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.

Measurement schemes of Majorana zero modes (MZMs) based on quantum dots (QDs) are of current interest as they provide a scalable platform for topological quantum computation. In a coupled qubit-QD setup we calculate the dependence of the charge of the QD and its differential capacitance on experimentally tunable parameters for both 2-MZM and 4-MZM measurements. We quantify the effect of noise on the measurement visibility by considering 1/f noise in detuning, tunneling amplitudes or phase. We find that on- or close-to-resonance measurements are generally preferable and predict, using conservative noise estimates, that noise coupling to the QDs is not a limitation to high-fidelity measurements of topological qubits.

Narrow-gap semiconductors with a large g-factor and low carrier density (such as InAs and InSb) are most commonly used, either as 1D nanowires [3] or 2D electron gases. [4] The first generation of semiconductor-superconductor hybrids was made using Nb [5] and NbTiN [6] as the superconductor. While these materials offer a large superconducting gap and resilience to high magnetic fields, the hybrids suffered from a finite in-gap conductance (often described as "soft-gap"). In addition, Nb-based hybrids have not been shown to host parity-conserving transport-a key ingredient for the development of topological qubits. [7] These drawbacks remained even after substantial improvements of the fabrication, such as epitaxial growth of the superconductor. [8] In the meantime, aluminum has emerged as the material of choice. Thin shells made of this metal combined with an oxide-free interface result in clean electronic transport. [9,10] This includes suppressed sub-gap tunneling conductance (hard induced gap) and parity-conserving transport, [11] which enables the search for topological superconductivity. For a topological phase to emerge, the minimal condition states that the Zeeman energy V g B Z B