Three-Dimensional Dirac Phonons with Inversion Symmetry.

Dirac semimetals associated with bulk Dirac fermions are well known in topological electronic systems. In sharp contrast, three-dimensional (3D) Dirac phonons in crystalline solids are still unavailable. Here we perform symmetry arguments and first-principles calculations to systematically investigate 3D Dirac phonons in all space groups with inversion symmetry. The results show that there are two categories of 3D Dirac phonons depending on their protection mechanisms and positions in momentum space. The first category originates from the four-dimensional irreducible representations at the high symmetry points. The second category arises from the phonon branch inversion, and the symmetry guarantees Dirac points to be located along the high symmetry lines. Furthermore, we reveal that nonsymmorphic symmetries and the combination of inversion and time-reversal symmetries play essential roles in the emergence of 3D Dirac phonons. Our work not only offers a comprehensive understanding of 3D Dirac phonons but also provides significant guidance for exploring Dirac bosons in both phononic and photonic systems.

Symmetry-Protected Topological Triangular Weyl Complex.

Weyl points are often believed to appear in pairs with opposite chirality. In this work, we show by first-principles calculations and symmetry analysis that single Weyl phonons with linear dispersion and double Weyl phonons with quadratic dispersion are simultaneously present between two specific phonon branches in realistic materials with trigonal or hexagonal lattices. These phonon Weyl points are guaranteed to locate at high-symmetry points due to the screw rotational symmetry, forming a unique triangular Weyl complex. In sharp contrast to conventional Weyl systems with surface arcs terminated at the projections of a pair of Weyl points with opposite chirality, the phonon surface arcs of the unconventional triangular Weyl complex connect the projections of one double Weyl point and two single Weyl points. Importantly, the phonon surface arcs originating from the triangular Weyl complex are extremely long and span the entire surface Brillouin zone. Furthermore, there are only nontrivial phonon surface states across the isofrequency surface, which facilitates their detection in experiments and further applications. Our work not only offers the promising triangular phonon Weyl complex but also provides guidance for exploring triangular Weyl bosons in both phononic and photonic systems.

Symmetry-Protected Ideal Type-II Weyl Phonons in CdTe.

Nontrivial low-energy excitations of crystalline solids have insightfully strengthened understanding of elementary particles in quantum field theory. Usually, topological quasiparticles are mainly focused on fermions in topological semimetals. We alternatively show by first-principles calculations and symmetry analysis that ideal type-II Weyl phonons are present in zinc-blende cadmium telluride, a well-known II-VI semiconductor. Importantly, these type-II Weyl phonons originate from the inversion between the longitudinal acoustic and transverse optical branches. Symmetry guarantees that the type-II Weyl points lie along the high-symmetry lines at the boundaries of the Brillouin zone even with a breaking of inversion symmetry, exhibiting the robustness of protected phonon features. The nontrivial phonon surface states and surface arcs projected on the semifinite (001) and (111) surfaces are investigated. The phonon surface arcs connecting the Weyl points with opposite chirality, guaranteed to be very long, are clearly visible. We not only offer a promising candidate for studying type-II Weyl phonons but also provide a route to realize symmetry-protected nontrivial phonons and related applications in realistic materials.

Robust Twin Pairs of Weyl Fermions in Ferromagnetic Oxides.

The ferromagnetic Weyl semimetals with inversion symmetry usually possess odd pairs of Weyl fermions. Here, we present an inversion eigenvalue argument to dictate the existence of even pairs of ferromagnetic Weyl fermions. We show, by a combination of first-principles calculations and symmetry analyses, that this exotic topological feature can be verified in ferromagnetic oxides in different space groups. In particular, a realistic candidate, i.e., hollandite RbCr_{4}O_{8} with a high Curie temperature (∼295 K), hosts intriguing twin pairs of Weyl fermions, which are robustly stable against perturbations. Moreover, our effective model and symmetry analysis show that the twin pairs of Weyl fermions originate from a mirrored nodal ring pair. The nontrivial surface states and Fermi arcs of RbCr_{4}O_{8} are clearly visible, further revealing the topological features. This work strengthens the understanding of the parity analysis in exploring ferromagnetic topological materials with unconventional fermionic excitations.