We explore the spontaneous formation of an excitonic insulator state at the semimetalsemiconductor transition of mixed-valence materials in the framework of the spinless Falicov-Kimball model with direct f -f electron hopping. Adapting the projector-based renormalization method, we obtain a set of renormalization differential equations for the extended Falicov-Kimball model parameters and finally derive analytical expressions for the order parameter, as well as for the renormalized c-and f -electron dispersions, momentum distributions, and wave-vector resolved single-particle spectral functions. Our numerical results proved the valence transition picture, related to the appearance of the excitonic insulator phase, in the case of overlapping c and f bands. Thereby the photoemission spectra show significant differences between the weak-to-intermediate and intermediateto-strong Coulomb attraction regimes, indicating a BCS-BEC transition of the excitonic condensate.

We show that the coupling to vibrational degrees of freedom can drive a semimetal excitonicinsulator quantum phase transition in an one-dimensional two-band f -c electron system at zero temperature. The insulating state typifies an excitonic condensate accompanied by a finite lattice distortion. Using the projector-based renormalization method we analyze the ground-state and spectral properties of the interacting electron-phonon model at half-filling. In particular we calculate the momentum dependence of the excitonic order parameter function and determine the finite critical interaction strength for the metal-insulator transition to appear. The electron spectral function reveals the strong hybridization of f -and c-electron states and the opening of a singleparticle excitation gap. The phonon spectral function indicates that the phonon mode involved in the transition softens (hardens) in the adiabatic (non-adiabatic and extreme anti-adiabatic) phonon frequency regime.

PACS 71.10.Li -Excited states and pairing interactions in model systems PACS 71.35.-y -Excitons and related phenomena PACS 71.30.+h -Metal-insulator transitions and other electronic transitionsAbstract. -Using the projector-based renormalization method we investigate the formation of the excitonic insulator phase in the two-dimensional (2D) spinless Falicov-Kimball model with dispersive f electrons and address the existence of excitonic bound states at high temperatures on the semiconductor side of the semimetal-semiconductor transition. To this end we calculate the imaginary part of the dynamical electron-hole pair susceptibility and analyze the wave-vector and energy dependence of excitonic resonances emerging in the band gap. We thereby confirm the existence of the exciton insulator and its exciton environment within a generic two-band lattice model with local Coulomb attraction.

We report a theoretical study of the many-body effects of electron-electron interaction on the ground-state and spectral properties of double-layer graphene. Using a projector-based renormalization method we show that if a finite-voltage difference is applied between the graphene layers, electron-hole pairs can be formed and-at very low temperatures-an excitonic instability might emerge in a double-layer graphene structure. The single-particle spectral function near the Fermi surface exhibits a prominent quasiparticle peak, different from neutral (undoped) graphene bilayers. Away from the Fermi surface, we find that the charge carriers strongly interact with plasmons, thereby giving rise to a broad plasmaron peak in the angle-resolved photoemission spectrum. 2 1. MotivationGraphene-based structures are most likely the building blocks of future nanoelectronic devices. The reasons for this are manifold, but one may highlight that many of the exceptional properties of this new class of low-dimensional materials, which arise from the special form of the energy spectrum near the so-called Dirac nodal points and the related non-trivial topological structure of the wave function, can be easily modified by the application of external electric and magnetic fields, as well as by confining the sample geometry, by chemical doping or by edge functionalization and substrate manipulation; for recent reviews see [1][2][3].Single-layer graphene (SLG) [4,5], a truly two-dimensional (2D) crystal with remarkable mechanical properties, can be considered to be a gapless semiconductor with zero density of states at the Fermi level and a linear energy dispersion close to the (inequivalent) corners of the Brillouin zone (K, K Dirac points). Thus the low-energy electrons are massless, chiral Dirac fermions. As a consequence, any backscattering is suppressed and the charge carriers are almost insensitive to disorder and electron-electron interactions. Bilayer graphene (BLG) [6,7], consisting of two AB-stacked, chemically bound graphene monolayers, is also a zero-gap semiconductor, if unbiased, but with a parabolic band dispersion. That is, in this material the low-energy electrons acquire a finite quasiparticle mass. Interestingly, there exists another physical realization of a graphene-based double-layer structure that can be fabricated: in this system-usually referred to as a graphene bilayer or double-layer graphene (DLG)-the two graphene sheets are separated by a dielectric so that the tunneling between the layers can be neglected [8][9][10][11].In BLG and DLG, the charge carrier concentration can be controlled by the simple application of a gate voltage [7,12]. This electric field effect is fundamental for potential technological applications. For BLG even the band structure might be manipulated by an electric field, so that a gap between the valence and conduction bands varies between zero and midinfrared energies [13].BLG, besides being at present the only known semiconductor with a tunable band gap, is intriguing also from a many-p...