Spatial Structure of the Cooper Pair

Abstract

The Cooper pair is generally analyzed in momentum space, but its real-space structure also follows directly from the Bardeen–Cooper–Schrieffer (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 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.