Restoration of the magnetic hc/e-periodicity in unconventional superconductors

TL;DR

This paper investigates how unconventional superconductors exhibit a restored hc/e-periodicity in magnetic flux due to energy differences between vortex states, which could be observed in nanoscale materials like underdoped YBCO.

Contribution

It demonstrates that the energy difference between hc/2e and hc/e vortices in unconventional superconductors removes the usual degeneracy, restoring the hc/e periodicity.

Findings

Energy difference between vortex states is finite and inversely proportional to ring radius.

Degeneracy between odd and even vortices is removed in unconventional superconductors.

Observable hc/e periodicity in nanosized unconventional superconductors with low phase stiffness.

Abstract

We consider the energy of the filled quasiparticle's Fermi sea of a macroscopic superconducting ring threaded by an hc/2e-vortex, when the material of the ring is of an unconventional pairing symmetry. The energy relative to the one for the hc/e-vortex configuration is finite, positive, and inversely proportional to ring's inner radius. We argue that the existence of this energy in unconventional superconductors removes the commonly assumed degeneracy between the odd and the even vortices, with the loss of the concomitant hc/2e periodicity in external magnetic field as a consequence. This macroscopic quantum effect should be observable in nanosized unconventional superconductors with a small phase stiffness, such as deeply underdoped YBCO with Tc < 5K.