Phase Controlled Topological Superconductivity and its detection

In this talk, we will discuss practical ways to engineer topological superconductivity using Josephson junction arrays. Here, phase control allows us to access topological states in systems with spin-dependent Fermi velocities. Next, we will demonstrate how geometry can change the long-standing problem of distinguishing topological from trivial superconductivity by a clear qualitative effect. We find that in circular Corbino junctions with broken rotational symmetry, topological superconductors exhibit an even–odd parity structure in the superconducting diode effect, which is hard to replicate in trivial systems. I will also present recent experimental evidence supporting this idea.