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Journal of Physics Condensed Matter

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

Pavol Farkašovský

Published Nov 10, 2023• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1361-648x/ad0b90

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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.
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.
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 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.
The density matrix renormalization group method is used to examine possibilities of electronic ferroelectricity in the spinless Falicov-Kimball model. The model is studied for a wide range of parameters including weak and strong interactions as well as the symmetric and unsymmetric case. In all examined cases the 〈d+f〉〈{d}^{+}f〉〈d+f〉-expectation value vanishes for vanishing hybridization V, indicating that the spinless Falicov-Kimball model does not allow for a ferroelectric ground state with a spontaneous polarization.
We investigate the effects of magnetic fields on excitonic condensation in the extended Falicov-Kimball model, which is a spinless two-orbital Hubbard model with orbital splitting. In lattice systems under magnetic fields up to several tens of teslas, Zeeman effects on electron spins have been extensively studied, while the impact on orbital motion has often been considered negligible. However, the recent capability to generate ultra-high magnetic fields exceeding 1000 T has renewed interest in understanding their influence on ordered phases in correlated electron systems, beyond spin-related phenomena. To examine these effects, we incorporate a magnetic field into the extended Falicov-Kimball model by introducing the Peierls phase into the transfer integrals, enabling the study of orbital motion. Using the Hartree-Fock approximation, we reveal a nonmonotonic response of the excitonic order parameter to increasing magnetic fields. At sufficiently high fields, the excitonic order is suppressed, resulting in a disordered insulating state characterized by partial occupation of the two orbitals with nonzero Chern numbers. This state is distinct from a fully orbital-polarized configuration. Furthermore, our analysis of an excitonic supersolid phase, in which excitonic and orbital orders coexist, demonstrates that orbital order remains robust under magnetic fields, while excitonic condensation is suppressed. These findings provide insights into the interplay between orbital motion and magnetic fields in multi-orbital correlated electron systems.
The electronic properties of excitonic insulators have been examined precisely in recent years. Pictures of exciton condensation may be applied to the spin-state transition observed in perovskite cobalt oxides. We examine the crystal-field and magnetic-field dependences of spatial spin structures on the basis of the density matrix renormalization group method using an effective model for the one-dimensional two-orbital Hubbard model in strong-coupling limit. We find an excitonic insulating (EI) phase and a spin-state ordering (SSO) phase in the intermediate region between low-spin and high-spin phases. In the EI phase, spin-triplet excitons are spatially fluctuating due to quantum effects, and an incommensurate spin correlation realizes. The analyses of a spin gap and degeneracy of entanglement spectra suggest the realization of the Haldane-like edge state in the EI phase. In the SSO phase, 3-fold or incommensurate SSO structures realize depending on the crystal-field splitting. These structures are stabilized as a result of the competition of exchange interactions between spin states.