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Degenerate points/lines in the bulk band structures of crystals have become astaple of the growing number of topological materials. The bulk-boundarycorrespondence provides a relation between bulk topology and surface states.While line degeneracies of bulk excitations have been extensivelycharacterized, line degeneracies of surface states are not well understood. Weshow that SnIP, a quasi-one-dimensional van der Waals material with a doublehelix crystal structure, exhibits topological nodal rings/lines in both thebulk phonon modes and their corresponding surface states. Using a combinationof first-principles calculations, symmetry-based indicator theories and Zakphase analysis, we find that two neighbouring bulk nodal rings form doublydegenerate lines in their drumhead-like surface states, which are protected bythe combination of time-reversal and glide mirror symmetries$\mathcal{T}\bar{M}_y$. Our results indicate that surface degeneracies can begenerically protected by symmetries such as $\mathcal{T}\bar{M}_y$, and phononsprovide an ideal platform to explore such degeneracies.

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