Coherence Factors Beyond the BCS Result

TL;DR

This paper extends the understanding of coherence factors in BCS superconductors by computing matrix elements between arbitrary eigenstates beyond the mean-field approximation, especially relevant out of equilibrium.

Contribution

It provides a method to compute coherence factors between any two eigenstates of the pairing Hamiltonian in the thermodynamic limit, surpassing mean-field limitations.

Findings

Computed coherence factors for arbitrary eigenstates

Extended understanding of superconductor dynamics out of equilibrium

Revealed limitations of mean-field theory in certain eigenstates

Abstract

The dynamics of BCS (Bardeen-Cooper-Schrieffer) superconductors is fairly well understood due to the availability of a mean field solution for the pairing Hamiltonian, a solution which gives the quantum state of superconductor as a state of almost-free fermions interacting only with a condensate. As a result, transition probabilities may be computed, and expressed in terms of matrix elements of electron creation and annihilation operators between approximate eigenstates. These matrix elements are also called 'coherent factors'. Mean-field theory is however not sufficient to describe all eigenstates of a superconductor, a deficiency which is hardly important in (or very close) to equilibrium, but one that becomes relevant in certain out of equilibrium situations. We report here on a computation of matrix elements (coherence factors) for the pairing Hamiltonian between any 'two-arc' eigenstates in the thermodynamic limit.