Second-Order Topological Superconductivity in π-Junction Rashba Layers

We consider a Josephson junction bilayer consisting of two tunnel-coupled two-dimensional electron gas layers with Rashba spin-orbit interaction, proximitized by a top and bottom s-wave superconductor with phase difference phi close to pi. We show that, in the presence of a finite weak in-plane Zeeman field, the bilayer can be driven into a second order topological superconducting phase, hosting two Majorana comer states (MCSs). If phi = pi, in a rectangular geometry, these zero-energy bound states are located at two opposite corners determined by the direction of the Zeeman field. If the phase difference phi deviates from It by a critical value, one of the two MCSs gets relocated to an adjacent corner. As the phase difference phi increases further, the system becomes trivially gapped. The obtained MCSs are robust against static and magnetic disorder. We propose two setups that could realize such a model: one is based on controlling phi by magnetic flux, the other involves an additional layer of randomly oriented magnetic impurities responsible for the phase shift of pi in the proximity-induced superconducting pairing.