Majorana States in 2D Topological Superconductor Hosting Abrikosov Vortices

We study Majorana states near Abrikosov vortices in a 2D topological superconductor in the applied magnetic field B. The Majorana fermions always arise in pairs. In the considered case, the first Majorana fermion localizes in the vortex core while the second, exterior, Majorana fermion localizes at the distance r ae 1/B away from the core. We calculate the hybridization between the vortex-core and the exterior Majorana fermions in the cases of a single vortex, two vortices, and the Abrikosov vortex lattice. We show that the hybridization can be effectively governed by the applied magnetic field if the chemical potential is tuned near the Dirac point. We also show that in the case of the vortex lattice, the hybridization between the vortex-core and external Majorana fermions affects significantly low-energy spectrum giving rise to the gap between two lowest Majorana energy bands.