Topological boundaries and bulk wavefunctions in the Su-Schreiffer-Heeger model

Working in the context of the Su-Schreiffer-Heeger model, the effect of topological boundaries on the structure and properties of bulk position-space wavefunctions is studied for a particle undergoing a quantum walk in a one-dimensional lattice. In particular, we consider what happens when the wavefunction reaches a boundary at which the Hamiltonian changes suddenly from one topological phase to another and construct an exact solution for the wavefunction on both sides of the boundary. The reflection and transmission coefficients at the boundary are calculated as a function of the system's hopping parameters, and it is shown that for some parameter ranges the transmission coefficient can be made very small. Therefore, it is possible to arrange a high degree of bulk wavefunction localization within each topological region, a fact that has information processing applications. This 'topologically-assisted' suppression of transitions, although not of direct topological origin itself, exists because of the presence of an abrupt change in the properties of the Hamiltonian at the topological boundary. We give a quantitative examination of the reflection and transmission coefficients of incident waves at the boundary between regions of different winding number.