First-principles design of excitonic insulators: A review

The excitonic insulator (EI) is a more than 60-year-old theoretical proposal that is still elusive. It is a purely quantum phenomenon involving the spontaneous generation of excitons in quantum mechanics and the spontaneous condensation of excitons in quantum statistics. At this point, the excitons represent the ground state rather than the conventional excited state. Thus, the scarcity of candidate materials is a key factor contributing to the lack of recognized EI to date. In this review, we begin with the birth of EI, presenting the current state of the field and the main challenges it faces. We then focus on recent advances in the discovery and design of EIs based on the first-principles Bethe–Salpeter scheme, in particular the dark-exciton rule guided screening of materials. It not only opens up new avenues for realizing excitonic instability in direct-gap and wide-gap semiconductors, but also leads to the discovery of novel quantum states of matter such as half-EIs and spin-triplet EIs. Finally, we will look ahead to possible research pathways leading to the first recognized EI, both theoretically and computationally.