Cooper pair is a composite particle of two paired electrons, which has both center-of-mass and inner-pair degrees of freedom. In most cases, these two different degrees of freedom can be well described by the macroscopic Ginzburg-Landau theory and the microscopic Bardeen-Cooper-Schrieffer (BCS) theory, respectively. Near the superconducting phase transition where the Cooper pair is fragile and unstable because of the small binding energy, there are non-trivial couplings between these two different degrees of freedom due to such as finite energy and/or momentum transfer. The non-trivial couplings make the original derivation of the Ginzburg-Landau theory from the BCS theory fail in principle as where these two different degrees of freedom should not be decoupled. In this article, we will present a renormalization formalism for an extended Ginzburg-Landau action for the superconducting phase transition where there is finite energy transfer between the center-of-mass and the inner-pair degrees of freedom of Cooper pairs. This renormalization formalism will provide a theoretical tool to study the unusual dynamical effects of the inner-pair time-retarded physics on the superconducting phase transition.