Bound fermion states in pinned vortices in the surface states of a superconducting topological insulator

Abstract

By analytically solving the Bogoliubov–de Gennes equations we study the fermion bound states at the center of the core of a vortex in a two-dimensional superconductor. The superconducting states are induced via proximity effect between an s-wave superconductor and the surface states of a strong topological insulator. The strong spin–orbit coupling locks the spin perpendicular to the momentum (Rashba interaction). A zero-energy Majorana state arises together with an equally spaced () sequence of fermion excitations. The spin–momentum locking is key to the formation of the Majorana state. We present analytical expressions for the energy spectrum and the wave functions of the bound states. The wave functions fall off exponentially with the distance ρ from the core of the vortex as . An analytic expression for the local density of states (LDOS) for the bound states is obtained. The particle–hole symmetry is broken in the LDOS as a consequence of the spin–orbit coupling. The spin-polarization of the bound states is discussed. We also obtain the energy shifts of the bound states in a small magnetic field. A unitary transformation relating the model with Rashba interaction to the Dirac Hamiltonian is presented.