We consider a half-filled two-dimensional Su-Schrieffer-Heeger lattice and examine the role of the long-range Coulomb electron-hole attractive interaction. We demonstrate that under specific conditions, a rare interplay of topological and excitonic-collective behavior emerges as a novel state of matter. A unique Bose-Einstein condensate of excitons forms, exhibiting the co-presence of pseudospin chiral texture. The emerging complex order parameter, a particle-hole pairing gap, has nonzero real and imaginary parts throughout the Brillouin zone (BZ) but vanish separately on two different nodal lines, which intersect at two Weyl points. The Weyl nodes possess opposite pseudospin chiralities, which act as source and drain of a Berry flux associated with the particle-hole pairing wave function, and are the cause of Bogoliubov–de Gennes Fermi-arc edge states. We self-consistently calculate the full momentum dependence of the particle-hole pairing gap throughout the entire BZ. Near the Weyl points, the pairing gap exhibits the unconventional $p_x+i{p}_y$ character. Finally, we discuss general potential experimental realizations of this novel state of matter.

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• Edge states
• Electronic structure
• Excitons
• Jahn-Teller effect
• Peierls transition
• Superconductivity
• Topological materials
• Topological order