Low-energy subgap states and the magnetic flux periodicity in d-wave superconducting rings

TL;DR

This paper analytically investigates low-energy quasiparticle states in d-wave superconducting rings threaded by magnetic flux, revealing broken h/2e periodicity and paramagnetic responses due to Doppler-shifted zero-energy states.

Contribution

It provides an analytical solution for quasiparticle states in d-wave rings and explains the broken h/2e periodicity observed in such systems.

Findings

Zero-energy states cause paramagnetic response at small fluxes.

States exist only for even angular momenta of Cooper pairs.

Broken h/2e periodicity with h/e behavior of supercurrent.

Abstract

Wave functions of low-energy quasiparticle subgap states in d-wave superconducting rings, threaded by Aharonov-Bohm magnetic flux, are found analytically. The respective energies are closest to the midgap position at small magnetic fluxes and deviate from the Fermi surface due to the Doppler shift, produced by the supercurrent. The Doppler-shifted zero-energy states result in a paramagnetic response of the ring at small fluxes. The states exist only for even angular momenta of the center of mass of Cooper pairs, in agreement with recent numerical studies of the problem. This macroscopic quantum effect in d-wave rings results in broken h/2e periodicity, retaining only the h/e periodic behavior of the supercurrent with varying magnetic flux.