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) over bar (y). Our results indicate that surface degeneracies can be generically protected by symmetries such as T (M) over bar (y) , and phonons provide an ideal platform to explore such degeneracies.

Automated summary

Degenerate points/lines in the band structures of crystals have become a staple feature of topological materials, with a relation between bulk topology and surface states. While line degeneracies of bulk excitations have been extensively studied, line degeneracies of surface states are still not well understood. This study shows that surface degeneracies can be protected by symmetries such as time-reversal symmetry and glide mirror symmetry, providing an ideal platform to explore such degeneracies.