Half-Excitonic Insulator: A Single-Spin Bose-Einstein Condensate.

First-principles calculations reveal an unusual electronic state (dubbed as half excitonic insulator) in monolayer 1T-MX_{2} (M=Co, Ni and X=Cl, Br). Its one spin channel has a many-body ground state due to excitonic instability, while the other is characterized by a conventional band insulator gap. This disparity arises from a competition between the band gap and exciton binding energy, which exhibits a spin dependence due to different orbital occupations. Such a state can be identified by optical absorption measurements and angle-resolved photoemission spectroscopy. Our theory not only provides new insights for the study of exciton condensation in magnetic materials but also suggests that strongly correlated materials could be fertile candidates for excitonic insulators.