Period Doubling in Small Multiply Connected Superconductors

TL;DR

This paper investigates how the magnetic response period of small superconductors approaches twice the bulk value as their size nears the coherence length, revealing a transition offset influenced by Cooper pair energy dependence.

Contribution

It demonstrates the period doubling effect in small superconductors and provides explicit calculations for s-wave cylinders, suggesting potential enhancement in nodal superconductors.

Findings

Minimal response period approaches hc/e for small superconductors.

Transition offset between current states is exponentially small for large radius.

The results may extend to superfluids responding to rotation.

Abstract

It is shown that for superconductors with circumference $2\pi R$ approaching BCS coherence length $\xi_0$ minimal period of the response of all thermodynamic quantities to external magnetic field is set by $hc/e$ i.e. twice the corresponding value for the bulk case. This is explained by the dependence of internal energy of Cooper pairs on their center of mass motion which leads, in particular, to a transition offset between different current-carrying states. Explicit calculation of the transition offset is done for the case of s-wave superconducting cylinder with $R \gg \xi_0$ and turns out to be exponentially small. A possible enhancement of the effect for nodal superconductors is suggested. Similar conclusions should also apply to the response of charged or neutral superfluids to rotation.