Signatures of topological superconductivity in quantum spin Hall/superconductor junctions

Interfacing s-wave superconductors with quantum spin Hall systems provides a highly favorable route to topological superconductivity and Majorana zero-modes. Indeed, once a proximity effect is successfully induced, topological superconductivity emerges very naturally -- tuning of the chemical potential in the quantum spin Hall system is unnecessary, and moreover disorder effects are greatly suppressed since time-reversal symmetry breaking is not required. The ability to implement such systems raises fundamental questions; for instance, how can one definitively expose the topological superconducting phase experimentally? We provide a possible answer by studying long Josephson junctions in quantum spin Hall systems. In particular, we predict fingerprints of topological superconductivity related to the ``fractional Josephson effect'' that, remarkably, survive even in the presence of parity relaxation processes.