Dissipation in a topological Josephson junction

Topological features of low dimensional superconductors have caused a lot of excitement recently because of their broad range of applications in quantum information and their potential to reveal novel phases of quantum matter. A potential problem for practical applications is the presence of phase-slips that break phase coherence. Dissipation in non-topological superconductors suppresses phase-slips and can restore long-range order. Here we investigate the role of dissipation in a topological Josephson junction. We show that the combined effects of topology and dissipation keeps phase and anti-phase slips strongly correlated so that the device is superconducting even under conditions where a non-topological device would be resistive. The resistive transition occurs at a critical value of the dissipation which is four times smaller than that expected for a conventional Josephson junction. We propose that this difference could be employed as a robust experimental signature of topological superconductivity.