Multiple types of van Hove singularities induced by band inversion*

Saddle-point Van Hove singularities in the electron density of states can cause system instabilities that lead to exotic phases of matter. Here, we show that such singularities are very common near the Fermi level of topological semimetals and insulators. Using a k.p model analysis, we find that multiple types of saddle points with different divergence behaviors can be induced by band inversion. In particular, we uncover a new type of saddle-like dispersion (called “saddle line”) that significantly enhances the divergence in the density of states. We present examples of ab initio electron band structures of topological materials including monolayer 1T’-WS₂, monolayer decorated stanene, and Dirac semimetal Na₃Bi. Our results suggest a new universal property of topological materials that can lead to further opportunities.