First-principles prediction of ideal type-II Weyl phonons in wurtzite ZnSe

Weyl materials, exhibiting topologically nontrivial touching points in band dispersion, are fascinating subjects of research, which have been extensively studied in electron-related systems. In this paper, by employing first-principles calculations of topological phonons in wurtzite-structured phases of $MX$ chalcogenides (where $M=\mathrm{Zn}$ and Cd and $X=\mathrm{O}$, S, Se, and Te), we demonstrate the existence of ideal type-II Weyl phonons in wurtzite ZnSe, a well-known II-VI semiconductor. There are in the ${\mathbf{q}}_z=0.0$ plane six pairs of Weyl points stemming from the inversion between the two optical branches. The nontrivial phonon surface states and surface arcs projected on the semifinite (0001) surfaces are investigated. Phonon surface arcs connecting each pair of Weyl points with opposite chirality, guaranteed to be $0.55{\AA }^{-1}$ and very long, are readily observable in experiment. The opposite chirality of Weyl points with quantized Berry curvature produces the Weyl phonon Hall effect. Our results propose a potential platform for future experimental study of type-II Weyl phonons in realistic materials.

Figure 1

(a) Crystal structure of wurtzite $MX$ (where $M=\mathrm{Zn}$ and Cd and $X=\mathrm{O}$, S, Se, and Te) chalcogenides. Orange and green spheres denote the $M$ and $X$ atoms, respectively. (b) BZ and the projected surface BZ for the (0001) surface of wurtzite $MX$ chalcogenides.

Figure 2

(a) Calculated phonon dispersion of wurtzite ZnSe along the high-symmetry momentum path. The phonon WP along the blue line indicated in the inset is shown in the right section of the phonon dispersion along the M-Q line with the shadow color. (b)–(d) The enlarged phonon dispersions of the blue shadow regions shown in Fig. 2. The colorful lines in the phonon dispersions highlight different vibrational modes.

Figure 3

(a) Perspective plot of the phonon WPs with positive and negative charge in the 3D momentum space. (b) The zoomed-in crossing phonon dispersion around one phonon WP. The WPs with opposite chirality are marked with different colors.

Figure 4

(a) and (b) Normalized Berry curvature ${\mathrm{\Omega }}_z$ of wurtzite ZnSe surrounding a pair of the phonon WPs with positive and negative charge on the ${\mathbf{q}}_z=0.0$ plane of the BZ. The length of each arrow is the magnitude of the in-plane Berry curvature. (c) and (d) The Wannier center evolution around WPs with (c) positive and (d) negative charges, respectively. Here, $\theta$ is the polar angle of orbitals, and $\phi$ shows the phase factor of the position operator on the orbitals.

Figure 5

(a) The surface arcs for wurtzite ZnSe projected onto the top (0001) surface (Zn-terminated surface) at the frequency of 5.49 THz. It is observed that the surface arc always connects two WPs with the opposite charges. (b) Surface band structure along the blue lines indicated in (a). (c) and (d) Same as (a) and (b), respectively, but for the bottom $\left(000\overline{1}\right)$ surface (Se-terminated surface). The length of one pair of WPs connecting with the topological surface arcs is near $0.55{\AA }^{-1}$.

Figure 6

The frequency-dependent evolution of the topologically protected phononic nontrivial surface states of wurtzite ZnSe for (a) Zn-terminated and (b) Se-terminated (0001) surfaces.