Vortex states in nanoscale superconducting squares: the influence of quantum confinement

TL;DR

This paper uses Bogoliubov-de Gennes theory to explore how quantum confinement in nanoscale superconducting squares influences vortex states, revealing unconventional configurations and stability features not predicted by classical Ginzburg-Landau theory.

Contribution

It demonstrates the impact of quantum size effects on vortex configurations, uncovering novel vortex states and stability properties in nanoscale superconductors.

Findings

Quantum confinement induces unconventional vortex states.

Vortex-antivortex pairs remain stable across all temperatures.

Giant vortices and vortex molecules are favored by inhomogeneous order parameters.

Abstract

Bogoliubov-de Gennes theory is used to investigate the effect of the size of a superconducting square on the vortex states in the quantum confinement regime. When the superconducting coherence length is comparable to the Fermi wavelength, the shape resonances of the superconducting order parameter have strong influence on the vortex configuration. Several unconventional vortex states, including asymmetric ones, giant multi-vortex combinations, and states comprising giant antivortex, were found as ground states and their stability was found to be very sensitive on the value of $k_F\xi_0$, the size of the sample $W$, and the magnetic flux $\Phi$. By increasing the temperature and/or enlarging the size of the sample, quantum confinement is suppressed and the conventional mesoscopic vortex states as predicted by the Ginzburg-Laudau (GL) theory are recovered. However, contrary to the GL results we found that the states containing symmetry-induced vortex-antivortex pairs are stable over the whole temperature range. It turns out that the inhomogeneous order parameter induced by quantum confinement favors vortex-antivortex molecules, as well as giant vortices with a rich structure in the vortex core - unattainable in the GL domain.