Giant Variations of Cooper-Pair Size in Nanoscale Superconductors

TL;DR

This paper demonstrates that quantum-size effects in nanoscale superconductors cause dramatic, size-dependent reductions in Cooper-pair size, resembling BCS-BEC crossover phenomena but driven by quantum confinement rather than interaction strength.

Contribution

It reveals that quantum confinement in nanowires can significantly reduce the Cooper-pair size, a phenomenon similar to BCS-BEC crossover but caused by transverse quantization.

Findings

Cooper-pair size drops by two to three orders of magnitude in nanowires.

Size-dependent coherence length reaches values typical of high-$T_c$ superconductors.

Quantum confinement effects mimic BCS-BEC crossover phenomena.

Abstract

The Cooper-pair size (i.e., the BCS coherence length) in low-dimensional superconductors is dramatically modified by quantum-size effects. In particular, for nanowires made of conventional superconducting materials, we show that the coherence length exhibits size-dependent drops by two-three orders of magnitude and reaches values found in high-$T_c$ superconductors. This phenomenon is surprisingly similar to the well-known BCS-BEC crossover but with one important exception: it is driven by the transverse quantization of the electron spectrum rather than by the strength of the fermion-fermion interaction. Similar results can be expected for other systems with the same structure of the single-particle spectrum, e.g, for superfluid Fermi gases confined in a quantum-wire or quantum-well geometry.