Topological acoustic triple point

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 $\mathcal{P}\mathcal{T}$ 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.

7+15 pages, 5+6 figures

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• Dirac phonons in two-dimensional materials
• Topological continuum charges of acoustic phonons in 2D
• Triple hourglass Weyl phonons
• Phase transitions of non-Abelian charged nodal links in a spring-mass system
• Landau Levels of the Euler Class Topology
• Universal higher-order bulk-boundary correspondence of triple nodal points
• Triple nodal points characterized by their nodal-line structure in all magnetic space groups
• Demonstration of non-Abelian frame charge flow in photonic crystals
• Topological phonons in arrays of ultracold dipolar particles
• Second Euler number in four dimensional synthetic matter
• Punctured-Chern topological invariants for semi-metallic bandstructures