Degenerate topological line surface phonons in quasi-1D double helix crystal SnIP

Degenerate points/lines in the band structures of crystals have become a staple of the growing number of topological materials. The bulk-boundary correspondence provides a relation between bulk topology and surface states. While line degeneracies of bulk excitations have been extensively characterised, line degeneracies of surface states are not well understood. We show that SnIP, a quasi-one-dimensional van der Waals material with a double helix crystal structure, exhibits topological nodal rings/lines in both the bulk phonon modes and their corresponding surface states. Using a combination of first-principles calculations, symmetry-based indicator theories and Zak phase analysis, we find that two neighbouring bulk nodal rings form doubly degenerate lines in their drumhead-like surface states, which are protected by the combination of time-reversal symmetry T ? and glide mirror symmetry M_{¯ y}?. Our results indicate that surface degeneracies can be generically protected by symmetries such as T M_{¯ y} ?, and phonons provide an ideal platform to explore such degeneracies.