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By analytically solving the Bogoliubov-de Gennes equations we study thefermion bound states at the center of the core of a vortex in a two-dimensionalsuperconductor. We consider three kinds of 2D superconducting models: (a) astandard type II superconductor in the mixed state with low density of vortexlines, (b) a superconductor with strong spin-orbit coupling locking the spinparallel to the momentum and (c) a superconductor with strong spin-orbitcoupling locking the spin perpendicular to the momentum. The 2D superconductingstates are induced via proximity effect between an $s$-wave superconductor andthe surface states of a strong topological insulator. In case (a) the energygap for the excitations is of order $\Delta_{\infty}^2/(2E_F)$, while for cases(b) and (c) a zero-energy Majorana state arises together with an equally spaced($\Delta^2_{\infty}/E_F$) sequence of fermion excitations. The spin-momentumlocking is key to the formation of the Majorana state. We present analyticalexpressions for the energy spectrum and the wave functions.

Bound fermion states in pinned vortices in the surface states of a superconducting topological insulator: The Majorana bound state