Extended Falicov-Kimball Model Research Articles

Influence of magnetic field on the electronic ferroelectricity in the extended Falicov-Kimball model

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 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.

Hartree-Fock exploration of electronic ferroelectricity, valence transitions, and metal-insulator transitions in the extended Falicov-Kimball model

Hartree-Fock exploration of electronic ferroelectricity, valence transitions, and metal-insulator transitions in the extended Falicov-Kimball model

Interplay between superconductivity and charge-order in an extended Falicov-Kimball model under orbital magnetic field

Interplay between superconductivity and charge-order in an extended Falicov-Kimball model under orbital magnetic field

Electron-phonon correlations inducing excitonic excitations in semimetal and semiconducting materials

The influence of phonons on the low-energy excitonic excitations at zero temperature in the extended Falicov-Kimball model has been investigated. In the framework of the unrestricted Hartree-Fock approximation, a set of self-consistent equations for the excitonic condensate order parameter and a lattice distortion is derived when both electron-phonon coupling and electron-hole Coulomb interaction are treated on an equal footing. The low-energy excitation properties of the excitonic condensate are addressed in signatures of the optical conductivity and the dynamical excitonic susceptibility function. The real part of the optical conductivity is evaluated by the Kubo linear response theory and the imaginary part of the dynamical excitonic susceptibility is found by adapting the random phase approximation. In the semimetal state, one always finds a sharp peak in the optical conductivity spectrum indicating the stability of the excitonic condensation in the BCS type if the correlation between electrons and phonons becomes significant. In contrast, the peak is smeared out on the semiconducting side indicating the stability of the BEC-type excitonic condensate. In this semiconducting side, the sharp peak signature appears and the system turns to the BCS-type excitonic condensation state by increasing the electron-phonon correlations. In either the semimetal or the semiconducting normal state, increasing the electron-phonon correlations always reinforces a low-energy sharp peak in the dynamical excitonic susceptibility spectrum, indicating the existence of the tightly bound excitonic excitations before the condensation state. Specifically, on the semiconducting side, the ``halo'' phase with the preformed excitons exiting outside of the BEC-excitonic condensation state has been specified. The halo phase becomes more recognizable by raising the electron-phonon correlations.

Effect of next to next-nearest-neighbor (NNNN) hopping interaction in mixed valence systems and study of the thermodynamic properties

The extended Falicov-Kimball model containing the next to next-nearest-neighbor hopping interaction (NNNN) is investigated using the exact diagonalization calculations in two dimensions. The f-electron density nf with the energy of f-level Ef is investigated using the allowable exact solutions. The temperature dependency of thermodynamical parameters such as specific heat(C) and entropy (S) are also studied here. The significant observations are (i) a discontinuous valence transition (insulator-to-metal) at a certain energy of f-level (Ec ) which varies with the value of NNNN interaction term (t 3), (ii) disorderedness of the system with the increasing value of t 3, (iii) the structures of single and double peaks in the specific heat versus temperature graphs varying with t 3 and E respectively.

Low-energy excitonic condensate excitations in semimetal and semiconducting materials

The low-energy excitation properties of the excitonic condensate in the semimetal and semiconducting materials are inspected in the extended Falicov-Kimball model. In the framework of the unrestricted Hartree-Fock approximation, we have released a set of self-consistent equations so the excitonic condensate order parameter and then the optical conductivity and the dynamical excitonic susceptibility function are evaluated. We find that the optical conductivity becomes significant and shows a sharp peak at a frequency that is twice as of the excitonic condensate order parameter once the system settles in the excitonic condensate. In the meanwhile, out of the excitonic condensation state, the dynamical excitonic susceptibility function in the semimetal state releases a dominant peak at low frequency if Coulomb interaction is sufficiently large. This character indicates the possibility of the resonance bound excitonic condensate even in high-temperature normal semimetals. The resonance is dramatically reinforced inside of the semiconducting state and that specifies the stability of the bound excitonic coherent state of the preformed excitons in the semiconducting materials.

Photoinduced metallization of excitonic insulators

Utilizing the time-dependent density-matrix renormalization group technique, we numerically prove photoinduced pairing states in the extended Falicov-Kimball model (EFKM) at half filling, both with and without internal SU(2) symmetry. In the time-dependent photoemission spectra an extra band appears above the Fermi energy after pulse irradiation, indicating an insulator-to-metal transition. Even in the absence of the SU(2) structure, the pair correlations are enhanced during the pump, and afterwards decrease over time. This implies the possible metallization of Ta$_2$NiSe$_5$, a strong candidate for an excitonic insulator material, for which the EFKM is considered to be the minimal theoretical model. Simulating the photoemission with optimized pulse parameters, we demonstrate a photoinduced quantum phase transition, in accord with recent findings in time- and angle-resolved photoemission spectroscopy experiments on Ta$_2$NiSe$_5$.

Excitonic condensation state in the assistance of the adiabatic and anti-adiabatic phonons

The excitonic condensate in semimetal and semiconducting materials with the assistance of the phonons in both the adiabatic and anti-adiabatic regimes has been investigated. In the framework of the random phase approximation, we analyse the static excitonic susceptibility function once the electrons and holes are described in the extended Falicov–Kimball model involving the electron–phonon interaction. The excitonic condensate transition point is detected as a divergence of the susceptibility function. The complex phase diagrams exhibit the significant impact of the adiabatic phonons on the stability of the excitonic condensation state. In contrast, phonons in the anti-adiabatic regime play a less role in the formation and the condensation of the excitons. Depending on the temperature or the external pressure, the excitonic condensate stability and its Bardeen–Cooper–Schrieffer–Bose–Einstein condensation crossover in the systems are also discussed in detail.

Mass Imbalance Effects in the Excitonic Condensation of the Extended Falicov–Kimball Model

Mass Imbalance Effects in the Excitonic Condensation of the Extended Falicov–Kimball Model

Interplay between Superconductivity and Charge-Order in an Extended Falicov-Kimball Model Under Orbital Magnetic Field

Interplay between Superconductivity and Charge-Order in an Extended Falicov-Kimball Model Under Orbital Magnetic Field

On Some Ground State and Finite Temperature Properties of Mixed-Valence Compounds Induced by Next to Next-Nearest-Neighbor (NNNN) Hopping

In the present study, effects of next to next-nearest-neighbor (NNNN) hopping of delectrons in the crystal of mixed valence compounds has been discussed. For convenient theoretical calculation and computer simulation within exact diagonalization method, a small cluster of eight lattice sites is considered here to investigate the valence transition through the study of the inter-site and on-site f-d correlation functions. Unusual magnetic behavior of mixed valence compounds has also been examined. Antiferromagnetic (AF) order has been developed in the compounds of rare earth elements with the addition of NNNN hopping interaction within the extended Falicov-Kimball model. The extrapolation of the curves of the reciprocal susceptibility (χ−1) intercept at a negative temperature which confirms AF order in the system.

Phase Diagrams of the Excitonic Insulator State: Analyzing the Excitonic Susceptibility

In this paper, the formation of the excitonic insulator state in the rare-earth chalcogenides hasbeen investigated through the extended Falicov-Kimball model. Adapting the unrestricted Hartree-Fockapproximation, we have derived a set of explicitly self-consistent equations determining expectationvalues and the excitonic susceptibility in the system. Analyzing the excitonic susceptibility, we haveestablished phase diagrams of the excitonic insulator state depending on the model parameters. The phasestructures confirmed the excitonic insulator state is found at low temperature and between two criticalvalues of the Coulomb interaction. The effect of the external pressure on the formation of the excitonicinsulator state is also shown.

Mass Imbalance Effects in the Excitonic Condensation of the Extended Falicov–Kimball Model

The ground‐state properties of the excitonic condensation state in the effects of the mass imbalance are discussed in the framework of the spinless extended Falicov–Kimball model, in which the hopping of the f electrons is involved. Using the unrestricted Hartree–Fock approximation, a set of self‐consistent equations are obtained so the excitonic condensate order parameter is determined. In this sense, the real part of the optical conductivity is analytically calculated based on the Kubo formula. Phase diagram releases a complex phase structure of the excitonic condensation state with a strong depression of its Bardeen–Cooper–Schrieffer (BCS)–Bose–Einstein condensation (BEC) crossover in the influence of the mass imbalance. The impression of the mass imbalance affecting the excitonic condensate is also addressed in the signature of the optical conductivity. The finding delivers the natural scenario of the excitonic condensation state applied for a wide range of materials, from transition‐metal dichalcogenides to double‐layer systems such as a semiconductor double quantum well, double‐bilayer graphene, or double‐layer graphene.

Finite-temperature photoemission in the extended Falicov-Kimball model: a case study for Ta$_2$NiSe$_5$

Utilizing the unbiased time-dependent density-matrix renormalization group technique, we examine the photoemission spectra in the extended Falicov-Kimball model at zero and finite temperatures, particularly with regard to the excitonic insulator state most likely observed in the quasi-one-dimensional material Ta_22NiSe_55. Working with infinite boundary conditions, we are able to simulate all dynamical correlation functions directly in the thermodynamic limit. For model parameters best suited for Ta_22NiSe_55 the photoemission spectra show a weak but clearly visible two-peak structure, around the Fermi momenta k\simeq\pm k_{F}k≃±kF, which suggests that Ta_22NiSe_55 develops an excitonic insulator of BCS-like type. At higher temperatures, the leakage of the conduction-electron band beyond the Fermi energy becomes distinct, which provides a possible explanation for the bare non-interacting band structure seen in time- and angle-resolved photoemission spectroscopy experiments.

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

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.

Extended Falicov-Kimball model at weak onsite and intersite Coulomb interactions

We analyze in detail a behavior of the order parameter in the half-filled extended Falicov-Kimball model for small Coulomb interactions (both onsite U and intersite V). The parameter is defined as the difference of localized electron concentrations in both sublattices of the Bethe lattice (in the limit of large coordination number). Using two methods, namely, the dynamic mean field theory and the Hartree-Fock approximation, we found the ranges of U and V for which the anomalous temperature dependence of the order parameter, characterized by the sharp reduction near T ≈ TC /2, occurs (TC is the temperature of the continuous order-disorder transition). In order to quantitatively describe this anomaly, we defined a function that measures the departure of the order parameter dependence from the standard mean-field S=1/2 Ising-like curve. We determined the U-dependent critical value VTC of V above which the anomaly disappears. Indicators of the anomalous behavior of the parameter dependence can be also observed in the temperature dependence of the specific heat.

Extended Falicov–Kimball model: Hartree–Fock vs DMFT approach

In this work, we study the extended Falicov–Kimball model at half-filling within the Hartree–Fock approach (HFA) (for various crystal lattices) and compare the results obtained with the rigorous ones derived within the dynamical mean field theory (DMFT). The model describes a system, where electrons with spin-↓ are itinerant (with hopping amplitude t), whereas those with spin-↑ are localized. The particles interact via on-site U and intersite V density–density Coulomb interactions. We show that the HFA description of the ground state properties of the model is equivalent to the exact DMFT solution and provides a qualitatively correct picture also for a range of small temperatures. It does capture the discontinuous transition between ordered phases at U = 2V for small temperatures as well as correct features of the continuous order–disorder transition. However, the HFA predicts that the discontinuous boundary ends at the isolated-critical point (of the liquid-gas type) and it does not merge with the continuous boundary. This approach cannot also describe properly a change of order of the continuous transition for large V as well as various metal–insulator transitions found within the DMFT.

Finite-Temperature Properties of Excitonic Condensation in the Extended Falicov–Kimball Model: Cluster Mean-Field-Theory Approach

We study the electron-hole pair (or excitonic) condensation in the extended Falicov-Kimball model at finite temperatures based on the cluster mean-field-theory approach, where we make the grand canonical exact-diagonalization analysis of small clusters using the sine-square deformation function. We thus calculate the ground-state and finite-temperature phase diagrams of the model, as well as its optical conductivity and single-particle spectra, thereby clarifying how the preformed pair states appear in the strong-coupling regime of excitonic insulators. We compare our results with experiment on Ta$_2$NiSe$_5$.

Onsite density matrix description of the extended Falicov-Kimball model at finite temperatures

We propose a single-site mean-field description, an analogue of Weiss mean-field theory, suitable for narrow-band systems with correlation-induced hybridisation at finite temperatures. Presently this approach, based on the notion of a fluctuating on-site density matrix (OSDM), is developed for the case of extended Falicov-Kimball model (EFKM). In an EFKM, an excitonic insulator phase can be stabilised at zero temperature. With increasing temperature, the excitonic order parameter (interaction-induced hybridisation on-site, characterised by the absolute value and phase) eventually becomes disordered, which involves fluctuations of both its phase and (at higher T) its absolute value. In order to build an adequate finite-temperature description, it is important to clarify the nature of degrees of freedom associated with the phase and absolute value of the induced hybridisation, and correctly account for the corresponding phase-space volume. We show that the OSDM-based treatment of the local fluctuations indeed provides an intuitive and concise description (including the phase-space integration measure). This allows to describe both the lower-temperature regime where phase fluctuations destroy the long-range order, and the higher temperature crossover corresponding to a decrease of the absolute value of hybridisation. In spite of the rapid progress in the studies of excitonic insulators, a unified picture of this kind has not been available to date. We briefly discuss recent experiments on ${\rm Ta_2 Ni Se_5 }$ and also address the amplitude mode of collective excitations in relation to the measurements reported for 1T--${\rm TiSe_2}$. Both the overall scenario and the theoretical framework are also expected to be relevant in other contexts, including the Kondo lattice model.

Ultrafast nonequilibrium evolution of excitonic modes in semiconductors

We study the time evolution of excitonic states after photo-excitation in the one-dimensional spin-less extended Falicov-Kimball model. Several numerical methods are employed and benchmarked against each other: time-dependent mean-field simulations, the second-Born approximation (2BA) within the Kadanoff-Baym formalism, the generalized Kadanoff-Baym Ansatz (GKBA) implemented with the 2BA and the infinite time-evolving block decimation (iTEBD) method. It is found that the GKBA gives the best agreement with iTEBD and captures the relevant physics. We find that excitations to the particle-hole continuum and resonant excitations of the equilibrium exciton result in a qualitatively different dynamics. In the former case, the exciton binding energy remains positive and the frequency of the corresponding coherent oscillations is smaller than the band gap. On the other hand, resonant excitations trigger a collective mode whose frequency is larger than the band gap. We discuss the origin of these different behaviors by evaluating the nonequilibrium susceptibility using the nonthermal distribution and a random phase approximation. The peculiar mode with frequency larger than the band gap is associated with a partial population inversion with a sharp energy cutoff. We also discuss the effects of the cooling by a phonon bath. We demonstrate the real-time development of coherence in the polarization, which indicates excitonic condensation out of equilibrium.