Spatial Structure of the Cooper Pair

TL;DR

This paper explores the real-space structure of Cooper pairs, revealing a layered, spherically symmetric wavefunction that influences the pairing interaction and offers insights into both conventional and exotic superconductors.

Contribution

It provides a detailed real-space analysis of Cooper pairs, showing their layered structure and charge modulation, which enhances understanding of superconducting interactions.

Findings

Cooper pairs have a spherically symmetrical, layered wavefunction.

Charge modulation in the pair induces lattice charge modulation.

The real-space interaction potential aligns with BCS theory.

Abstract

The Cooper pair is generally analyzed in momentum space, but its real-space structure also follows directly from the BCS theory. It is shown here that this leads to a spherically symmetrical quasi-atomic wavefunction, with an identical "onion-like" layered structure for each of the electrons constituting the Cooper pair, with charge layers ~ 0.1 nm and a radius ~ 100 nm for a classic BCS superconductor. This charge modulation induces a corresponding charge modulation in the background ionic lattice, and the attractive interaction between these two opposite charge modulations produces the binding energy of the Cooper pair. This physically-based interaction potential is similar to that in the simple BCS approximation. The implications of this real-space picture for understanding conventional and exotic superconductors are discussed.