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

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. We consider three kinds of 2D superconducting models: (a) a standard type II superconductor in the mixed state with low density of vortex lines, (b) a superconductor with strong spin-orbit coupling locking the spin parallel to the momentum and (c) a superconductor with strong spin-orbit coupling locking the spin perpendicular to the momentum. The 2D superconducting states are induced via proximity effect between an $s$-wave superconductor and the surface states of a strong topological insulator. In case (a) the energy gap 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 (${\Delta }_{\infty }^2/E_F$) 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.

arXiv comment14 pages, 0 figures

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