Figure 3: Phase transition between topological and trivial band insulators.

(a) A domain wall between a topological insulator (ts=tp=tsp, Δy=0, left) and a trivial insulator (ts=tp=tsp=0, right). The circle represents the delocalized fermion shared by two neighbouring rungs as depicted in Fig. 2a, whereas the ellipse represents localized fermion without hopping. The additional charge 1/2 in the middle is the fractional charge carried on the domain wall. (b) The derivative of density fluctuation, −(dδρ2/dΔy). It develops sharp peaks, measurable in experiments, along the line of topological critical points.