Effects of correlated hopping on electronic ferroelectricity in the extended Falicov-Kimball model in two dimensions

We use the Hartree-Fock (HF) approximation with the charge-density-wave (CDW) instability to study the effect of correlated hopping on the stability of electronic ferroelectricity in the extended Falicov-Kimball model (FKM) in two dimensions. It is shown that the effects of correlated hopping term are very strong, especially for negative values of the $f$-level energy $E_f$, where they lead to: (i) stabilization of the ferroelectric ground state with a spontaneous hybridization $P_{df}=⟨d^{+}f⟩$ for positive values of correlated hopping parameter $t_d^{\mathrm{\prime }}$, (ii) stabilization of the antiferroelectric phase for $t_d^{\mathrm{\prime }}<t_{d,crit\mathrm{.}}^{\mathrm{\prime }}<0$ and (iii) suppression of the ferroelectric ground state for $t_{d,crit\mathrm{.}}^{\mathrm{\prime }}⩽t_d^{\mathrm{\prime }}<0$, The effects of correlated hopping on valence transitions are also discussed.