Topological states of the diatomic linear chain: effect of impedance matching to the fixed ends

The diatomic linear chain with nearest-neighbor spring constants C 1 and C 2 has topologically different bulk states for C 1 ≷ C 2. A finite chain of N unit cells and fixed ends (the first and last spring is C 1) exhibits two topological end states within the gap for C 1 > C 2. We investigate the effect of an impedance mismatch by varying the first and last ‘boundary’ spring constant termed C F from its ideal value C 1. C F = 0 represents an open end and does never lead to topological states. C F → ∞ means that also the next site to the boundary is fixed, leading to topological states only for C 1 < C 2 since now the first movable spring is C 2. Within a range of C F around C 1 topological end states are preserved for C 1 > C 2. For C 2 > C 1, topological end states occur when C F exceeds a certain value.