Flux sensitivity of quantum spin Hall rings

TL;DR

This paper investigates how the flux periodicity of persistent currents in quantum spin Hall rings is affected by superconducting coverage, revealing regimes with different flux periodicities influenced by symmetry and topology.

Contribution

It provides a detailed analysis of flux periodicity in quantum spin Hall rings with superconducting segments, highlighting the effects of symmetry and topology on persistent current behavior.

Findings

Periodic spectrum periodicity shifts from Φ₀ to Φ₀/2 with superconductor length.

Time reversal symmetry and parity influence the persistent current period.

Identifies regimes with 2Φ₀ periodicity linked to Josephson and Aharonov-Bohm effects.

Abstract

We analyse the periodicity of persistent currents in quantum spin Hall loops, partly covered with an $s$-wave superconductor, in the presence of a flux tube. Much like in normal (non-helical) metals, the periodicity of the single-particle spectrum goes from $\Phi_0 = h/e$ to $\Phi_0/2$ as the length of the superconductor is increased past the coherence length of the superconductor. We further analyze the periodicity of the persistent current, which is a many-body effect. Interestingly, time reversal symmetry and parity conservation can significantly change the period. We find a $2\Phi_0$-periodic persistent current in two distinct regimes, where one corresponds to a Josephson junction and the other one to an Aharonov-Bohm setup.