Exponential suppression of the topological gap in self-consistent intrinsic Majorana nanowires

Predictions of topological p-wave superconductivity and Majorana zero modes (MZMs) in hybrid superconductor-semiconductor nanowires have been difficult to realize experimentally. Consequently, researchers are actively exploring alternative platforms for MZMs. In this work, we theoretically study depleted nanowires with intrinsic superconductivity (as opposed to proximity-induced). Using a self-consistent Hartree-Fock-Bogoliubov mean field theory, we compute the topological phase diagram versus Zeeman field and filling for intrinsic wires with attractive interactions. We find that, although intrinsic wires could be less vulnerable than hybrids to topology-adverse effects, such as disorder and metallization, they are hindered by a fundamental limitation of their own. Although a topological p-wave gap is indeed possible, it is far less robust than in hybrid Majorana nanowires. Instead of remaining stable beyond the topological transition, it is found to decay exponentially with Zeema field, greatly reducing the parameter region with an appreciable topological gap.