Two pairing parameters in superconducting grains

TL;DR

This paper reveals that small superconducting grains have two distinct pairing parameters, each associated with different physical properties, unlike the single energy gap in bulk superconductors.

Contribution

The study introduces and characterizes two separate pairing parameters in small superconducting grains, highlighting their different behaviors and size scales.

Findings

Two pairing parameters exist in small grains.

Both parameters converge to the bulk gap at different sizes.

Distinct physical properties are associated with each parameter.

Abstract

Unlike bulk superconductivity, where one energy scale, the energy gap, characterizes pairing correlations, we show that in small superconducting grains there exist two different such quantities. The first characterizes cumulative properties of the grain, such as the condensation energy, and the second single-particle properties. To describe these two energy scales, we define two corresponding pairing parameters, and show that although both reduce to the bulk gap for large grains, this occurs at different size scales.