Topological charge-2 Dirac phonons in three dimensions: Theory and realization

Abstract

Topological Dirac semimetals have been attracting considerable attention. Recently, a new class of Dirac points with a topological charge of $\ifmmode\pm\else\textpm\fi{}2$, named charge-2 Dirac points (C-2 DPs), were proposed in spinless systems. In this paper, we conduct an exhaustive search of all 230 space groups (SGs), finding that six SGs host C-2 DP at high-symmetry points (HSPs) and nine SGs host the C-2 DP on their high-symmetry lines (HSLs). Based on the symmetry analysis, we find the lowest symmetry requirements that enforce a C-2 DP and construct the corresponding effective models. Furthermore, we investigate the difference between C-2 DPs at HSPs and on HSLs, finding that the type-II C-2 DP only appears on HSLs. Via the first-principles calculations, we identify the corresponding realistic materials that host C-2 DPs. Therefore, our paper not only offers the guidelines to identify the materials that host C-2 DPs in spinless systems based on symmetry requirements, but also paves the effective way to study the C-2 DPs in spinless systems.