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 calculate the critical temperature below which an excitonic insulator exists at the pressureinduced semiconductor-semimetal transition. Our approach is based on an effective-mass model for valence and conduction band electrons interacting via a statically screened Coulomb potential. Assuming pressure to control the energy gap, we derive, in the spirit of a BEC-BCS crossover scenario, a set of equations which determines, as a function of the energy gap (pressure), the chemical potentials for the two bands, the screening wave number, and the critical temperature. We (i) show that in leading order the chemical potentials are not affected by the exciton states, (ii) verify that on the strong coupling (semiconductor) side the critical temperatures obtained from the linearized gap equation coincide with the transition temperatures for BEC of non-interacting bosons, (iii) demonstrate that mass asymmetry strongly suppresses BCS-type pairing, and (iv) discuss in the context of our theory recent experimental claims for exciton condensation in TmSe0.45Te0.55.

Motivated by the possibility of pressure-induced exciton condensation in intermediate-valence Tm[Se,Te] compounds we study the Falicov-Kimball model extended by a finite f-hole valence bandwidth. Calculating the Frenkel-type exciton propagator we obtain excitonic bound states above a characteristic value of the local interband Coulomb attraction. Depending on the system parameters coherence between c-and f-states may be established at low temperatures, leading to an excitonic insulator phase. We find strong evidence that the excitonic insulator typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate (BEC) of preformed excitons (strong-coupling regime), which points towards a BCS-BEC transition scenario as Coulomb correlations increase.PACS numbers: 71.28.+d, 71.35.Lk, 71.30.+h, 71.28.+d. 71.27.+a That excitons in solids might condense into a macroscopic phase-coherent quantum state-the excitonic insulator-was theoretically proposed about more than four decades ago 1 , for a recent review see Ref.2. The experimental confirmation has proved challenging, because excitonic quasiparticles are not the ground state but bound electron-hole excitations that tend to decay on a very short timescale. Thus a large number of excitons has to be created, e.g. by optical pumping, with sufficiently long lifetimes as a steady-state precondition for the Bose-Einstein condensate (BEC) realizing process.The obstacles to produce a BEC out of the faroff-equilibrium situation caused by optical excitation might be circumvented by pressure-induced generation of excitons. Hints that pressure-sensitive, narrow-gap semiconducting materials, such as intermediate-valent TmSe 0.45 Te 0.55 , might host an excitonic BEC in solids came from a series of electric and thermal transport measurements. 3 Fine-tuning the excitonic level, by applying pressure, to the level of electrons in the narrow 4f-valence band, excitons can form near the semiconductor semimetal transition in thermodynamical equilibrium and might give rise to collective excitonic phases. A phase diagram has been deduced out of the resistivity, thermal diffusity and heat conductivity data, which contains, below 20 K and in the pressure range between 5 and 11 kbar, a superfluid Bose condensed state. 4 The experimental claims for excitonic condensation in TmSe 0.45 Te 0.55 have been analysed from a theoretical point of view. 5,6 Adapting the standard effective-mass, (statically) screened Coulomb interaction model to the Tm[Se,Te] electron-hole system, the valence-band-hole conduction-band-electron mass asymmetry was found to suppress the excitonic insulator (EI) phase on the semimetallic side, as observed experimentally. But also on the semiconducting side, the EI instability might be prevented-within this model-by either electron-hole liquid phases 6,7 or, at very large electron-hole mass ratios ( 100), by Coulomb crystallization. 8 The effective-mass Mott-Wannier-type exciton model neglects, however, important band structure effec...

Guided by the analogy to Mie scattering of light on small particles we show that the propagation of a Dirac-electron wave in graphene can be manipulated by a circular gated region acting as a quantum dot. Large dots enable electron lensing, while for smaller dots resonant scattering entails electron confinement in quasibound states. Forward scattering and Klein tunneling can be almost switched off for small dots by a Fano resonance arising from the interference between resonant scattering and the background partition.

Several applications of PIC simulations for understanding basic physics phenomena in low-temperature plasmas are presented: capacitive radiofrequency discharges in Oxygen, dusty plasmas and negative ion sources for heating of fusion plasmas. The analysis of these systems based on their microscopic properties as accessible with PIC gives improved insight into their complex behavior. These studies are results of joint efforts over about one decade