# Double-Weyl phonons in transition-metal monosilicides

## TL;DR

This paper predicts topological phonons with double Weyl points in certain transition-metal monosilicides, revealing novel surface states and providing new avenues for experimental study of topological phononics at THz frequencies.

## Contribution

It identifies a new class of topological phonons in noncentrosymmetric materials with specific Weyl points and complex surface dispersions, expanding the understanding of topological states in atomic vibrations.

## Key findings

- Presence of double Weyl points in phonon spectra of $M$Si materials.
- Surface phonon dispersions form double helicoidal sheets.
- Analytical expression of surface bands as Weierstrass elliptic functions.

## Abstract

Topological states of electrons and photons have attracted significant interest recently. Topological mechanical states also being actively explored, have been limited to macroscopic systems of kHz frequency. The discovery of topological phonons of atomic vibrations at THz frequency can provide a new venue for studying heat transfer, phonon scattering and electron-phonon interaction. Here, we employed ab initio calculations to identify a class of noncentrosymmetric materials of $M$Si ($M$=Fe,Co,Mn,Re,Ru) having double Weyl points in both their acoustic and optical phonon spectra. They exhibit novel topological points termed "spin-1 Weyl point" at the Brillouin zone~(BZ) center and "charge-2 Dirac point" at the zone corner. The corresponding gapless surface phonon dispersions are double helicoidal sheets whose isofrequency contours form a single non-contractible loop in the surface BZ. In addition, the global structure of the surface bands can be analytically expressed as double-periodic Weierstrass elliptic functions. Our prediction of topological bulk and surface phonons can be experimentally verified by neutron scattering and electron energy loss spectroscopy, opening brand new directions for topological phononics.