Topological acoustic triple point

Sungjoon Park,Hong Chul Choi,Bohm-Jung Yang,Yoonseok Hwang

doi:10.1038/s41467-021-27158-y

Sungjoon Park, Hong Chul Choi + Show 2 more

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https://doi.org/10.1038/s41467-021-27158-y

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Abstract

Acoustic phonon is a classic example of triple degeneracy point in band structure. This triple point always appears in phonon spectrum because of the Nambu–Goldstone theorem. Here, we show that this triple point can carry a topological charge {mathfrak{q}} that is a property of three-band systems with space-time-inversion symmetry. The charge {mathfrak{q}} can equivalently be characterized by the skyrmion number of the longitudinal mode, or by the Euler number of the transverse modes. We call triple points with nontrivial {mathfrak{q}} the topological acoustic triple point (TATP). TATP can also appear at high-symmetry momenta in phonon and spinless electron spectrums when Oh or Th groups protect it. The charge {mathfrak{q}} constrains the nodal structure and wavefunction texture around TATP, and can induce anomalous thermal transport of phonons and orbital Hall effect of electrons. Gapless points protected by the Nambu–Goldstone theorem form a new platform to study the topology of band degeneracies.

Highlights

Acoustic phonon is a classic example of triple degeneracy point in band structure
Because three translational symmetries are broken, there are three gapless acoustic phonons forming a triple point at the Brillouin zone (BZ) center, which we refer to as the acoustic triple point (ATP)
We show that an ATP in elastic crystals with time-reversal symmetry can carry a topological charge q. q is a topological charge that can be defined for a real-symmetric three-band Hamiltonian, and consists of a pair of well-known topological charges: the skyrmion number nsk and the Euler number e

Summary

Introduction

Acoustic phonon is a classic example of triple degeneracy point in band structure. This triple point always appears in phonon spectrum because of the Nambu–Goldstone theorem. A characteristic feature of both the linearly and quadratically dispersing TATPs is the energy gap between the highest energy band (L mode) and the two lower energy bands (T modes), except at the triple point, see Fig. 1a This gap is necessary to define the topological charge q, and this feature distinguishes the TATPs from the triple points created by band inversion[19,20,21,22,23,24,25,26] and the spin-1 Weyl point[27,28,29,30,31,32], see Fig. 1b

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