Multiband Superconductors: Two Characteristic Lengths for Each Contributing Condensate

TL;DR

This paper investigates the spatial characteristics of condensates in multiband superconductors, revealing that the characteristic lengths of the gap function and Cooper-pair wave function differ at lower temperatures, unlike in single-band superconductors.

Contribution

It clarifies the relationship between gap and wave-function characteristic lengths in two-band superconductors across different temperatures, highlighting their divergence at lower temperatures.

Findings

Lengths coincide near the critical temperature.

Lengths significantly deviate at lower temperatures.

Implications for defining the spatial scale of condensates.

Abstract

Traditionally, the characteristic length of a superconducting condensate is associated with the spatial distribution of the corresponding gap function. However, the superconducting condensate is the quantum condensate of Cooper pairs and thus, the broader readership is more familiar with the concept of the Cooper-pair wave function. For conventional single-band superconductors, the gap function coincides with the center-of-mass wave function of a Cooper pair up to the coupling constant, and the corresponding gap- and wave-function characteristic lengths are the same. Surprisingly, we find that in two-band superconductors, these lengths are the same only near the critical temperature. At lower temperatures they can significantly deviate from each other, and the question arises as to which of these lengths should be given the preference when specifying the spatial scale of the band-dependent condensate in multiband superconducting materials.