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Europhysics Letters (EPL)

The influence of the interband Coulomb interaction and the f-electron hopping on excitonic correlations in the extended Falicov-Kimball model

Pavol Farkašovský

Published May 1, 2015• 12 citations
Publisher

Abstract

The density matrix renormalization group (DMRG) method is used to examine the effects of the interband Coulomb interaction U between f and d electrons as well as the f -electron hopping on the stability of the excitonic phase in the one-dimensional Falicov-Kimball model (FKM) with local hybridization V . It is found that the interband Coulomb interaction significantly enhances the excitonic average and that this effect is especially strong in the limit of small hybridization, where the interacting excitonic value is enhanced several hundred times in comparison to its non-interacting value. The further increase in P df is observed due to the non-zero f -electron hopping, but these changes are considerable only if the d and f bands have opposite parity. In addition, the examination of the interplay between the excitonic effects and the charge density wave (CDW) instability showed that the CDW and excitonic phase coexist up to relatively large values of local hybridization . The ground-state phase diagram of the model in the plane is discussed.

DOI
10.1209/0295-5075/110/47007

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The density matrix renormalization group (DMRG) method is used to examine the effects of the interband Coulomb interaction U between f and d electrons as well as the f -electron hopping on the stability of the excitonic phase in the one-dimensional Falicov-Kimball model (FKM) with local hybridization V . It is found that the interband Coulomb interaction significantly enhances the excitonic average and that this effect is especially strong in the limit of small hybridization, where the interacting excitonic value is enhanced several hundred times in comparison to its non-interacting value. The further increase in P df is observed due to the non-zero f -electron hopping, but these changes are considerable only if the d and f bands have opposite parity. In addition, the examination of the interplay between the excitonic effects and the charge density wave (CDW) instability showed that the CDW and excitonic phase coexist up to relatively large values of local hybridization . The ground-state phase diagram of the model in the plane is discussed.
The formation and condensation of excitonic bound states of conduction-band electrons and valence-band holes surely belongs to one of the most exciting ideas of contemporary solid state physics.In this short review we present the latest progress in this field reached by the density-matrix-renormalization-group (DMRG) calculations within various extensions of the Falicov-Kimball model.Particular attention is paid to a description of crucial mechanisms (interactions) that affect the stability of the excitonic phase, and namely: (i) the interband d-f Coulomb interaction, (ii) the f -electron hopping, (iii) the nonlocal hybridization with odd and even parity, (iv) combined effects of the local and nonlocal hybridization, (v) the nearest-neighbor Coulomb interaction between d and f electrons and (vi) the correlated hopping.The relevance of numerical results obtained within different extensions of the Falicov-Kimball model for a description of the real d-f materials is widely discussed.
Abstract The density-matrix-renormalization-group method is used to study the influence of external magnetic field on the stability of the excitonic phase induced by local hybridization in the one-dimensional spin-1/2 Falicov-Kimball model. It is shown that a fine tuning of external magnetic field through the quantum critical point is able to induce significant changes (continuous as well as discontinuous) in the excitonic ⟨ d + f ⟩ expectation average providing new set of physical properties and technological applications, like possibilities of faster switching ferroelectrics and controlling their optical properties with magnetic fields. Moreover, effects of some other interactions (which may be present in real d-f materials) on the stability of excitonic phase are examined and it is shown that the Hubbard interaction in the d-electron subsystem, the interband d-f Coulomb interaction, as well as the exchange d-f interaction stabilize significantly excitonic correlations below the quantum critical point, while the anisotropic spin-dependent interaction of the Ising type between f and d electrons as well as the f-electron hopping suppress the excitonic correlations for magnetic fields below as well as above the quantum critical point.
We present a Hartree-Fock study of the Falicov-Kimball model extended by both on-site and nonlocal hybridization. We examine the interplay between excitonic effects and the charge-density wave (CDW) instability known to exist at zero hybridization. It is found that the CDW state remains stable in the presence of finite hybridization; for on-site hybridization the Coulomb interaction nevertheless strongly enhances the excitonic average above its value in the noninteracting system. In contrast, for nonlocal hybridization, we observe no such enhancement of the excitonic average or a spontaneous on-site hybridization potential. Instead, we find only a significant suppression of the excitonic correlations in the CDW state. A phenomenological Ginzburg-Landau analysis is also provided to understand the interplay.
We consider the excitonic insulator state (often associated with electronic ferroelectricity), which arises on the phase diagram of an extended spinless Falicov-Kimball model (FKM) at half-filling. Within the Hartree--Fock approach, we calculate the spectrum of low-energy collective excitations in this state up to second order in the narrow-band hopping and/or hybridization. This allows to probe the mean-field stability of the excitonic insulator. The latter is found to be unstable when the case of the pure FKM (no hybridization with a fully localized band) is approached. The instability is due to the presence of another, lower-lying ground state and not to the degeneracy of the excitonic phase in the pure FKM. The excitonic phase, however, may be stabilized further away from the pure FKM limit. In this case, the low-energy excitation spectrum contains important information about the properties of the excitonic condensate (including the strongly suppressed critical temperature).
The density-matrix-renormalization-group method and the Hartree-Fock approximation with the charge-density-wave 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, such as the f-electronf\text{-electron}f-electron hopping, the local and nonlocal hybridizations, as well as the increasing dimension of the system on the excitonic momentum distribution N(q)N(q)N(q) and especially on the number of zero-momentum excitons N0=N(q=0){N}_{0}=N(q=0)N0​=N(q=0) in the condensate. It is found that the negative values of the f-electronf\text{-electron}f-electron hopping integrals tf{t}_{f}tf​ support the formation of a zero-momentum condensate, whereas the positive values of tf{t}_{f}tf​ have the fully opposite effect. The opposite effects on the formation of the condensate exhibit also the local and nonlocal hybridizations. The first one strongly supports the formation of the condensate, whereas the second one destroys it completely. Moreover, it was shown that the zero-momentum condensate remains robust with increasing dimension of the system.
Two-dimensional spinless Falicov-Kimball model (FKM) with correlated hopping is studied perturbatively in the limit of large on-site Coulomb interaction U. In the half filled case (i.e., ${\ensuremath{\rho}}_{i}+{\ensuremath{\rho}}_{e}=1,$ where ${\ensuremath{\rho}}_{i},{\ensuremath{\rho}}_{e}$ are densities of ions and electrons, respectively) the effective Hamiltonian in spin variables is derived up to terms proportional to ${U}^{\ensuremath{-}3}.$ Unlike the simplest FKM case, it contains odd parity terms (resulting from the correlated hopping) in addition to even parity ones. The ground-state phase diagram of the effective Hamiltonian is examined in the (a/t,h)(a/t,h)(a/t,h) plane, where a/ta/ta/t is a parameter characterizing strength of the correlated hopping and h is a difference of chemical potentials of two sorts of particles present in the system. It appears to be asymmetric with respect to the change $\stackrel{\ensuremath{\rightarrow}}{h}\ensuremath{-}h$ and an additional ordered phase is found for a certain interval of a/t.a/t.a/t.