  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 inter-chain 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 intra-orbital 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 novel real material realization of a nodal ring semimetal and
possibly topological superconductivity, our results provide a new 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.
