The effect of boundary disorder on electronic systems is particularly interesting for topological phases with surface and edge states. Using exact diagonalization, it has been demonstrated that the surface states of a three-dimensional (3D) topological insulator survive strong surface disorder, and simply get pushed to a clean part of the bulk. Here we explore a method which analytically eliminates the clean bulk and reduces a $D$-dimensional problem to a Hamiltonian-diagonalization problem within the $(D-1)$-dimensional disordered boundary. This dramatic reduction in complexity allows the analysis of significantly bigger systems than is possible with exact diagonalization. We use our method to analyze a 2D topological spin-Hall insulator with nonmagnetic and magnetic edge impurities, and we calculate the disorder-induced redistribution of probability density (or local density of states) in the insulating bulk, as well as the transport effects of edge impurities. The analysis reveals how the edge recovers from disorder scattering as the disorder strength increases.

• Received 3 May 2015

DOI:https://doi.org/10.1103/PhysRevB.92.075110