Planar magnetic texture on the surface of a topological insulator

TL;DR

This paper investigates magnetic textures on topological insulator surfaces, revealing how radial vortices confine Dirac states and can host Majorana zero modes when coupled to superconductors, with implications for quantum computing.

Contribution

It introduces a novel analysis of radial magnetic vortices on topological insulators and their ability to confine Dirac states and support Majorana modes under superconducting proximity.

Findings

Radial vortices confine Dirac states similar to a 2D hydrogen atom.

Zero energy bound states resemble Landau levels of Dirac electrons.

Majorana zero modes depend on exchange coupling and pairing strength.

Abstract

We study the planar magnetic textures in an insulating magnetic film coupled to the Dirac surface state of a topological insulator. It is shown that the radial vortex with winding number $w=\pm1$ leads to the confinement of Dirac states, where an exact mapping to the Schr\"{o}dinger equation of a two-dimensional hydrogen atom is found. The fully spin polarized zero energy bound state resembles the zeroth Landau level of Dirac electrons in a uniform out-of-plane magnetic field. Interestingly, when the hybrid system is proximity coupled to an $s$-wave superconductor, the existence of Majorana zero modes at 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.