Heavy-boundary mode patterning and dynamics of topological phonons in polymer chains and supramolecular lattices on surfaces.

In topological band theory, phonon boundary modes consequence of a topologically non-trivial  band structure feature desirable properties for atomically-precise technologies, such as robustness against defects, waveguiding, and one-way transport. These topological phonon boundary modes remain to be studied both theoretically and experimentally in synthetic materials, such as polymers and supramolecular assemblies at the atomistic level under thermal fluctuations. Here we show by means of molecular simulations, that surface-confined Su-Schrieffer-Heeger (SSH) phonon analogue models express robust topological phonon boundary modes at heavy boundaries and under thermal fluctuations. The resulting bulk-heavy boundary correspondence enables patterning of boundary modes in polymer chains and weakly-interacting supramolecular lattices. Moreover, we show that upon excitation of a single molecule, propagation along heavy-boundary modes differs from free boundary modes. Our work is an entry to topological vibrations in supramolecular systems, and may find applications in the patterning of phonon circuits and realization of Hall effect phonon analogues at the molecular scale.