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.PACS numbers: 71.30.+h, 71.35.Lk The challenging suggestion of electron-hole pair condensation in thermal equilibrium into the excitonic insulator (EI) phase at the semimetal (SM) to semiconductor (SC) transition 1 , where the SM-EI transition may be described in analogy with BCS theory of superconductivity and the SC-EI transition is discussed in terms of a BoseEinstein condensation (BEC) of preformed excitons 2-4 , is of topical interest. This is due to the growing amount of experimental data on materials which are candidates for the realization of the EI, where different situations with respect to the SM/SC-EI transition are given. For example, in the rare-earth chalcogenide TmSe 0.45 Te 0.55 , that is, an intermediate-valent SC, the pressure-induced resistivity anomaly at low temperatures was ascribed to exciton formation and a subsequent SC-EI transition 5-8 . An EI state in semiconducting Ta 2 NiSe 5 was recently probed by photoemission 9 . On the other hand, in the layered transition-metal dichalcogenide 1T -TiSe 2 , which is a SM, a BCS-like electron-hole pairing was considered as the driving force for the periodic lattice distortion 10 . Here evidence suggests electron-hole 'Cooper-pair' fluctuations above the SM-EI transition temperature. A BCSlike electron-hole pair condensation was also studied for graphene bilayers 11 . In this system a BCS-BEC crossover might be realized by a magnetic field that creates a gap and magneto-excitons which may condense. From a theoretical point of view, one of the main issues in this field is the better understanding and a detailed description of the normal phase above the SM/SC-EI transition, especially of the electron-hole pair fluctuations and of the BCS-BEC crossover scenario 12 that characterizes the EI instability and has not been observed in a solid so far.In this Rapid Communication we address this topic and the mechanisms behind in terms of a minimal two-band model, the so-called extended Falicov-Kimball model (EFKM) 3,13,14 which covers direct c-and f -band hopping and admits the pairing of c electrons with f holes via a strongly screened Coulomb interaction. Thereby we focus on the normal phase that surrounds the EI and look for precursor effects in the electron-hole pair susceptibility. In particular we analyze the nature of the electronhole bound states and determine their number and spectral weight....
We re-examine the three-dimensional spinless Falicov-Kimball model with dispersive f electrons at half-filling, addressing the dispute about the formation of an excitonic condensate, which is closely related to the problem of electronic ferroelectricity. To this end, we work out a slave-boson functional integral representation of the suchlike extended Falicov-Kimball model that preserves the SO(2) ⊗ U (1) ⊗2 invariance of the action. We find a spontaneous pairing of c electrons with f holes, building an excitonic insulator state at low temperatures, also for the case of initially nondegenerate orbitals. This is in contrast to recent predictions of scalar slave-boson mean-field theory but corroborates previous Hartree-Fock and RPA results. Our more precise treatment of correlation effects, however, leads to a substantial reduction of the critical temperature. The different behavior of the partial densities of states in the weak and strong inter-orbital Coulomb interaction regimes supports a BCS-BEC transition scenario.
The influence of phonons on the formation of the excitonic insulator has hardly been analyzed so far. Recent experiments on Ta2NiSe5, 1T -TiSe2, and TmSe0.45Te0.55, being candidates for realizing the excitonic-insulator state, suggest, however, that the underlying lattice plays a significant role. Employing the Kadanoff-Baym approach we address this issue theoretically. We show that owing to the electron-phonon coupling a static lattice distortion may arise at the excitonic instability. Most importantly such a distortion will destroy the acoustic phase mode being present if the electron-hole pairing and condensation is exclusively driven by the Coulomb interaction. The absence of offdiagonal long-range order, when lattice degrees of freedom are involved, challenges that excitons in these materials form a superfluid condensate of Bose particles or Cooper pairs composed of electrons and holes.
We address the question of the origin of the recently discovered chiral property of the charge-10 density-wave phase in 1T -TiSe2 which so far lacks a microscopic understanding. We argue that the 11 lattice degrees of freedom seems to be crucial for this novel phenomenon. We motivate a theoretical 12 model that takes into account one valence and three conduction bands, a strongly screened Coulomb 13 interaction between the electrons, as well as the coupling of the electrons to a transverse optical 14 phonon mode. The Falicov-Kimball model extended in this way possesses a charge-density-wave 15 state at low temperatures, which is accompanied by a periodic lattice distortion. The charge ordering 16 is driven by a lattice deformation and electron-hole pairing (excitonic) instability in combination. 17We show that both electron-phonon interaction and phonon-phonon interaction must be taken into 18 account at least up to quartic order in the lattice displacement to achieve a stable chiral charge order. 19The chiral property is exhibited in the ionic displacements. Furthermore, we provide the ground- Obviously the pattern (c) describes an anticlockwise CDW: That is, for a chiral CDW mirror symmetry is broken.
We analyze the stability of excitonic ground states in the two-band Hubbard model with additional electron-phonon and Hund's rule couplings using a combination of mean-field and variational cluster approaches. We show that both the interband Coulomb interaction and the electron-phonon interaction will cooperatively stabilize a charge density wave (CDW) state which typifies an "excitonic" CDW if predominantly triggered by the effective interorbital electron-hole attraction or a "phononic" CDW if mostly caused by the coupling to the lattice degrees of freedom. By contrast, the Hund's rule coupling promotes an excitonic spin density wave. We determine the transition between excitonic charge and spin density waves and comment on a fixation of the phase of the excitonic order parameter that would prevent the formation of a superfluid condensate of excitons. The implications for exciton condensation in several material classes with strongly correlated electrons are discussed.
Based on the 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.
We study the effects of interband hybridization within the framework of an extended FalicovKimball 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.
We show that double-layer graphene (DLG), where an external potential induces a charge imbalance between n-and p-type layers, is a promising candidate to realize an exciton condensate in equilibrium. To prove this phenomenon experimentally, we suggest coupling two DLG systems, separated by a thin insulating barrier, and measuring the excitonic Josephson effect. For this purpose we calculate the ac and dc Josephson currents induced by tunneling excitons and show that the former only occurs when the gate potentials of the DLG systems differ, irrespective of the phase relationship of their excitonic order parameters. A dc Josephson current develops if a finite order-parameter phase difference exists between two coupled DLG systems with identical gate potentials. The search for the long ago predicted excitonic insulator (EI) state has recently stimulated a lot of experimental work, e.g., on pressure sensitive rare-earth chalgogenides, transitionmetal dichalcogenides, or tantalum chalcogenides [1][2][3][4][5]. Theoretically the excitonic instability is expected to happen, when semimetals with very small band overlap or semiconductors with very small band gap are cooled to very low temperatures [6,7]. To date there exists no free of doubt realization of the EI, however, and even the applicability of the original EI scenario to the above material classes is a controversial issue [5,[8][9][10]. There are serious arguments why the EI in these bulk materials, if present at all, resembles rather a charge-density-wave state than a "true" superfluid exciton condensate exhibiting off-diagonal long-range order [11,12].On these grounds a nonambiguous experimental proof of a macroscopic phase coherent exciton condensate would be highly desirable. Spectroscopic analyses have not established an exciton condensate so far. The characteristics of junction devices, where at least in one component an EI is realized, may lead to valuable insights in this respect [13]. Due to the proximity effect a high resistance should appear across a semimetal-EI junction that distinctly differs from that of a semimetal-semiconductor device [14]. In coupled quantum wells, Josephson oscillations should accompany exciton condensation [15,16]. Here we will pursue a similar idea, namely, that a Josephson-type tunnel current might appear when two EI systems are coupled to each other by a thin insulating barrier such that coherence is established between the condensates. Two-layer systems of spatially separated electrons and holes that feature an attractive interlayer electron-hole coupling are particularly suitable for a Josephson-type tunnel experiment. In this case a condensate of excitons might occur when the tunneling between the layers is negligible, but the corresponding Coulomb interaction is not [17]. Double-layer systems thereby inhibit the obstacles coming from interband transitions or the coupling to phonons, which inevitably occur in bulk materials and prevent a possible exciton condensation by destroying the U (1) symmetry [12,18,19]. It is al...
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