  The effect of surface 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 3D
topological insulator survive strong surface disorder, and simply get pushed to
a clean part of the bulk. Here we explore a new method which analytically
eliminates the clean bulk, and reduces a $D$-dimensional problem to a
Hamiltonian-diagonalization problem within the $(D-1)$-dimensional disordered
surface. 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
non-magnetic and magnetic edge impurities, and we calculate the probability
density (or local density of states) of the zero-energy eigenstates as a
function of edge-parallel momentum and layer index. Our analysis reveals that
the system size needed to reach behavior in the thermodynamic limit increases
with disorder. We also compute the edge conductance as a function of disorder
strength, and chart a lower bound for the length scale marking the crossover to
the thermodynamic limit.
