Magnetic-field induced quantum-size cascades in superconducting nanowires

TL;DR

This paper demonstrates that in superconducting nanowires with diameters below 15 nm, the magnetic-field induced transition occurs as a cascade of jumps in the order parameter due to quantum confinement effects, revealing quantum-size oscillations and resonant enhancements.

Contribution

It introduces a detailed numerical analysis of the superconductor-to-normal transition in nanowires, showing a cascade of jumps caused by subband depairing, a phenomenon not previously characterized.

Findings

Transition occurs as a cascade of jumps for D < 15 nm

Pronounced quantum-size oscillations of the critical magnetic field

Giant resonant enhancements in the critical field

Abstract

In high-quality nanowires, quantum confinement of the transverse electron motion splits the band of single-electron states in a series of subbands. This changes in a qualitative way the scenario of the magnetic-field induced superconductor-to-normal transition. We numerically solve the Bogoliubov-de Gennes equations for a clean metallic cylindrical nanowire at zero temperature in a parallel magnetic field and find that for diameters D < 10-15 nm, this transition occurs as a cascade of subsequent jumps in the order parameter (this is opposed to the smooth second-order phase transition in the mesoscopic regime). Each jump is associated with the depairing of electrons in one of the single-electron subbands. As a set of subbands contribute to the order parameter, the depairing process occurs as a cascade of jumps. We find pronounced quantum-size oscillations of the critical magnetic field with giant resonant enhancements. In addition to these orbital effects, the paramagnetic breakdown of Cooper pairing also contributes but only for smaller diameters, i. e., D < 5 nm.