  We investigate the effect of spatially correlated disorder on two-dimensional
topological insulators and on the quantum spin Hall effect which the helical
edge states in these systems give rise to. Our work expands the scope of
previous investigations which found that uncorrelated disorder can induce a
nontrivial phase called the topological Anderson insulator (TAI). In extension
of these studies, we find that spatial correlations in the disorder can
entirely suppress the emergence of the TAI phase. We show that this phenomenon
is associated with a quantum percolation transition and quantify it by
generalizing an existing effective medium theory to the case of correlated
disorder potentials. The predictions of this theory are in good agreement with
our numerics and may be crucial for future experiments.
