Interaction effects in superconductor/quantum spin Hall devices: Universal transport signatures and fractional Coulomb blockade

Interfacing s-wave superconductors and quantum spin Hall edges produces time-reversal-invariant topological superconductivity of a type that cannot arise in strictly one-dimensional systems. With the aim of establishing sharp fingerprints of this phase, we use renormalization-group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as leads. We determine scaling forms for the conductance through a grounded superconductor and show that the results depend sensitively on the interaction strength in the leads, the size of the superconducting region, and the presence or absence of time-reversal-breaking perturbations. We also study transport across a floating superconducting island isolated by magnetic barriers. Here, we predict e-periodic Coulomb-blockade peaks, as recently observed in nanowire devices [S. M. Albrecht et al., Nature (London) 531, 206 (2016)], with the added feature that the island can support fractional charge tunable via the relative orientation of the barrier magnetizations. As an interesting corollary, when the magnetic barriers arise from strong interactions at the edge that spontaneously break time-reversal symmetry, the Coulomb-blockade periodicity changes from e to e/2. These findings suggest several future experiments that probe unique characteristics of topological superconductivity at the quantum spin Hall edge.