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The three-chain Hubbard model for Ta 2 NiSe 5 , known as a candidate material for an excitonic insulator, is investigated over the wide range of the energy gap D between the twofold degenerate conduction bands and the nondegenerate valence band including both semiconducting (D > 0) and semimetallic (D < 0) cases. In the semimetallic case, the difference in the band degeneracy inevitably causes the imbalance of each Fermi wavenumber, resulting in a remarkable excitonic state characterized by the condensation of excitons with finite center-of-mass momentum q, the so-called Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) excitonic state. With decreasing D corresponding to increasing pressure, the obtained excitonic phase diagram shows a crossover from BEC (D > ∼ 0) to BCS (D < ∼ 0) regime, and then shows a distinct phase transition at a certain critical value D c (< 0) from the uniform (q = 0) to the FFLO (q 0) excitonic state, as expected to be observed in Ta 2 NiSe 5 under high pressure.Recently, Ta 2 NiSe 5 has attracted much attention as a strong candidate for the excitonic insulator (EI) which is characterized by the condensation of excitons and has been argued since about half a century ago.

We examine the free energy and the thermodynamic properties in the three-chain Hubbard model for Ta 2 NiSe 5 to clarify the phase transitions between the uniform and the FFLO excitonic states which are expected to be observed in Ta 2 NiSe 5 under high pressure.The narrow gap semiconductor Ta 2 NiSe 5 shows an orthorhombic-to-monoclinic phase transition at T c =328 K, 1) below which the flattening of the valence band top is observed in the ARPES experiments 2, 3) and is well interpreted as excitonic condensation from a normal semiconductor to the excitonic insulator (EI) on the basis of the three-chain Hubbard model simulating a quasi-one-dimensional Ta-NiSeTa chain. 4,5) The model has been investigated also for the semimetallic case, 6) where the difference in the band degeneracy between the conduction and valence bands inevitably causes the imbalance of each Fermi wavenumber and results in a remarkable Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) excitonic state characterized by the condensation of excitons with finite center-of-mass momentum q, as expected to be observed in Ta 2 NiSe 5 under high pressure. 7) To clarify the feature of the phase transition between the uniform (q = 0) and FFLO (q 0) excitonic phases (EPs), this paper examines the free energy and the thermodynamic properties which have not been discussed in the previous paper 6) but would be important for the comparison with experiments under pressure. 7)Our model Hamiltonian is given bywhere c kασ (c iασ ) and f kσ ( f iσ ) are the annihilation operators for conduction (c) and valence ( f ) electrons with wavenumber k (site i), spin σ =↑, ↓ and chain degrees of freedom for the c electron α = 1, 2. The noninteracting c( f ) band dispersion is given by ǫ momentum q takes place, the excitonic order parameterbecomes finite, where ∆ q and φ q are the magnitude and the relative phase of the order parameter, respectively, 6) and N is the total number of unit cells. Within the mean-field approximation, the Hamiltonian Eq. (1) is diagonalized to yield the mean-field band dispersion as. We obtain ∆ q and φ q by solving the self-consistent equations, 6) that generally yield non-unique solutions with different values of q. Therefore, we determine the most stable solution by minimizing the free energywith respect to q, where s is the band index and µ is the chemical potential determined so as to fix the number of electrons per unit cell to n = n c + n f = 2. Figure 1 shows the excitonic phase diagram on the D − T plane around the phase boundary between the uniform and FFLO EPs. As shown in the previous paper, 6) the phase transition between the normal phase and the EPs is always secondorder at the phase transition temperature T c which shows a peak around the crossover region between the BEC (D > ∼ 0) and BCS (D < ∼ 0) regimes. As for the phase transition between the uniform and FFLO EPs, the previous paper 6) has revealed that the order parameter changes continuously at high temperatures while discontinuously at low temperatures indicating the second-and first-o...

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Transition metal chalcogenide Ta 2 NiSe 5 , a promising material for the excitonic insulator, is investigated on the basis of the three-chain Hubbard model with two conduction (c) bands and one valence ( f ) band. In the semimetallic case where only one of two c bands and the f band cross the Fermi level, the transition from the c-f compensated semimetal to the uniform excitonic order, the so-called excitonic insulator, takes place at low temperature as the same as in the semiconducting case. On the other hand, when another c band also crosses the Fermi level, the system shows three types of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) excitonic orders characterized by the condensation of excitons with finite center-of-mass momentum q corresponding to the three types of nesting vectors between the imbalanced two c and one f Fermi surfaces. The obtained FFLO excitonic states are metallic in contrast to the excitonic insulator and are expected to be observed in the semimetallic Ta 2 NiSe 5 under high pressure. The effect of the electron-lattice coupling is also discussed briefly and is found to induce the monoclinic distortion not only in the uniform excitonic state but also in the FFLO one resulting in the orthorhombic-monoclinic structural phase transition for both cases as observed in Ta 2 NiSe 5 for both low-pressure semiconducting and high-pressure semimetallic regimes.