Theory of spin-selective Andreev reflection in the vortex core of a topological superconductor

Abstract

Majorana zero modes (MZMs) have been predicted to exist in a topological insulator (TI)/superconductor (SC) heterostructure. A recent spin-polarized scanning tunneling microscope (STM) experiment [Sun et al., Phys. Rev. Lett. 116, 257003 (2016)] has observed a spin-polarization dependence of the zero bias differential tunneling conductance at the center of a vortex core. Here, we consider a helical electron system described by a Rashba spin-orbit coupling Hamiltonian on a spherical surface with an s-wave superconducting pairing due to proximity effect. We examine the in-gap excitations of a pair of vortices with one at the north pole and the other at the south pole. While the MZM is not a spin eigenstate, the spin wave function of the MZM at the center of the vortex core, r=0, is parallel to the magnetic field, and the local Andreev reflection of the MZM is spin selective, namely, occurs only when the STM tip has the spin polarization parallel to the magnetic field, similar to the case in a one-dimensional nanowire [He et al., Phys. Rev. Lett. 112, 037001 (2014)]. The total local differential tunneling conductance consists of the normal term proportional to the local density of states and an additional term arising from the Andreev reflection. We also discuss the finite size effect, for which the MZM at the north pole is hybridized with the MZM at the south pole. We apply our theory to examine the recently reported spin-polarized STM experiments and show good agreement with the experiments.

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