Fig. 2: The creation of topological interface states via counter-propagating wave mode conversion is analytically described using a spring-mass model.
a Chain 1 (blue) models the propagation of antisymmetric A0 waves while chain 2 (red) models the propagation of symmetric S0 waves. b When the chains are disconnected, no coupling occurs and band crossing is observed. c The introduction of elastic connections couples the two modes, opening a complete bandgap (d) where distinct Zak phases guarantee the existence of non-trivial topological states. e The introduction of an interface between the initial chain, having stiffness k1-k2, k3-k4 and its mirrored counterpart, i.e. k2-k1, k4-k3, enables two topological states, here demonstrated from a supercell dispersion analysis (f). The color map of the dispersion curves shows the relative polarization of the waves, with blue points corresponding to vertical (out-of-plane) polarization, while red refers to horizontal (in-plane) polarization, i.e. A0 and S0 waves.
