Theory of hysteretic magneto-transport on the surface of a magnetic three-dimensional topological insulator

We study the magneto-conductance of the surface of a magnetic strong three-dimensional topological insulator (MTI)\footnote{Cui-Zu Chang {\it et al}. Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator. {\it Science} \textbf{340}, 167-170 (2013)}{$^{,}$}\footnote{W. Wang {\it et al}. Visualizing ferromagnetic domain behavior of magnetic topological insulator thin films. {\it NPJ Quantum Materials} \textbf{1}, 16023 (2016)}. An MTI surface is characterized by a two-dimensional Dirac cone dispersion which is gapped by the local magnetization. While the magnetization causes a gap, magnetic domain walls support one-dimensional chiral states within the bulk and surface gaps. These domain-wall states carry current and therefore influence the system’s magneto-conductance. Our model reproduces a hysteretic feature in magneto-conductance which is seen in experiment\footnote{Y. Nakajima {\it et al}. One-dimensional edge state transport in a topological Kondo insulator. {\it Nature Physics} \textbf{12}, 213-217 (2016)}.