Excitonic collective modes in Weyl semi-metals

TL;DR

This paper investigates collective excitonic modes in Weyl semi-metals, revealing that weak interactions produce exponentially small binding energies, but intermediate interactions can generate sharp spin excitonic resonances, with implications for experimental studies.

Contribution

It demonstrates the existence and properties of excitonic modes in Weyl semi-metals using a minimal interaction model and GRPA analysis, highlighting the effects of linear dispersion and interaction strength.

Findings

Weak interactions lead to exponentially small exciton binding energies.

Intermediate interactions can produce sharp spin-carrying excitonic resonances.

Leading instability is an intra-valley spin density wave, not a gap-opening order.

Abstract

Weyl semi-metals are three dimensional generalizations of graphene with point-like Fermi surfaces. Their linear electronic dispersion leads to a window in the particle-hole excitation spectrum which allows for undamped propagation of collective excitations. We argue that interactions in Weyl semi-metals generically lead to well-defined exciton modes. However, using a minimal model for interactions, we show that the exciton binding energy is exponentially small for weak interactions. This is due to effective two-dimensional character in the space of particle-hole pairs that are available for bound state formation. This is ultimately a consequence of linear electronic dispersion in three dimensions. Nevertheless, intermediate interaction strengths can lead to sharp spin-carrying excitonic resonances. We demonstrate this in a model Weyl semi-metal with broken time-reversal symmetry and Hubbard interactions, using GRPA (generalized random phase approximation) analysis. Excitons in Weyl semi-metals have evoked interest as their condensation could lead to an axionic charge density wave order. However, we find that the leading instability corresponds to intra-valley spin density wave order which shifts the Weyl points without opening a gap. Our results suggest interesting directions for experimental studies of three dimensional Dirac systems.