Formation and condensation of excitonic bound states in the generalized Falicov-Kimball model

Abstract

The density-matrix-renormalization-group (DMRG) method and the Hartree-Fock (HF) approximation with the charge-density-wave (CDW) instability are used to study a formation and condensation of excitonic bound states in the generalized Falicov-Kimball model. In particular, we examine effects of various factors, like the f -electron hopping, the local and nonlocal hybridization, as well as the increasing dimension of the system on the excitonic momentum distribution N (q) and especially on the number of zero momentum excitons N 0 = N (q = 0) in the condensate. It is found that the negative values of the f -electron hopping integrals t f support the formation of zero-momentum condensate, while the positive values of t f have the fully opposite effect. The opposite effects on the formation of condensate exhibit also the local and nonlocal hybridization. The first one strongly supports the formation of condensate, while the second one destroys it completely. Moreover, it was shown that the zero-momentum condensate remains robust with increasing dimension of the system.

Combined effects of local and nonlocal hybridization on formation and condensation of excitons in the extended Falicov-Kimball model

“…The stability of the zero-momentum (q = 0) condensate against the f -electron hopping has been studied in our very recent paper [21]. It was found that the negative values of the f -electron hopping integrals t f support the formation of zero-momentum condensate, while the positive values of t f have the fully opposite effect.…”

DMRG study of exciton condensation in the extended Falicov-Kimball model

“…With regard to the situation in real materials, where there always exists a finite overlap of f orbitals on the neighbouring sites, it is interesting to ask what happens if the f -electron hopping H t f = −t f <i, j> f + i f j is also taken into account [37]. In accordance with some previous theoretical studies, which documented strong effects of the parity of f band on the stability of the excitonic phase [22,23], we have examined the model for both the positive (the even parity) and negative (the odd parity) values of the f -electron hopping integrals t f .…”

“…So far we have presented the results exclusively for E f = 0. Let us now briefly discuss the effect of the change of the f -level position [37]. This study is also interesting from the point of view that taking into account the parametrization between the external pressure and the position of the f level (E f ∼ p), one can also deduce, at least qualitatively, their p dependences from the E f dependences of the ground state characteristics [42].…”

The influence of nonlocal interactions on valence transitions and formation of excitonic bound states in the generalized Falicov–Kimball model

“…showed that this quantity diverges for q = 0, signalizing a Bose-Einstein condensation of preformed excitons. The stability of the zero-momentum (q = 0) condensate against the f -electron hopping has been studied in our very recent paper [21]. It was found that the negative values of the f -electron hopping integrals t f support the formation of zero-momentum condensate, while the positive values of t f have the fully opposite effect.…”