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

TL;DR

This paper investigates how a disordered superconductor-magnetic insulator bilayer influences topological superconductivity in semiconductor nanowires, revealing limitations due to superconductivity destruction and effects of scattering on topological phase realization.

Contribution

It provides a self-consistent quasiclassical analysis of topological superconductivity in nanowires near a disordered bilayer, highlighting the impact of magnetic and impurity scattering on topological phases.

Findings

Magnetic-insulator-induced Zeeman splitting cannot induce topological phase alone due to superconductivity suppression.

Applying an external field can reduce the critical field needed for topological transition, especially with antiparallel magnetization.

Magnetic impurities degrade the topological phase, while spin-orbit scattering can increase the critical field for phase transition.

Abstract

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.