Topological acoustic triple point
Sungjoon Park, Yoonseok Hwang, Hong Chul Choi, Bohm-Jung Yang

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 that is a property of three-band systems with symmetry, where and are the inversion and the time-reversal symmetries, respectively. We therefore call triple points with nontrivial the topological acoustic triple point (TATP). The topological charge 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…
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