Topology-Inspired Interfaces in Non-Local Mass-Spring Lattices

Abstract

Non-local couplings offer a means of engineering the dynamics and topology of discrete lattices beyond the constraints of nearest-neighbour (NN) interactions. Here, we extend the mass-spring Su-Schrieffer-Heeger (SSH) model to incorporate beyond-nearest-neighbour (BNN) connections that preserve the chiral symmetry of the diatomic unit cell, investigating how their range and strength shape the bulk response. We show that the accessible winding numbers are bounded by the lattice connectivity, while the spring stiffnesses select the specific topological phase. We further investigate the challenges posed by non-local interfaces, where the extended connectivity inherently introduces local boundary perturbations. The dynamic freedom afforded by BNN couplings is exploited by examining interfaces between dynamically and topologically dissimilar bulk media, revealing a band-gap-induced asymmetry in the localisation of interface states. We show that the interfacial configuration provides a means of controlling the existence and character of localised interface modes, with changes to the interface enabling the tuning of mode frequencies, localisation and hybridisation with the bulk bands.