J. Ranninger

Superconductivity of locally paired electrons

Abstract Phonon mediated superconductivity is examined in two extreme limits: the weak coupling BCS strong coupling bi-polaronic behaviour. The difference in excitation spectra between those two forms of superconductivity and the thermodynamic properties resulting from them are discussed. A model of coexisting bi-polarons and free electron pairs is proposed for intermediate electron-lattice coupling and the phase diagram for the model is presented.

Nonlinear feedback effects in coupled boson-fermion systems

We address ourselves to a class of systems composed of two coupled subsystems without any intra-subsystem interaction: itinerant Fermions and localized Bosons on a lattice. Switching on an interaction between the two subsystems leads to feedback effects which result in a rich dynamical structure in both of them. Such feedback features are studied on the basis of the flow equation technique - an infinite series of infinitesimal unitary transformations - which leads to a gradual elimination of the inter-subsystem interaction. As a result the two subsystems get decoupled but their renormalized kinetic energies become mutually dependent on each other. Choosing for the inter - subsystem interaction a charge exchange term (the Boson-Fermion model) the initially localized Bosons acquire itinerancy through their dependence on the renormalized Fermion dispersion. This latter evolves from a free particle dispersion into one showing a pseudogap structure near the chemical potential. Upon lowering the temperature both subsystems simultaneously enter a macroscopic coherent quantum state. The Bosons become superfluid, exhibiting a soundwave like dispersion while the Fermions develop a true gap in their dispersion. The essential physical features described by this technique are already contained in the renormalization of the kinetic terms in the respective Hamiltonians of the two subsystems. The extra interaction terms resulting in the process of iteration only strengthen this physics. We compare the results with previous calculations based on selfconsistent perturbative approaches.

DYNAMICAL PROPERTIES OF SMALL POLARONS

On the basis of the two-site polaron problem, which we solve by exact diagonalization, we analyse the spectral properties of polaronic systems in view of discerning localized from itinerant polarons and bound polaron pairs from an ensemble of single polarons. The corresponding experimental techniques for that concern photoemission and inverse photoemission spectroscopy. The evolution of the density of states as a function of concentration of charge carriers and strength of the electron-phonon interaction clearly shows the opening up of a gap between single polaronic and bi-polaronic states, in analogy to the Hubbard problem for strongly correlated electron systems. The crossover regime between adiabatic and anti-adiabatic small polarons is triggered by two characteristic time scales: the renormalized electron hopping rate and the renormalized vibrational frequency becoming equal. This crossover regime is then characterized by temporarily alternating self- localization and delocalization of the charge carriers which is accompanied by phase slips in the charge and molecular deformation oscillations and ultimately leads to a dephasing between these two dynamical components of the polaron problem. We visualize these features by a study of the temporal evolution of the charge redistribution and the change in molecular deformations. The spectral and dynamical properties of polarons discussed here are beyond the applicability of the standard Lang Firsov approach to the polaron problem.

Manifestations of the pseudogap in the boson-fermion model for Bose-Einstein-condensation-driven superconductivity.

In the boson-fermion model for short-coherence-length superconductors, a pseudogap opens up in the density of states of the fermions as the temperature is lowered towards the superconducting transition temperature. For a two-dimensional square lattice we study here the effects of this phenomenon on the specific heat, the NMR relaxation rate, and the optical conductivity within a fully self-consistent lowest-order diagrammatic theory and compare our results to the experimental situation. {copyright} {ital 1996 The American Physical Society.}

Metal-insulator crossover in the boson-fermion model in infinite dimensions.

The Boson-Fermion model, describing a mixture of tightly bound electron pairs and quasi-free electrons hybridized with each other via a charge exchange term, is studied in the limit of infinite dimensions, using the Non-Crossing Approximation within the Dynamical Mean Field Theory. It is shown that a metal-insulator crossover, driven by strong pair fluctuations, takes place as the temperature is lowered. It manifests itself in the opening of a pseudogap in the electron density of states, accompanied by a corresponding effect in the optical and dc conductivity.

Local dynamical lattice instabilities: Prerequisites for resonant pairing superconductivity

Fluctuating local diamagnetic pairs of electrons, embedded in a Fermi sea, are candidates for non-phonon-mediated superconductors without the stringent conditions on

Interplay between single-particle and collective features in the boson fermion model

{T}_{c}

Hall coefficient and angle-resolved photoemission in systems with strong pair fluctuations

which arise in phonon-mediated BCS classical low-

From local to macroscopic coherence in systems with composite quasiparticles

{T}_{c}

Pseudogap in underdoped high-T{sub c} superconductors in the framework of the boson-fermion model

superconductors. The local accumulations of charge, from which such diamagnetic fluctuations originate, are irrevocably coupled to local dynamical lattice instabilities and form composite charge-lattice excitations of the system. For a superconducting phase to be realized, such excitations must be itinerant spatially phase-coherent modes. This can be achieved by resonant pair tunneling in and out of polaronic cation-ligand sites. Materials in which superconductivity driven by such local lattice instability can be expected have a