Flux Periodicities in Loops of Nodal Superconductors

TL;DR

Supercurrents in nodal superconducting loops can exhibit hc/e flux periodicity due to Doppler shifts affecting quasiparticle occupations, contrasting with the hc/2e periodicity in conventional s-wave superconductors.

Contribution

This paper demonstrates that nodal superconductors can have an hc/e periodic supercurrent component, unlike conventional s-wave superconductors, due to flux-induced quasiparticle effects.

Findings

hc/e periodic component decreases with loop radius

Doppler shift causes flux-dependent quasiparticle occupation

Temperature affects the hc/e component magnitude

Abstract

Supercurrents in superconducting flux threaded loops are expected to oscillate with the magnetic flux with a period of hc/2e. This is indeed true for s-wave superconductors larger than the coherence length xi_0. Here we show that for superconductors with gap nodes, there is no such strict condition for the supercurrent to be hc/2e rather than hc/e periodic. For nodal superconductors, the flux induced Doppler shift of the near nodal states leads to a flux dependent occupation probability of quasi-particles circulating clockwise and counter clockwise around the loop, which leads to an hc/e periodic component of the supercurrent, even at zero temperature. We analyze this phenomenon on a cylinder in an approximative analytic approach and also numerically within the framework of the BCS theory. Specifically for d-wave pairing, we show that the hc/e periodic current component decreases with the inverse radius of the loop and investigate its temperature dependence.