Breaking the Synergy between the Quasiparticle Band Gap and Exciton Binding Energy, Bright–Dark Exciton Transition, and Realization of the Excitonic Insulator State in Quantum Spin Hall Insulators

In condensed matter physics, the excitonic insulator (EI) state has always been the key for macroscopic quantum coherence, the experimental detection of which, however, remains elusive. In this work, we propose a new mechanism for realizing the EI phase in quantum spin Hall insulators (QSHIs), in which the synergy between exciton binding energy (<i>E</i>_b) and quasi-particle (QP) band gap (<i>E</i>_g) can be broken. In GeCH₃ and SnCH₃, we verify that <i>E</i>_b > <i>E</i>_g, signaling spontaneous exciton formation and condensation to a reconstructed many-body ground state. In accordance with the Pauli exclusion, the exchange interaction of the Fermion constituents of the composite bosonic excitons causes bright-dark conversion, and these "indirectly photo-excited" dark excitons turn into the ground state due to the interband Coulomb interaction. In the case where bright and dark excitons coexist, the "gray condensate" forms, which will provide feasible solutions to the challenges in the experimental detection of EI.