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Excitonic collective modes in Weyl semi-metals

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.