Engineering topological superconductivity in InAs Josephson junctions*

Josephson junctions can be used to engineer topological superconductivity in semiconductors with strong spin-orbit coupling. Proposals to achieve this include proximitizing the edge of the material or applying a superconducting phase bias across the junction. Using superconducting quantum interference measurements on an InAs junction we demonstrate that in the trivial regime edge state transport gives rise to a SQUID-like pattern. More strikingly, we find that SQUID signal is h/e (not h/2e) periodic. While this is considered a hallmark of the topological regime, we explain how crossed Andreev states in the trivial regime can give rise to the same effect. To avoid complications arising from such trivial edges we also explore the possibility of phase biasing InAs Josephson junctions. This is predicted to significantly bring down the Zeeman field needed for a topological phase transition. We study the response to phase bias and develop tunnel probes to measure the local density of states in the junction.