Topological van Hove singularities at phase transitions in Weyl metals

TL;DR

This paper identifies special van Hove singularities in 3D topological metals that occur at topological phase transitions, linking their origin to saddle points between Weyl points and exploring their effects on magnetotransport.

Contribution

It introduces the concept of topological van Hove singularities, showing their origin, topological nature, and manifestation in Weyl systems through minimal models and the 3D Hofstadter model.

Findings

Topological van Hove singularities occur at phase transitions in Weyl metals.

These singularities originate from saddle points between Weyl points with opposite chiralities.

Their presence affects magnetotransport properties in the ballistic regime.

Abstract

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.