  Direct-gap materials hold promises for excitonic insulator. In contrast to
indirect-gap materials, here the difficulty to distinguish from a Peierls
charge density wave is circumvented. However, direct-gap materials still suffer
from the divergence of polarizability when the band gap approaches zero,
leading to 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. First-principles calculations of two-dimensional
GaAs and experimentally mechanically exfoliated single-layer TiS 3 lend solid
supports to the new principle.
