Discrete transverse superconducting modes in nano-cylinders

TL;DR

This paper investigates how quantum confinement in cylindrical nanowires affects superconductivity, revealing discrete transverse modes, spatial variations, and gapless states under magnetic fields, especially at small diameters.

Contribution

It provides a detailed analysis of superconducting properties in nanowires considering quantum confinement effects, extending understanding beyond Ginzburg-Landau theory.

Findings

Discrete transverse modes cause spatial variations in the order parameter.

Gapless superconductivity occurs above a certain magnetic field.

Small diameters lead to increased order parameter magnitude and complex magnetic response.

Abstract

Spatial variation in the superconducting order parameter becomes significant when the system is confined at dimensions well below the typical superconducting coherence length. Motivated by recent experimental success in growing single-crystal metallic nanorods, we study quantum confinement effects on superconductivity in a cylindrical nanowire in the clean limit. For large diameters, where the transverse level spacing is smaller than superconducting order parameter, the usual approximations of Ginzburg-Landau theory are recovered. However, under external magnetic field the order parameter develops a spatial variation much stronger than that predicted by Ginzburg-Landau theory, and gapless superconductivity is obtained above a certain field strength. At small diameters, the discrete nature of the transverse modes produces significant spatial variations in the order parameter with increased average magnitude and multiple shoulders in the magnetic response.