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

Abstract

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....

Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings

“…From the theoretical side, the extended FalicovKimball model was considered as a paradigmatic model to describe the EI formation and the closely related phenomenon of electronic ferroelectricity [30][31][32][33][34][35][36][37][38][39][40][41] . Here the spin degrees of freedom were not taken into account, however.…”

Exciton Condensation and Superfluidity in TmSe<sub>0.45</sub>Te<sub>0.55</sub>

“…Extensively discussed has also been an effective mass model [26] with large differences between electron and hole mass, just as we proposed above. In a further paper [27] it has been shown, that weakly overlapping Frenkel type excitons can condense. Especially the coupling of excitons with phonons has been discussed in Ref.…”

Excitonic Insulator State of the Extended Falicov–Kimball Model in the Cluster Dynamical Impurity Approximation

“…[33][34][35][36][37][38][39][40][41] Assuming a two-dimensional square lattice, we define the Hamiltonian of the EFKM as…”

“…With increasing U from the noninteracting semimetallic state, the EI state shows a smooth crossover from the weak-coupling BCS state to the strong-coupling BEC state. [36][37][38][39] Thus, the EFKM is used to discuss the BCS-BEC crossover of the excitonic condensation.…”

“…The spinless extended Falicov-Kimball model (EFKM) is the simplest lattice model for describing the excitonic phases, and has been used to discuss, for example, the BCS-BEC crossover of the excitonic condensation. [33][34][35][36][37][38][39][40][41] The multiband Hubbard model, taking into account the spin de- * ohta@faculty.chiba-u.jp grees of freedom, has also been used to discuss, for example, the relative stability of the spin-singlet and spintriplet excitonic phases. [42][43][44][45][46][47][48][49] We have so far studied the excitonic phases of the EFKM and multiband Hubbard models using the variational cluster approximation (VCA) based on the exact diagonalization of small clusters.…”