Fig. 1: CDW interactions in Weyl semimetals.
From: Causal structure of interacting Weyl fermions in condensed matter systems
a Schematic illustration of two Weyl nodes with an energy difference and CDW Q-vector (QCDW) is not equal to the separation of the two Weyl nodes (\({{{{{{{{\bf{k}}}}}}}}}_{{{{{{{{{\rm{W}}}}}}}}}_{1}}-{{{{{{{{\bf{k}}}}}}}}}_{{{{{{{{{\rm{W}}}}}}}}}_{2}}\)). The yellow arrow represents QCDW, and the blue arrow represents \({{{{{{{{\bf{k}}}}}}}}}_{{{{{{{{{\rm{W}}}}}}}}}_{1}}-{{{{{{{{\bf{k}}}}}}}}}_{{{{{{{{{\rm{W}}}}}}}}}_{2}}\). The red/blue structures represent the conduction/valence dispersion cones. The kx, ky, and kz represent the directions in momentum space. b Positions of the four Weyl nodes in our model. The chirality of each Weyl node is presented by the plus/minus sign. c–e Band structure as a function of kx with A = 0.3, θ = 0, k1 = 1.3π/2, ky = 0, and kz = π/2. c Without CDW, four Weyl nodes are at the ± (1.3π/2, 0, ± π/2) with an energy difference around 0.6 eV. d Without CDW (δ = 0), the folded bands in the double supercell BZ along the x-direction. Weyl nodes with opposite chirality are nested out of each other’s dispersion cone. The vertical blue lines indicate the boundary of the reduced BZ along kx, as used consistently throughout the paper. e With CDW, CDW Q-vector is along (π,0,0) and the CDW strength δ = 0.1. The Weyl nodes cannot be gapped and the system remains in the semimetal phase. f–h Band structure along the kx with A = 0.3, k1 = 1.1π/2, ky = 0, and kz = π/2. f Without CDW, four Weyl nodes are at the ± (1.1π/2, 0, ± π/2). g Without CDW (δ = 0), the folded bands in the double supercell BZ along the x-direction. Weyl nodes with opposite chirality are nested into each other’s dispersion cones. h With CDW, CDW Q-vector is along (π, 0, 0) and the CDW strength δ = 0.1. A global gap was opened by the CDW around Fermi energy.
