Born approximation study of the strong disorder in magnetized surface states of a topological insulator

In this study we investigate the effect of random point disorder on surface states a topological insulator with out-of-plane magnetization. We consider within high order Born approximation. The series converges to one branch self-consistent approximation (SCBA) solution at low disorder. As strength increases, another SCBA finite density magnetization induced gap. Further increase leads divergence series, showing limits applicability find that convergence properties are closely related logistic map, which is known as prototypical model chaos. also calculate longitudinal and Hall conductivities Kubo formulas zero temperature vertex corrections for velocity operator. Vertex important describing transport in strong regime. case disorder, conductivity weakly dependent strength, while decreases increasing