Symmetry-Enforced Topology of Chiral Band Crossings

Chiral band crossings, like Weyl points, are points where two or more energy bands become degenerate. They are of interest since they emit Berry flux, which is in turn related to the Chern number as a topological invariant. The latter characterizes the surface states and the anomalous responses to external perturbations. In this work we use the relation between screw rotation symmetries and the chiralities to obtain constraints on the total number of chiral crossings. By utilizing the fermion doubling theorem it becomes possible to predict the existence of a non-zero number of topological crossings independently of the specific system. Our discussion explains how this amplifies 2D band crossings, nodal planes, with a nontrivial topology and it yields an overlooked type of double Weyl point. To show the validity of the method, we study the band topology of general tight-binding models and propose example materials.