A 2D topological insulator has an insulating bulk but conducting edge states whose direction of motion is locked to spin (or, in the quantum Hall case, to the field). With no counter-propagating partner mode, backscattering is forbidden for non-magnetic disorder, so the edge conductance stays quantised at G = e²/h per channel while the bulk states localise.

Here the bulk carrier is a lattice random walk with blocked sites: each hop attempt succeeds with probability 1 − p, so the blocked-hop rate tends to p and the diffusion constant falls roughly as D ≈ D0(1 − p), reaching zero at the site-percolation threshold p ≈ 0.407. The Trivial regime removes the protection: the edge carrier then diffuses like the bulk one.

Simplifications: a classical walk stands in for quantum transport; real edge channels are protected only against disorder that preserves time-reversal symmetry and while the bulk gap stays open; no interactions, finite temperature or spin texture are modelled.