Dirac point phonons at high-symmetry points: Towards materials realization

Abstract

Dirac point semimetals and related Fermi arc surface states are extremely important in topological electronic systems. In 2021, Chen et al. [Phy. Rev. Lett. 126, 185301 (2021)] proposed that Dirac points can appear on high-symmetry lines (HSLs) or at high-symmetry points (HSPs) in three-dimensional (3D) phonon systems as an extension from Dirac points in electronic systems. Inspired by this work, we present an exhaustive list of Dirac point phonons (DPPs) at HSPs in 230 space groups (SGs) by checking the encyclopedia of emergent particles in 3D crystals. The DPPs are divided into four categories: charge-zero (C-0) DPPs, charge-two (C-2) DPPs, quadratic DPPs (QDPPs), and cubic crossing DPPs (CCDPPs). 29 SGs, 6 SGs, 19 SGs, and 5 SGs are identified as candidate SGs for obtaining C-0 DPPs, C-2 DPPs, QDPPs, and CCDPPs at HSPs, respectively. Importantly, herein we contribute to the realization of materials with DPPs at HSPs and through the following: (i) we propose five realistic materials, namely, $Pna{2}_{1}$-type ${\mathrm{Li}}_{3}{\mathrm{AsS}}_{3}, P{2}_{1}$-type NiSbS, $P\overline{4}{2}_{1}c$-type ${\mathrm{NaBH}}_{4}$, and $Pm\overline{3}n$-type ${\mathrm{Ti}}_{3}\mathrm{Au}$ and ${\mathrm{Ta}}_{3}\mathrm{Sn}$ as materials with C-0 DPPs, C-2 DPPs, QDPPs, and CCDPPs at HSPs, respectively, based on the first-principles calculations. The surface states for these five materials are also examined in this work. (ii) We present 626 candidates with C-0 DPPs, 183 candidates with C-2 DPPs, 433 candidates with QDPPs, and 102 candidates with CCDPPs at HSPs, which were discovered by checking the phonon dispersions of 10 037 materials listed in the phonon database at Kyoto University. (iii) Due to the materials with SGs 103, 104, 106, 158, 184, 222, 223, 226, and 228 are not included in the phonon database at Kyoto University, we propose 18 candidates with C-0 DPPs, 5 candidates with QDPPs, and 8 candidates with CCDPPs at HSPs with above-mentioned SGs by screening the Inorganic Crystal Structure Database (ICSD). Therefore, our findings can be used to guide research into Dirac points at HSPs in 3D phonon systems.