Phononic Weyl points and one-way topologically protected nontrivial phononic surface arc states in noncentrosymmetric WC-type materials

Abstract

By means of first-principles calculations, we have predicted the existence of phononic Weyl points (WPs) along the high-symmetric K($\frac{1}{3},\frac{1}{3},0$)-H($\frac{1}{3},\frac{1}{3},\frac{1}{2}$) line in the Brillouin zone for a series of noncentrosymmetric hexagonal WC-type materials (HfS, HfSe, IrB, MoC, MoN, MoP, NbN, NbS, TaN, TaS, TiO, TiS, WN, ZrS, ZrSe, and ZrTe) and these WPs carry nonzero topological charges. In terms of symmetry analysis, we have further derived two-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ models to describe these WPs. For most WPs a first-order theory is sufficient to reproduce well the phonon spectra around these WPs. However, for some WPs a second-order theory has to be required. Particularly, when the second-order term plays a leading role, a topological charge $\ifmmode\pm\else\textpm\fi{}1\phantom{\rule{0.16em}{0ex}}\mathrm{WP}$ on the K-H line is accompanied by three nearby WPs with the opposite charges ($\ensuremath{\mp}1$) off the K-H line. These four spatially close (in the reciprocal space) WPs have a total topological charge of $\ensuremath{\mp}2$. On the crystal ($10\overline{1}0$) and ($01\overline{1}0$) surfaces, we have observed clear one-way topologically protected nontrivial phononic surface arc states connecting two WPs with opposite chirality. Our results pave the way for future experimental studies of the topological phonons for those WC-type materials.