Topological superconductivity in semiconductor-superconductor-magnetic insulator heterostructures.

Hybrid superconductor-semiconductor heterostructures are promising platforms for realizing topological superconductors and exploring Majorana bound states physics. Motivated by recent experimental progress, we theoretically study how the introduction of magnetic insulators offers an alternative to external magnetic fields for reaching the topological regime. We consider different setups: (1) the magnetic insulator induces an exchange field in the superconductor, which leads to a splitting in the semiconductor by proximity effect, and (2) the magnetic insulator acts as a spin-filter tunneling barrier between the superconductor and the semiconductor. We show that the spin splitting in the superconductor alone cannot induce a topological transition in the semiconductor. To overcome this limitation, we propose to use a spin-filter barrier which enhances the magnetic exchange and provides a mechanism for a topological phase transition. Moreover, the spin-dependent tunneling introduces a strong dependence on band alignment which can be crucial in quantum-confined systems. This mechanism opens up a route towards networks of topological wires with less constrains on device geometry as compared to using external magnetic fields.