Topological acoustic triple point.

Park, Sungjoon; Hwang, Yoonseok; Choi, Hong Chul; Yang, Bohm-Jung · Nat Commun · 2021

basic_science · Level V

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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 [Formula: see text] that is a property of three-band systems with space-time-inversion symmetry. The charge [Formula: see text] 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 [Formula: see text] the topological acoustic triple point (TATP). TATP can also appear at high-symmetry momenta in phonon and spinless electron spectrums when O<sub>h</sub> or T<sub>h</sub> groups protect it. The charge [Formula: see text] 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.