Weyl nodal-ring semimetallic behavior and topological superconductivity in crystalline forms of Su-Schrieffer-Heeger chains

We consider a three-dimensional model of coupled Su-Schrieffer-Heeger (SSH) chains. The analytically soluble model discussed here reliably reproduces the features of the band structure of crystalline polyacetylene as obtained from density-functional theory. We show that when a certain interchain coupling is sufficiently increased, the system develops a ring of Weyl nodes. We argue that such an increase could be achieved experimentally by intercalation or extreme pressure. With the addition of a simple intraorbital pairing term we find that the system supports an exotic superconducting state with drumhead surface states and annular Majorana states localized on the surface. In addition to suggesting a real material realization of a nodal ring semimetal and possibly topological superconductivity, our results provide a different perspective on the SSH model, demonstrating that a simple extension of this broadly impacting model can once again provide fundamental insights on the topological behavior of condensed matter systems.