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

Abstract

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 $${{{\mathcal{T}}}}$$ T and glide mirror symmetry $${\bar{M}}_{y}$$ M ¯ y . Our results indicate that surface degeneracies can be generically protected by symmetries such as $${{{\mathcal{T}}}}{\bar{M}}_{y}$$ T M ¯ y , and phonons provide an ideal platform to explore such degeneracies.

Topology and Symmetry in Quantum Materials

“…Effects of local surface symmetries and atomic and magnetic structures on dispersions and properties of nontrivial states deserve greater attention in topological research. [85,134,135,[143][144][145] Even though, the existence of topological surface states is guaranteed by the nontrivial geometry of the bulk electronic states, details of their actual energy dispersions and the energymomentum-space windows in which they lie, and even their topological character can be sensitive to the symmetries over the surface. Depending on the nature of the bulk states and the crystalline symmetries involved, topological surface states with a variety of energy dispersions and characters have been predicted.…”

“…Examples include saddle-like states, [85,87] helicoid states, [143] Seifert states, [144] and linked-node states. [134,135,145] Notably, crystalline surfaces that lack rotational symmetry C n;n>2 support saddle points in their dispersions, [85] which would generate van Hove singularities (VHSs) with diverging (logarithmic or higher-order) densities of states (Figure 3(c)). These VHSs may amplify electron correlation effects and drive quantum instabilities in the topological matrix involving the charge, lattice, and spin degrees of freedom.…”

Inorganic SnIP-type double helices: promising candidates for high-efficiency photovoltaic cells

“…20 Recent studies revealed that SnIP also has special topological properties which can exhibit topological nodal rings/lines in both the bulk phonon modes and their corresponding surface states. 21 In addition, strained SnIP can achieve highly tunable polarization after absorbing water molecules. 22 Besides, SnIP nanorods can be easily exfoliated due to the weak vdW interactions, and isolated one-dimensional (1D) double-helix strands have been obtained in SnIP@C 3 N 4 (F,Cl) heterostructure systems or in carbon nanotubes.…”

Complex nodal structure phonons formed by open and closed nodal lines in CoAsS and Na2CuP solids

“…29 Compared to the large number of studies in the field of twodimensional (2D) and three-dimensional (3D) topological electronic materials, the research concerning 3D topological phononic materials has only been initiated in the past few years. Roughly, the topological phonons in 3D solids can be divided into nodal point phonons, [36][37][38][39][40][41][42][43][44][45] nodal line phonons, [46][47][48][49][50][51][52][53][54][55][56][57][58] and nodal surface phonons, [59][60][61][62] respectively, corresponding to zerodimensional (0D), one-dimensional (1D), and 2D phonon band degeneracies in the 3D Brillouin zone (BZ). Note that the types of nodal line phonons are more diverse than those of nodal points and nodal surface phonons.…”