Abstract
In spinful electronic systems, time-reversal symmetry makes that all Kramers pairs at the time-reversal-invariant momenta are Weyl points (WPs) in chiral crystals. Here, we find that such symmetry-enforced WPs can also emerge in bosonic systems (e.g. phonons and photons) due to nonsymmorphic symmetries. We demonstrate that for some nonsymmorphic chiral space groups, several high-symmetry k-points can host only WPs in the phononic systems, dubbed symmetry-enforced Weyl phonons (SEWPs). The SEWPs, enumerated in Table 1, are pinned at the boundary of the three-dimensional (3D) Brillouin zone (BZ) and protected by nonsymmorphic crystal symmetries. By performing first-principles calculations and symmetry analysis, we propose that as an example of SEWPs, the twofold degeneracies at P are monopole WPs in K2Sn2O3 with space group 199. The two WPs of the same chirality at two nonequivalent P points are related by time-reversal symmetry. In particular, at ~17.5 THz, a spin-1 Weyl phonon is also found at H, since two Weyl phonons at P carrying a non-zero net Chern number cannot exist alone in the 3D BZ. The significant separation between P and H points makes the surface arcs long and clearly visible. Our findings not only present an effective way to search for WPs in bosonic systems, but also offer some promising candidates for studying monopole Weyl and spin-1 Weyl phonons in realistic materials.
Highlights
Topological phonons[1,2,3,4,5,6,7,8], referring to the quantized excited vibrational states of interacting atoms, have most recently attracted attention in condensed matter physics because of their unique physical nature[8,9,10,11,12,13]
We have checked that irreps corresponds to the number of bands that meet at the high- there is no symmetry-protected degeneracy on the highsymmetry k-points
By performing symmetry analysis in 230 space groups (SGs) in the presence of TR symmetry, we demonstrate that there are symmetry-enforced Weyl points (WPs) in the bosonic systems, e.g. phonons
Summary
Topological phonons[1,2,3,4,5,6,7,8], referring to the quantized excited vibrational states of interacting atoms, have most recently attracted attention in condensed matter physics because of their unique physical nature[8,9,10,11,12,13]. In similarity to various quasiparticles in electronic systems, topological phonons, such as (spin-1/2 or monopole) Weyl, Dirac, spin-1 Weyl, and charge-2 Dirac phonons, have been predicted/observed in 3D momentum space of solid crystals[14,15,16,17,18,19,20,21,22], strengthening largely our understanding of elementary particles in the universe. Phonons can be excited to all energy space to generate unusual transport behaviors, since they are not limited by Pauli exclusion principle and Fermi surfaces in materials. The phononic systems with these particular properties provide a good platform for studying topological bosonic states in experiments
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