Extended Falicov-Kimball Model Research Articles

The influence of f-electron hopping on ground states and valence transitions in the extended Falicov-Kimball model

The ground-state phase diagram of the extended Falicov-Kimball model with f-f electron hopping is studied numerically in the one-dimensional case. To identify the nature of ground states three complementary numerical methods are used, and namely, (i) the small-cluster exact-diagonalization method, (ii) the density-matrix-renormalization-group method (DMRG) and (iii) an approximate, but very accurate, numerical method based on the reduction of the Hilbert space. It is found that the physics of the Falicov-Kimball model found for the zero value of the f-electron hopping integral tf (including the existence of the devil’s staircase structure) persists also at finite values of tf. The critical values of tcf below which the physics of the Falicov-Kimball model dominates are calculated numerically and it is shown that they depend very strongly on the f-electron concentration nf and only very weakly on the Coulomb interaction. In particular, we have found that for strong Coulomb interactions the value of tcf rapidly increases from tcf ~ 0.003 found for nf = 1 / 4 up to relatively large tcf ~ 0.4 found for nf near the half-filled band case nf = 1 / 2. In addition, the complete picture of valence transitions is presented for non-zero tf and strong Coulomb interactions.

Superfluid phase transition in two-dimensional excitonic systems

We study the superfluid phase transition in the two-dimensional (2D) excitonic system. Employing the extended Falicov–Kimball model (EFKM) and considering the local quantum correlations in the system composed of conduction band electrons and valence band holes we demonstrate the existence of the excitonic insulator (EI) state in the system. We show that at very low temperatures, the particle phase stiffness in the pure-2D excitonic system, governed by the non-local cross correlations, is responsible for the vortex–antivortex binding phase-field state, known as the Berezinskii–Kosterlitz–Thouless (BKT) superfluid state. We demonstrate that the existence of excitonic insulator phase is a necessary prerequisite, leading to quasi-long-range order in the 2D excitonic system. • Excitonic superfluidity is studied in two-dimensional extended Falicov–Kimball model. • Correlations considers to derive the gap and phase-stiffness parameter. • The Berezinskii–Kosterlitz–Thouless transition critical temperature is calculated.

Order, Criticality, and Excitations in the Extended Falicov-Kimball Model

Using exact numerical techniques, we investigate the nature of excitonic (electron-hole) bound states and the development of exciton coherence in the one-dimensional half-filled extended Falicov-Kimball model. The ground-state phase diagram of the model exhibits, besides band-insulator and staggered orbital ordered phases, an excitonic insulator (EI) with power-law correlations. The criticality of the EI state shows up in the von Neumann entropy. The anomalous spectral function and condensation amplitude provide the binding energy and coherence length of the electron-hole pairs which, on their part, point towards a Coulomb interaction driven crossover from BCS-like electron-hole pairing fluctuations to tightly bound excitons. We show that while a mass imbalance between electrons and holes does not affect the location of the BCS-BEC crossover regime, it favors staggered orbital ordering to the disadvantage of the EI. Within the Bose-Einstein condensation (BEC) regime, the quasiparticle dispersion develops a flat valence-band top, in accord with the experimental finding for Ta2NiSe5.

Exact-diagonalization study of exciton condensation in electron bilayers

We report on small-cluster exact-diagonalization calculations which prove the formation of electron-hole pairs (excitons) as a prerequisite for spontaneous interlayer phase coherence in double-layer systems described by the extended Falicov-Kimball model. Evaluating the anomalous Green's function and momentum distribution function of the pairs, and thereby analyzing the dependence of the exciton binding energy, condensation amplitude, and coherence length on the Coulomb interaction strength, we demonstrate a crossover between a BCS-like electron-hole pairing transition and a Bose-Einstein condensation of tightly bound preformed excitons. We furthermore show that a mass imbalance between electrons and holes tends to suppress the condensation of excitons.

Phase transitions in a spinless, extended Falicov–Kimball model on the triangular lattice

A numerical diagonalization technique with canonical Monte-Carlo simulation algorithm is used to study the phase transitions from low temperature (ordered) phase to high temperature (disordered) phase of spinless Falicov–Kimball model on a triangular lattice with correlated hopping (t′). It is observed that the low temperature ordered phases (i.e. regular, bounded and segregated) persist up to a finite critical temperature (Tc). In addition, we observe that the critical temperature decreases with increasing the correlated hopping in regular and bounded phases whereas it increases in the segregated phase. Single and multi peak patterns seen in the temperature dependence of specific heat (Cv) and charge susceptibility (χ) for different values of parameters like on-site Coulomb correlation strength (U), correlated hopping (t′) and filling of localized electrons (nf) are also discussed.

Instability of the chiral phase and electronic ferroelectricity in the extended Falicov–Kimball model

AbstractWe consider a spinless extended Falicov–Kimball model (EFKM) at half‐filling, for the case of opposite‐parity bands. Within the Hartree–Fock approach, we calculate the excitation energies in the chiral phase, which is a possible mean‐field solution in the presence of a hybridisation. It is shown that the chiral phase is unstable. We then briefly review the accumulated results on stability and degeneracies of the excitonic insulator phase. Based on these, we conclude that the presence of both hybridisation and narrow‐band hopping is required for electronic ferroelectricity (EFE).

A BCS-BEC crossover in the extended Falicov-Kimball model: Variational cluster approach

Motivated by recent experimental and theoretical studies of excitonic insulators, we use the variational cluster approximation to calculate the single-particle Green's function and anomalous Green's function of the Falicov-Kimball model extended by including a finite valence bandwidth. We thus determine the single-particle excitation gap due to the bound-state formation of an electron and a hole. We also evaluate the order parameter of the excitonic insulating state indicating quantum coherence of condensed excitons. We thereby discuss the excitonic insulator that typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate of preformed excitons (strong-coupling regime). A BCS-BEC crossover of the model thus manifests itself as a function of the Coulombic coupling strength.

Variational cluster approach to the extended Falicov-Kimball model: A BCS-BEC crossover in the Excitonic insulators

We study the Coulomb-interaction induced spontaneous symmetry breaking of the excitonic insulator state in the two-dimensional extended Falicov-Kimball model. Using the variational cluster approximation, we evaluate the order parameter, single-particle excitation gap, momentum distribution functions, and anomalous Green's function as a function of U at zero temperature. We find that in the weak-to-intermediate couplinb regime, the Fermi surface is well-defined and the calculated results can be understood in the close correspondence with the BCS theory, whereas in the strong-coupling regime, the Fermi surface is ill-defined and the results are consistent with the picture of BEC.

Publisher's Note: Collective excitations and stability of the excitonic phase in the extended Falicov-Kimball model [Phys. Rev. B86, 155134 (2012)

Publisher's Note: Collective excitations and stability of the excitonic phase in the extended Falicov-Kimball model [Phys. Rev. B<b>86</b>, 155134 (2012)

Collective excitations and stability of the excitonic phase in the extended Falicov-Kimball model

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).

Electron-hole pair condensation at the semimetal-semiconductor transition: A BCS-BEC crossover scenario

We act on the suggestion that an excitonic insulator state might separate---at very low temperatures---a semimetal from a semiconductor and ask for the nature of these transitions. Based on the analysis of electron-hole pairing in the extended Falicov-Kimball model, we show that tuning the Coulomb attraction between both species, a continuous crossover between a BCS-like transition of Cooper-type pairs and a Bose-Einstein condensation of preformed tightly-bound excitons might be achieved in a solid-state system. The precursor of this crossover in the normal state might cause the transport anomalies observed in several strongly correlated mixed-valence compounds.

Nonlocal Coulomb interaction in the two-dimensional spin-1/2 Falicov–Kimball model

The two-dimensional (2D) extended Falicov–Kimball model has been studied to observe the role of nonlocal Coulomb interaction (Unc) using an exact diagonalization technique. The f-state occupation (nf), the f–d intersite correlation function (cfd), the specific heat (C), entropy (S) and the specific heat coefficient (γ) have been examined. Nonlocal Coulomb interaction-induced discontinuous insulator-to-metal transition occurs at a critical f-level energy. More ordered state is obtained with the increase of Unc. In the specific heat curves, two-peak structure as well as a single-peak structure appears. At low-temperature region, a sharp rise in the specific heat coefficient γ is observed. The peak value of γ shifts to the higher temperature region with Unc.

BCS-BEC crossover in the extended Falicov-Kimball model: Variational cluster approach

We study the spontaneous symmetry breaking of the excitonic insulator state induced by the Coulomb interaction $U$ in the two-dimensional extended Falicov-Kimball model. Using the variational cluster approximation (VCA) and Hartree-Fock approximation (HFA), we evaluate the order parameter, single-particle excitation gap, momentum distribution functions, coherence length of excitons, and single-particle and anomalous excitation spectra, as a function of $U$ at zero temperature. We find that in the weak-to-intermediate coupling regime, the Fermi surface plays an essential role and calculated results can be understood in close correspondence with the BCS theory, whereas in the strong-coupling regime, the Fermi surface plays no role and results are consistent with the picture of BEC. Moreover, we find that HFA works well both in the weak- and strong-coupling regime, and that the difference between the results of VCA and HFA mostly appears in the intermediate-coupling regime. The reason for this is discussed from a viewpoint of the self-energy. We thereby clarify the excitonic insulator state that typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate of preformed excitons (strong-coupling regime).

Slave-boson field fluctuation approach to the extended Falicov-Kimball model: Charge, orbital, and excitonic susceptibilities

Based on the $\mathrm{SO}(2)$-invariant slave-boson scheme, the static charge, orbital, and excitonic susceptibilities in the extended Falicov--Kimball model are calculated. Analyzing the phase without long-range order, we find instabilities toward charge order, orbital order, and the excitonic insulator (EI) phase. The instability toward the EI is in agreement with the saddle-point phase diagram. We also evaluate the dynamic excitonic susceptibility, which allows the investigation of uncondensed excitons. We find qualitatively different features of the exciton dispersion at the semimetal-EI and at the semiconductor-EI transition supporting a crossover scenario between a BCS-type electron-hole condensation and a Bose--Einstein condensation of preformed bound electron-hole pairs.

Metal-insulator transition caused by coupling to localized charge-frustrated systems under ice-rule local constraint

We report the results of our theoretical and numerical study on electronic and transport properties of fermion systems with charge frustration. We consider an extended Falicov-Kimball model in which itinerant spinless fermions interact repulsively by U with localized particles whose distribution satisfies a local constraint under geometrical frustration, the so-called ice rule. We numerically calculate the density of states, optical conductivity, and inverse participation ratio for the models on the pyrochlore, checkerboard, and kagome lattices, and discuss the nature of metal-insulator transitions at commensurate fillings. As a result, we show that the ice-rule local constraint leads to several universal features in the electronic structure; a charge gap opens at a considerably small U compared to the bandwidth, and the energy spectrum approaches a characteristic form in the large U limit, that is, the noninteracting tight-binding form in one dimension or the $\delta$-functional peak. In the large U region, the itinerant fermions are confined in the macroscopically-degenerate ice-rule configurations, which consist of a bunch of one-dimensional loops: We call this insulating state the charge ice. On the other hand, transport properties are much affected by the geometry and dimensionality of lattices; e.g., the pyrochlore lattice model exhibits a transition from a metallic to the charge-ice insulating state by increasing U, while the checkerboard lattice model appears to show Anderson localization before opening a gap. Meanwhile, in the kagome lattice case, we do not obtain clear evidence of Anderson localization. Our results elucidate the universality and diversity of phase transitions to the charge-ice insulator in fully frustrated lattices.

Role of correlated hopping in mixed valence phenomena

Role of correlated hopping is studied using extended Falicov–Kimball model in a small cluster. A discontinuous insulator-to-metal transition is observed at a critical f-level energy. Transition is sharper for larger correlated hopping. In the specific heat curves a two-peak structure consisting of a sharp peak followed by a Schottky-type broad peak is exhibited. In a limited parameter region, some heavy-fermion like characteristics have been observed.

Competing chiral and multipolar electric phases in the extended Falicov-Kimball model

We study the effects of interband hybridization within the framework of an extended Falicov-Kimball model with itinerant $c$ and $f$ electrons. An explicit interband hybridization breaks the U(1) symmetry associated with the conservation of the difference between the total number of particles in each band. As a result, the degeneracy between multipolar electric and chiral orderings is lifted. We analyze the weak- and strong-coupling limits of the $c$-$f$ electron Coulomb interaction at zero temperature, and derive the corresponding mean-field quantum phase diagrams at half-filling for a model defined on a square lattice.

A ground state phase diagram of a spinless, extended Falicov–Kimball model on thetriangular lattice

Correlated systems with hexagonal layered structures have come to thefore with renewed interest in cobaltates, transition metal dichalcogenides andGdI2. While superconductivity, unusual metal and possible exotic states (prevented fromlong-range order by strong local fluctuations) appear to come from frustration andcorrelation working in tandem in such systems, they freeze at a lower temperature tocrystalline states. The underlying effective Hamiltonian in some of these systems is believedto be the Falicov–Kimball model and therefore, a thorough study of the ground state ofthis model and its extended version on a non-bipartite lattice is important. Using a MonteCarlo search algorithm, we identify a large number of different possible ground states withcharge order as well as valence and metal–insulator transitions. Such competing states,close in energy, give rise to complex charge order and other broken symmetry structures aswell as the phase segregations observed in the ground state of these systems.

Quantum Melting of Charge Ice and Non-Fermi-Liquid Behavior: An Exact Solution for the Extended Falicov-Kimball Model in the Ice-Rule Limit

An exact solution is obtained for a model of itinerant electrons coupled to ice-rule variables on the tetrahedron Husimi cactus, an analogue of the Bethe lattice of corner-sharing tetrahedra. It reveals a quantum critical point with the emergence of non-Fermi-liquid behavior in melting of the "charge ice" insulator. The electronic structure is compared with the numerical results for the pyrochlore-lattice model to elucidate the physics of electron systems interacting with the tetrahedron ice rule.

Spectral signatures of the BCS-BEC crossover in the excitonic insulator phase of the extended Falicov-Kimball model

We explore the spontaneous formation of an excitonic insulator state at the semimetal-semiconductor transition of mixed-valence materials in the framework of the spinless Falicov-Kimball model with direct $f$-$f$ electron hopping. Adapting the projector-based renormalization method, we obtain a set of renormalization differential equations for the extended Falicov-Kimball model parameters and finally derive analytical expressions for the order parameter, as well as for the renormalized $c$- and $f$-electron dispersions, momentum distributions, and wave-vector resolved single-particle spectral functions. Our numerical results proved the valence transition picture, related to the appearance of the excitonic insulator phase, in the case of overlapping $c$ and $f$ bands. Thereby the photoemission spectra show significant differences between the weak-to-intermediate and intermediate-to-strong Coulomb attraction regimes, indicating a BCS-BEC transition of the excitonic condensate.