Excitonic insulator and the extended Falicov-Kimball model away from half-filling

We consider an extended spinless Falicov-Kimball model at an arbitrary doping level, focusing on the range of parameter values where a uniform excitonic insulator is stabilized at half-filling. In the two-dimensional case, we compare the properties of possible uniform phases and construct the Hartree–Fock phase diagrams, which include sizable phase separation regions. It is seen that the excitonic insulator can appear as a component phase in a mixed-phase state in a broad interval of doping levels. In addition, in a certain range of parameter values the excitonic metal (doped excitonic insulator) is identified as the lowest-energy uniform phase. We suggest that this phase, which is unstable with respect to phase separation, may be stabilized when the phase separation is suppressed by the long-range Coulomb interaction. Overall, we find that excitonic correlations can affect the behavior of the system relatively far away from half-filling.