Realizing an excitonic insulator by decoupling exciton binding energy from the minimum band gap

Realizing excitonic insulator state in real materials has long been an attractive subject of condensed matter physics, as motivated by both fundamental interest in many-body physics and the potential application in transport devices due to its bosonic nature. Direct-gap materials serve as promising candidates for excitonic insulators, where the difficulty to distinguish from a Peierls charge density wave is avoided. However, direct-gap materials still suffer from a divergence of polarizability when the band gap approaches zero, leading to a diminishing exciton binding energy. We propose that one can decouple the exciton binding energy from the band gap in materials where band-edge states have the same parity. As a concrete example, we show by first-principles calculations that two-dimensional GaAs and experimentally mechanically exfoliated single-layer TiS₃ support prefectly to this principle, thus hold the possiblility for experimental realization of excitonic insulators.