Planar magnetic texture on the surface of a topological insulator

Abstract

We study the planar magnetic textures coupled to a two-dimensional Dirac surface state, where both the magnetic texture and surface state form in the magnetic topological insulator surface layer. It is shown that the radial vortex with winding number $w=\ifmmode\pm\else\textpm\fi{}1$ leads to the confinement of Dirac states, where a mapping to the Schr\"odinger equation of a two-dimensional hydrogen atom is found. The fully spin-polarized zero-energy bound state forms a flat band that resembles the zeroth Landau level of Dirac electrons in a uniform out-of-plane magnetic field. Remarkably, the number of the zero-energy state is topologically robust. Interestingly, when such a system is proximity coupled to an $s$-wave superconductor, the existence of Majorana zero modes at the Abrikosov vortex depends only on the relative value of the magnetic exchange coupling and the pairing strength. We conclude with a brief discussion on the physical realization with such magnetic textures.