Topological van Hove singularities at phase transitions in Weyl metals

Abstract

We study 3D topological phase transitions between topological and trivial metals and we show that a subset of Van Hove (VH) singularities of the density of states sits exactly at the transition. We may refer to these as topological VH singularities. By investigating a minimal model, we show that they originate from energy saddle points located between Weyl points with opposite chiralities. We exemplify the relation between VH singularities and topological phase transitions in tightbinding Weyl systems by analysing the 3D Hofstadter model, which offers a simple and interesting playground to consider different kinds of Weyl metals and understand the features of their density of states. In this model, as a function the magnetic flux, the occurrence of topological VH singularities can be explicitly checked.