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

TL;DR

This paper demonstrates the existence of topological nodal lines in both bulk and surface phonon modes of the quasi-1D crystal SnIP, revealing symmetry-protected degeneracies in surface states using first-principles and symmetry analysis.

Contribution

It uncovers topological phonon surface states in SnIP and shows they are protected by specific symmetries, expanding understanding of surface degeneracies in topological materials.

Findings

Bulk phonon modes exhibit topological nodal rings and lines.

Surface states form doubly degenerate drumhead-like features.

Surface degeneracies are protected by time-reversal and glide mirror symmetries.

Abstract

Degenerate points/lines in the bulk 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 characterized, 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 and glide mirror symmetries $\mathcal{T}\bar{M}_y$. Our results indicate that surface degeneracies can be generically protected by symmetries such as $\mathcal{T}\bar{M}_y$, and phonons provide an ideal platform to explore such degeneracies.