A New Interpretation of Flux Quantization

TL;DR

This paper proposes a new interpretation of flux quantization in superconductors, emphasizing the role of flux-dependent pairing interactions rather than kinetic energy minima, and explains the origin of Little-Parks oscillations.

Contribution

It introduces a novel perspective that flux quantization arises from flux-dependent pairing interactions, challenging the traditional kinetic energy-based explanation.

Findings

Kinetic energies do not produce flux-dependent free energy oscillations.

Flux dependence of pairing interaction explains flux quantization.

Degenerate-state pairing leads to Little-Parks oscillations.

Abstract

We study the effect of Aharonov-Bohm flux on the superconducting state in metallic cylinders. Although Byers and Yang attributed flux quantization to the flux-dependent minimum of kinetic energies of the Cooper pairs, it is shown that kinetic energies do not produce any discernible oscillations in the free energy of the superconducting state (relative to that of normal state) as a function of the flux. This result is indeed anticipated by the observation of persistent current in normal metal rings at low temperature. Instead, we have found that pairing interaction depends on the flux, leading to flux quantization. When the flux $(\Phi$) is given by $\Phi=n\times hc/2e$ (with integer n), the pairing interaction and the free energy become unchanged (even n) or almost unchanged (odd n), due to degenerate-state pairing resulting from the energy level crossing. As a result, flux quantization and Little-Parks oscillations follow.