Topological van Hove singularities at phase transitions in Weyl metals

We show that in three-dimensional (3D) topological metals, a subset of the van Hove singularities of the density of states sits exactly at the transitions between topological and trivial gapless phases. We may refer to these as topological van Hove singularities. By investigating two minimal models, we show that they originate from energy saddle points located between Weyl points with opposite chiralities, and we illustrate their topological nature through their magnetotransport properties in the ballistic regime. We exemplify the relation between van Hove singularities and topological phase transitions in Weyl systems by analyzing the 3D Hofstadter model, which offers a simple and interesting playground to consider different kinds of Weyl metals and to understand the features of their density of states. In this model, as a function of the magnetic flux, the occurrence of topological van Hove singularities can be explicitly checked.

Automated summary

In three-dimensional topological metals, certain van Hove singularities are located precisely at the transitions between topological and trivial gapless phases, which are referred to as topological van Hove singularities. These singularities originate from energy saddle points between Weyl points with opposite chiralities, and their topological nature is illustrated through their magnetotransport properties. Analyzing the 3D Hofstadter model further exemplifies the relationship between van Hove singularities and topological phase transitions in Weyl systems.