Supercurrent vortices and Majorana zero modes induced by an in-plane Zeeman field on the surface of a three-dimensional topological insulator

Abstract

A nonuniform in-plane Zeeman field can induce spontaneous supercurrents of spin-orbit-coupled electrons in superconducting two-dimensional systems and thin films. In this work it is shown that current vortices can be created at the ends of a long homogeneously magnetized strip of a ferromagnetic insulator, which is deposited on the surface of a three-dimensional topological insulator. The $s$-wave superconductivity on its surface is assumed to have an intrinsic origin, or to be induced by the proximity effect. It is shown that vortices with the odd vorticity can localize Majorana zero modes. The latter may also be induced by sufficiently narrow domain walls inside the strip, which opens a way for manipulating these modes by moving the walls. It is shown that the vorticity can be tuned by varying the magnetization and width of the strip. A stability of the strip magnetization with respect to the Berezinsky-Kosterlitz-Thouless transition has been analyzed.