Motivated by the possibility of pressure-induced exciton condensation in intermediate-valence Tm[Se,Te] compounds we study the Falicov-Kimball model extended by a finite f-hole valence bandwidth. Calculating the Frenkel-type exciton propagator we obtain excitonic bound states above a characteristic value of the local interband Coulomb attraction. Depending on the system parameters coherence between c-and f-states may be established at low temperatures, leading to an excitonic insulator phase. We find strong evidence that the excitonic insulator typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate (BEC) of preformed excitons (strong-coupling regime), which points towards a BCS-BEC transition scenario as Coulomb correlations increase.PACS numbers: 71.28.+d, 71.35.Lk, 71.30.+h, 71.28.+d. 71.27.+a That excitons in solids might condense into a macroscopic phase-coherent quantum state-the excitonic insulator-was theoretically proposed about more than four decades ago 1 , for a recent review see Ref.2. The experimental confirmation has proved challenging, because excitonic quasiparticles are not the ground state but bound electron-hole excitations that tend to decay on a very short timescale. Thus a large number of excitons has to be created, e.g. by optical pumping, with sufficiently long lifetimes as a steady-state precondition for the Bose-Einstein condensate (BEC) realizing process.The obstacles to produce a BEC out of the faroff-equilibrium situation caused by optical excitation might be circumvented by pressure-induced generation of excitons. Hints that pressure-sensitive, narrow-gap semiconducting materials, such as intermediate-valent TmSe 0.45 Te 0.55 , might host an excitonic BEC in solids came from a series of electric and thermal transport measurements. 3 Fine-tuning the excitonic level, by applying pressure, to the level of electrons in the narrow 4f-valence band, excitons can form near the semiconductor semimetal transition in thermodynamical equilibrium and might give rise to collective excitonic phases. A phase diagram has been deduced out of the resistivity, thermal diffusity and heat conductivity data, which contains, below 20 K and in the pressure range between 5 and 11 kbar, a superfluid Bose condensed state. 4 The experimental claims for excitonic condensation in TmSe 0.45 Te 0.55 have been analysed from a theoretical point of view. 5,6 Adapting the standard effective-mass, (statically) screened Coulomb interaction model to the Tm[Se,Te] electron-hole system, the valence-band-hole conduction-band-electron mass asymmetry was found to suppress the excitonic insulator (EI) phase on the semimetallic side, as observed experimentally. But also on the semiconducting side, the EI instability might be prevented-within this model-by either electron-hole liquid phases 6,7 or, at very large electron-hole mass ratios ( 100), by Coulomb crystallization. 8 The effective-mass Mott-Wannier-type exciton model neglects, however, important band structure effec...
