Effective Multi-orbital 1D Models of Majorana Nanowires including Electronic Interactions

Semiconductor-nanowires proximity coupled to superconductors are a promising platform for hosting and manipulating Majorana zero energy modes. The occupation of multiple confinement-induced bands and the associated electrostatic effects play a key role in these systems. We propose an efficient method to construct effective multi-orbital 1D models starting from microscopic 3D Hamiltonians, which incorporates the multiband physics as well as electronic interactions at the mean field level. The “orbitals” of the effective model are associated with transverse low-energy modes that are self-consistent solutions of the corresponding infinite wire problem with parameters matching the local conditions. This leads to band- and position-dependent effective parameters, such as effective potentials, spin-orbit coefficients, diagonal and off-diagonal hopping, etc. The electron-electron interactions are efficiently incorporated by finding a Green’s function, either numerically or analytically, and storing the results. Using this approach, we investigate various properties of the nanowire system, including the response to an applied magnetic field and the features induced by wire inhomogeneities.