The time reversal invariant fractional Josephson effect

One of the most basic consequences of topological superconductivity is the fractional Josephson effect, which arises due to the coherent tunneling of single electrons between two superconductors, leading to an ac Josephson effect with half the usual Josephson frequency. In this paper we will review the theoretical and experimental foundations of topological superconductivity and the fractional Josephson effect. We will then describe recent work in which we have clarified the role of time reversal symmetry. We find that time reversal symmetric Josephson junctions are classified by two distinct Z2 topological invariants. One of these characterizes a junction mediated by the edge states of a quantum spin Hall insulator. In that case, we showed that electron interactions stabilize a ‘Z4 fractional Josephson effect’ with one quarter the usual Josephson frequency. For strong interactions this Josephson effect is associated with the tunneling of charge e 2 quasiparticles. For weak tunneling, this theory describes a fourfold ground state degeneracy that is similar to that of coupled ‘fractional’ Majorana modes, but is protected by time reversal symmetry.