Relativistic horizon of interacting Weyl fermions in condensed matter systems

TL;DR

This paper explores the analogy between relativistic causality concepts and interacting Weyl fermions in condensed matter, revealing a horizon-like behavior where interactions are confined within energy-momentum cones, and discusses candidate materials for Weyl CDW phases.

Contribution

It introduces a novel framework linking causality and event horizons to interacting Weyl fermions in condensed matter systems, bridging high-energy physics concepts with material phenomena.

Findings

Interacting Weyl fermions can open a band gap within their dispersion cone.

Overlapping dispersion cones enable causal interactions analogous to event horizons.

Identification of candidate materials hosting Weyl charge-density wave phases.

Abstract

The intersections of topology, geometry and strong correlations offer many opportunities for exotic quantum phases to emerge in condensed matter systems. Weyl fermions, in particular, provide an ideal platform for exploring the dynamical instabilities of single-particle physics under interactions. Despite its fundamental role in relativistic field theory, the concept of causality and the associated spacetime light cone and event horizon has not been considered in connection with interacting Weyl fermionic excitations in quantum matter. Here, by using charge-density wave (CDW) as an example, we unveil the behavior of interacting Weyl fermions and show that a Weyl fermion in a system can open a band gap by interacting only with other Weyl fermions that lie within its energy-momentum dispersion cone. In this sense, causal connections or interactions are only possible within overlapping dispersion cones and each dispersion cone thus constitutes a solid-state analogue of the more conventional `event horizon' of high-energy physics. Our study provides a universal framework for considering interacting relativistic quasiparticles in condensed matter by separating them into energy-like and momentum-like relationships in analogy with the time-like and space-like events in high-energy physics. Finally, we consider two different candidate materials for hosting the Weyl CDW phase: (TaSe$_4$)$_2$I and Mo$_3$Al$_2$C. Our study greatly enriches the phenomenology and unveils new connections between condensed matter and high-energy physics.