Spin-orbit semimetals in the layer groups

Since the discovery of graphene, there has been great interest in finding other nodal semimetals in two and three dimensions. Over the past few years, numerous examples of these materials have been proposed or observed. However, the explanations for the symmetry and topology mechanisms protecting nodal features in these materials have generally been provided on a case-by-case basis. In this paper, we use a mathematical consideration of crystal lattices on flat manifolds like Mquotobius strips and Klein bottles, most recently revived by Watanabe, Po, Vishwanath, and Zaletel, to develop a framework for discussing all possible two-dimensional and quasi-two-dimensional semimetals in systems with strong spin-orbit interactions. Using this framework, we draw connections to known nodal features in two- and three-dimensional semimetals like SrIrO₃, and we predict new ones, including an exotic ``Cat's Cradle'' Weyl fermion feature.