How to identify and characterize strongly correlated topological semimetals

TL;DR

This paper explores how strong electronic correlations influence the topological properties of Weyl semimetals, especially in the context of the recently discovered Weyl-Kondo semimetal, providing phase diagrams and scaling relations.

Contribution

It constructs a prototype phase diagram for Weyl-Kondo semimetals and introduces scaling plots linking Hall response to correlation strength and carrier concentration.

Findings

Topological Hall response is maximized by strong correlations and low carrier density.

Weyl-Kondo semimetals exhibit characteristic temperature-magnetic field phase diagrams.

Scaling relations suggest ways to identify and optimize correlated topological semimetals.

Abstract

How strong correlations and topology interplay is a topic of great current interest. In this perspective paper, we focus on correlation-driven gapless phases. We take the time-reversal symmetric Weyl semimetal as an example because it is expected to have clear (albeit nonquantized) topological signatures in the Hall response and because the first strongly correlated representative, the noncentrosymmetric Weyl-Kondo semimetal Ce$_3$Bi$_4$Pd$_3$, has recently been discovered. We summarize its key characteristics and use them to construct a prototype Weyl-Kondo semimetal temperature-magnetic field phase diagram. This allows for a substantiated assessment of other Weyl-Kondo semimetal candidate materials. We also put forward scaling plots of the intrinsic Berry-curvature-induced Hall response vs the inverse Weyl velocity -- a measure of correlation strength, and vs the inverse charge carrier concentration -- a measure of the proximity of Weyl nodes to the Fermi level. They suggest that the topological Hall response is maximized by strong correlations and small carrier concentrations. We hope that our work will guide the search for new Weyl-Kondo semimetals and correlated topological semimetals in general, and also trigger new theoretical work.