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

Abstract

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 . For C _2 > C _1 , topological end states occur when C _F exceeds a certain value.

Keywords

• topology
• vibration
• molecule