Vortex states and Majorana fermions in spin-orbit coupled semiconductor-superconductor hybrid structures

We study the energy spectrum of a vortex core in a two-dimensional semiconductor with Rashba spin-orbit interaction and proximity coupled to a conventional superconductor and a ferromagnetic insulator. We perform self-consistent calculations using the microscopic tight-binding Bogoliubov-de Gennes method on a lattice and confirm the existence of Majorana fermions in the nontrivial topological phase. We also find two different topologically trivial bulk superconducting phases, only differing in the type of vortex core structure they support and separated by a zero-energy excitation. Furthermore, we find an asymmetry in the energy spectrum with respect to both Zeeman splitting and vortex rotation direction and explain its physical origin.