Spin-triplet topological excitonic insulators in two-dimensional materials

Quantum spin-Hall insulators (QSHIs) possess nontrivial band topology. Using first-principles many-body perturbation theory (GW+Bathe-Salpeter equation), we show that excitonic insulators (EIs) can exist in QSHIs AsO and Mo₂TiC₂O₂ with nonvanishing band gaps. Their single-particle topological properties can be described by the same low-energy model, and we show that the EI phase in this model is of spin-triplet type due to the nontrivial band geometry. The rotational symmetry is broken by the s-wave EI order parameter, and the anisotropic absorption together with possible lattice reconstruction can be used as signatures for this spin-triplet topological EI phase. Large amounts of spin-triplet excitons emerge spontaneously when an EI is achieved and exciton spin-Hall effect may be observed.