Hybrid versus intrinsic Majorana nanowires, a self-consistent Hartree-Fock-Bogoliubov analysis

In this work, we employ a Hartree-Fock-Bogoliubov mean-field theoretical framework to compare the topological properties of extrinsic and instrinsic Majorana nanowires. The class of hybrid Majorana devices explored experimentally to date are of the extrinsic type, where the p-wave superconductivity is induced by proximity to a conventional s-wave superconductor. It has been proposed that a topological superconductor with instrinsic superconductivity (e.g. a low-density Majorana nanowire with attractive electron-electron interations) should have practical advantages, as it would avoid metallization and interface disorder issues that plague current experiments. However, and contrary to such expectation, we demonstrate that the topological minigap in the intrinsic case is exponentially suppressed by Zeeman fields, quickly delocalizing Majorana zero modes. Our results reveal the crucial stabilising role of the external superconductor when engineering p-wave superconductivity through the Oreg-Lutchyn approach.