Reflectionless Transport of Surface Dirac Fermions on Topological Insulators with Induced Ferromagnetic Domain Walls

TL;DR

This paper provides an exact analytical study of surface Dirac fermions on topological insulators with magnetic domain walls, revealing reflectionless transport phenomena linked to supersymmetry in the system.

Contribution

It introduces a novel analytical approach to understanding Dirac fermions on topological insulators with magnetic textures, highlighting reflectionless transport due to supersymmetry.

Findings

Oscillations in domain wall resistance as a function of wall width.

Complete absence of reflections at certain domain wall widths.

Reflectionless potentials related to supersymmetry.

Abstract

The properties of surface Dirac Fermions on a 3D topological insulator in proximity to a magnetic insulator with spatially textured magnetization are considered. We present an exact analytical treatment of the spectrum, the bound states and the domain wall resistance for an extended generic domain wall with in-plane and out-of-plane magnetizations. In the latter case, we find oscillations in the domain wall resistance as a function of the wall width and for certain widths a complete absence of reflections for all incoming momenta. The surprising occurrence of oscillations and the reflectionless potentials can be related to a supersymmetry of the surface Dirac Hamiltonian combined with the domain wall profile.