Fig. 1: Topological phases, their vibrational boundary modes and heavy-boundary mode patterning in phonon Su-Schrieffer-Heeger (SSH) analogue models. | Nature Communications

Fig. 1: Topological phases, their vibrational boundary modes and heavy-boundary mode patterning in phonon Su-Schrieffer-Heeger (SSH) analogue models.

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

Fig. 1

a A topological vibrational boundary mode occurs when a heavy boundary is formed in polymers or lattices of coupled chains, with alternating weak/strong (or soft/stiff) spring constants (denoted by κ), terminating in a stiff spring connected to a heavier atom (M) (a topological SSH phase); as opposed to b. a soft spring termination. These principles can be extended to c, d. a chain adsorbed on a surface (aSSH model), and e, f a double chain (daSSH model). g A heavy-boundary can be employed to pattern a topological mode at a desired point in a polymer chain . The exponentially localised vibrations spanning few atoms (amplitude in g representing the longitudinal eigendisplacements) have properties unique to the global topology of the vibrational space, as opposed to the local chemical environment. Molecular dynamics simulations further explore the properties of the topological boundary modes under excitation and thermal fluctuations.

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