Topological superconductivity in nanowires proximate to a diffusive superconductor-magnetic-insulator bilayer

We study semiconductor nanowires coupled to a bilayer of a disordered superconductor and a magnetic insulator, motivated by recent experiments reporting possible Majorana-zero-mode signatures in related architectures. Specifically, we pursue a quasiclassical Usadel equation approach that treats superconductivity in the bilayer self-consistently in the presence of spin-orbit scattering, magnetic-impurity scattering, and Zeeman splitting induced by both the magnetic insulator and a supplemental applied field. Within this framework we explore prospects for engineering topological superconductivity in a nanowire proximate to the bilayer. We find that a magnetic-insulator-induced Zeeman splitting, mediated through the superconductor alone, cannot induce a topological phase since the destruction of superconductivity (i.e., Clogston limit) preempts the required regime in which the nanowire's Zeeman energy exceeds the induced pairing strength. However, this Zeeman splitting does reduce the critical applied field needed to access the topological phase transition, with fields antiparallel to the magnetization of the magnetic insulator having an optimal effect. Finally, we show that magnetic-impurity scattering degrades the topological phase, and spin-orbit scattering, if present in the superconductor, pushes the Clogston limit to higher fields yet simultaneously increases the critical applied field strength.