Spin-orbital robust Dirac points in two-dimensional systems

Graphene, as the prominent example of two-dimensional (2D) Dirac semimetals, has attracted tremendous attention. However, Dirac points in 2D systems including graphene are greatly influenced by spin-orbit coupling (SOC), and easily open gaps. Besides, although several layer groups (LGs) with SOC Dirac points have been reported, a large number of LGs and actual materials are still missing. Here, based on symmetry analysis, the first-principles calculation, and the high-throughput search, we find that 27 of the 80 nonmagnetic LGs contain spin-orbit Dirac points (SODPs), and screen 65 actual materials from the huge 2D inorganic crystal database (6351). Based on symmetry analysis, SODPs can be classified into two categories: centrosymmetric and non-centrosymmetric systems. In addition, we also discover that the highest order of the SODP is linear, which can be read off from their effective model. Under breaking the symmetries, a Dirac point can be transformed into a pair of Weyl points with opposite chirality. Our work not only provides theoretical guidance for the study of Dirac points in 2D systems, but also provides a large number of concrete candidate materials.