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arXiv:2501.09925 · Journal of the Physical Society of Japan

Magnetic-Field Effect on Excitonic Condensation Emergent in Extended Falicov–Kimball Model

Naoya Ohta, Joji Nasu

Published Apr 14, 2025• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.7566/jpsj.94.054702

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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.
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.
Combined effects of correlated electron hopping, electron correlations and orbital magnetic field are studied on ground state properties of spinless Falicov-Kimball model (FKM). Results are obtained for finite size triangular lattice with periodic boundary conditions using numerical diagonalization and Monte-Carlo simulation techniques. It is found that the ground state configurations of electrons strongly depend on correlated electron hopping, onsite Coulomb interaction and orbital magnetic field. Several interesting configurations e.g. regular, segregated, axial and diagonal striped and hexagonal phases are found with change in correlated hopping and magnetic field. Study of density of states reveals that magnetic field induces a metal to insulator transition accompanied by segregated phase to an ordered phase. These results are applicable to the systems of recent interest like GdI2, NaTiO2 and MgV2O4 and can also be seen experimentally in cold atomic set up.
Excitonic condensation and stripe formation are two distinct manifestations of electronic correlations. While excitonic order naturally arises in multi-orbital systems, stripe order is a prominent feature of doped correlated-electron models. Here, we investigate an excitonic analogue of stripe order in the two--orbital Hubbard-Kanamori model on the square lattice, characterized by a spatial modulation of inter-orbital particle-hole coherence and, in the orbital-parity-symmetric limit, spontaneous breaking of a relative orbital Z2\mathbb{Z}_2Z2​ symmetry. Using unrestricted real-space Hartree-Fock calculations complemented by random-phase-approximation instability analysis, we determine how the Kanamori interactions select different excitonic channels. The sign of Hund's exchange controls the spin character of the condensate: ferromagnetic Hund coupling favors triplet excitonic order, whereas antiferromagnetic Hund coupling stabilizes singlet excitonic order. Upon doping, commensurate excitonic density waves develop incommensurate textures, including excitonic stripes and, in the triplet sector, spiral excitonic density waves. We further show that crystal-field splitting strongly reorganizes the excitonic instability by modifying inter-orbital nesting and can stabilize triplet excitonic order even in the absence of pair hopping. Our results establish excitonic stripes as a distinct symmetry-broken state of multi-orbital correlated systems and identify microscopic routes for their stabilization.
We study the effects of a perpendicular magnetic field on the excitonic insulator (EI) phase in the semiconductor regime using an extended planar four-Fermi model. Within the large-NNN approximation, we determine the coupled scalar and excitonic condensates at finite temperature, chemical potential, and magnetic field. The field enhances the EI condensate and raises its critical temperature, providing an excitonic realization of magnetic catalysis, while the scalar condensate remains constant throughout the EI phase. By contrast, the critical chemical potential depends nonmonotonically on the field because of the successive occupation of Landau levels. The magnetic field also shifts the mean-field tricritical point and enlarges the first-order region of the temperature--chemical-potential phase diagram. We further analyze the Hall conductivity and find that increasing the field reduces the number of plateaus and modifies the threshold for a finite Hall response. For the parameters considered, the emergence of the EI condensate is accompanied by a characteristic change in the Hall conductivity, including a field-dependent change of slope near a continuous transition. These results show that the combined phase structure and Hall response can provide complementary signatures of excitonic ordering in planar fermionic systems.
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.