Topological Exciton Density Wave in Monolayer WSe_{2}

Based on the first-principles calculations coupled with the Bethe-Salpeter equation, the topological exciton density wave is investigated in two-dimensional monolayer WSe_{2}. We find that the topological excitonic insulator phase can exist in monolayer WSe_{2}, and it is robust against in-plane strain. In this system, the energy minimum of exciton bands is shifted to a finite in-plane momentum, forming a Fulde-Ferrell-Larkin-Ovchinnikov-like state. Using the Gross-Pitaevskii equations, stripe-patterned exciton density waves with a nonzero velocity emerge in monolayer WSe_{2}. Our findings pave a new way for exploring the interplay between electron correlation and nontrivial topology.