Influence of magnetic disorders on quantum anomalous Hall effect in magnetic topological insulator films beyond the two-dimensional limit

Quantum anomalous Hall effect (QAHE) has been experimentally realized in magnetic topological insulator (MTI) thin films fabricated onmagnetically doped (Bi, Sb)₂Te₃. In anMTI thin filmwith the magnetic easy axis along the normal direction (z-direction), orientations of magnetic dopants are randomly distributed around the magnetic easy axis, acting as magnetic disorders. With the aid of the non-equilibrium Green's function and Landauer-Büttiker formalism, we numerically study the influence of magnetic disorders onQAHEin an MTI thin film modeled by a three-dimensional tightbinding Hamiltonian. It is found that, due to the existence of gapless side surface states,QAHEis protected even in the presence of magnetic disorders as long as the z-component of magnetic moment of all magnetic dopants are positive. More importantly, such magnetic disorders also suppress the dissipation of the chiral edge states and enhance the quality ofQAHEin MTI films. In addition, the effect of magnetic disorders depends very much on the film thickness, and the optimal influence is achieved at certain thickness. These findings are new features forQAHEin three-dimensional systems, not present in two-dimensional systems.