Spin-Orbit Nodal Semimetals in the Layer Groups

Recent interest in point and line node semimetals has lead to the proposal and discovery of these phenomena in numerous systems. Frequently, though, these nodal systems are described in terms of individual properties reliant on specific space group intricacies or band-tuning conditions. Restricting ourselves to cases with strong spin-orbit interaction, we develop a more general framework which captures existing systems and predicts new examples of nodal materials. In many previously proposed systems, the three-dimensional nature of the space group has obscured key generalities. Therefore, we show how within our framework one can predict and characterize a diverse set of nodal phenomena even in two-dimensional systems constructed of three-dimensional sites, known as the ``Layer Groups''. Introducing a set of simple models, we characterize the allowed semimetallic structures in the layer groups and draw connections to analogous three-dimensional systems.