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The three-chain Hubbard model for Ta$_2$NiSe$_5$ known as a candidatematerial for the excitonic insulator is investigated over the wide range ofenergy gap $D$ between the two-fold degenerate conduction bands and thenondegenerate valence band including both semiconducting ($D>0$) andsemimetallic ($D<0$) cases. In the semimetallic case, the difference of theband degeneracy inevitably causes the imbalance of each Fermi wavenumber,resulting in a remarkable excitonic state characterized by the condensation ofexcitons with finite center-of-mass momentum $q$, the so-calledFulde-Ferrell-Larkin-Ovchinnikov (FFLO) excitonic state. With decreasing $D$corresponding to increasing pressure, the obtained excitonic phase diagramshows a crossover from BEC ($D\simg 0$) to BCS ($D\siml 0$) regime, and thenshows a distinct phase transition at a certain critical value $D_c(<0)$ fromthe uniform ($q=0$) to the FFLO ($q\ne 0$) excitonic state, as expected to beobserved in Ta$_2$NiSe$_5$ under high pressure.

FFLO Excitonic State in the Three-Chain Hubbard Model for Ta$_2$NiSe$_5$