Reprint of : Flux sensitivity of quantum spin Hall rings

• We analyze the periodicity of persistent currents in quantum spin Hall (QSH) loops.
• One loop is partly covered by a superconductor.
• Time-reversal symmetry and parity conservation can constrain the period.
• A period of twice the quantum of flux is characteristic of QSH insulators.

We analyze 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 Φ0=h/eΦ0=h/e to Φ0/2Φ0/2 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 2Φ0-periodic persistent current in two distinct regimes, where one corresponds to a Josephson junction and the other one to an Aharonov–Bohm setup.