Renormalization of competing interactions and superconductivity on small scales

TL;DR

This paper investigates how the competition between Coulomb and Fröhlich interactions affects the magnetic response and superconductivity in nanoscale systems, revealing size-dependent transitions from diamagnetic to paramagnetic behavior.

Contribution

It provides a detailed analysis of the renormalization effects on interactions and their impact on magnetic susceptibility in small superconducting systems.

Findings

Magnetic susceptibility can switch from diamagnetic to paramagnetic as system size decreases.

Renormalized interactions determine the nature of the magnetic response.

Fluctuations of the superconducting order parameter contribute significantly above the bulk transition temperature.

Abstract

The interaction-induced orbital magnetic response of a nanoscale ring is evaluated for a diffusive system which is a superconductor in the bulk. The interplay of the renormalized Coulomb and Fr\"{o}hlich interactions is crucial. The magnetic susceptibility which results from the fluctuations of the uniform superconducting order parameter is diamagnetic (paramagnetic) when the renormalized combined interaction is attractive (repulsive). Above the transition temperature of the bulk the total magnetic susceptibility has contributions from many wave-vector- and (Matsubara) frequency-dependent order parameter fluctuations. Each of these contributions results from a different renormalization of the relevant coupling energy, when one integrates out the fermionic degrees of freedom. The total diamagnetic response of the large superconductor may become paramagnetic when the system's size decreases.