Interplay of finite-energy and finite-momentum superconducting pairing

TL;DR

This paper explores how finite-energy and finite-momentum Cooper pairs coexist and influence superconducting properties, revealing that odd-frequency correlations are crucial for understanding the Meissner effect in various superconductors.

Contribution

It demonstrates the independent persistence of finite-energy pairs and their role in odd-frequency superconductivity, contrasting with zero-energy pair dominance.

Findings

Finite-energy pairs persist independently of finite-momentum pairing.

Odd-frequency correlations are essential for the Meissner effect.

Zero-energy pairs mainly drive even-frequency correlations.

Abstract

Understanding the nature of Cooper pairs is essential to describe the properties of superconductors. The original proposal of Bardeen, Cooper, and Schrieffer (BCS) was based on electrons pairing with same energy and zero center-of-mass momentum. With the advent of new superconductors, different forms of pairing have been discussed. In particular, Cooper pairs with finite center-of-mass momentum have received large interest. Along with such finite-momentum pairs, pairing of electrons at different energies is also central to understanding some superconductors. Here, we investigate the interplay of finite-momentum and finite-energy Cooper pairs considering two different systems: a conventional $s$-wave superconductor under applied magnetic field and a $d$-wave finite-momentum pairing state in the absence of magnetic field relevant to correlated superconductors. Investigating both these systems, we find finite-energy pairs persisting independently of finite-momentum pairing, and that they lead to odd-frequency superconducting correlations. We contrast this finding by showing that the even-frequency correlations are predominantly driven by zero-energy pairs for most frequencies. We further calculate the Meissner effect and find that odd-frequency correlations are essential for correctly describing the Meissner effect.