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.