Topological acoustic triple point

TL;DR

This paper introduces the concept of topological acoustic triple points (TATP) in phonon band structures, characterized by a topological charge, and explores their properties, protection mechanisms, and potential effects on thermal and electronic transport.

Contribution

It defines topological charges for phonon triple degeneracies, classifies TATP using symmetry and topology, and links these points to observable transport phenomena.

Findings

TATP characterized by a topological charge $rak{q}$

TATP can be symmetry-protected by $O_h$ and $T_h$ groups

Nontrivial TATP can induce anomalous thermal and orbital Hall effects

Abstract

Acoustic phonon in a crystalline solid is a well-known and ubiquitous example of elementary excitation with a triple degeneracy in the band structure. Because of the Nambu-Goldstone theorem, this triple degeneracy is always present in the phonon band structure. Here, we show that the triple degeneracy of acoustic phonons can be characterized by a topological charge $\mathfrak{q}$ that is a property of three-band systems with $\mathcal{PT}$ symmetry, where $\mathcal{P}$ and $\mathcal{T}$ are the inversion and the time-reversal symmetries, respectively. We therefore call triple points with nontrivial $\mathfrak{q}$ the topological acoustic triple point (TATP). The topological charge $\mathfrak{q}$ can equivalently be characterized by the skyrmion number of the longitudinal mode, or by the Euler number of the transverse modes, and this strongly constrains the nodal structure around the TATP. The TATP can also be symmetry-protected at high-symmetry momenta in the band structure of phonons and spinless electrons by the $O_h$ and the $T_h$ groups. The nontrivial wavefunction texture around the TATP can induce anomalous thermal transport in phononic systems and orbital Hall effect in electronic systems. Our theory demonstrates that the gapless points associated with the Nambu-Goldstone theorem are an avenue for discovering new classes of degeneracy points with distinct topological characteristics.