F. Marsiglio

Pairing in the Holstein model in the dilute limit

Abstract The Holstein model in one dimension is examined using a variety of techniques, i.e. exact diagonalization, perturbation theory, and the adiabatic approximation. In agreement with other authors we find that the model is polaronic for all coupling strengths. In the case of two electrons we examine the regimes under which binding occurs. We find that binding decreases as the phonon frequency increases, for a given coupling strength. We provide a numerical verification for the effect of retardation, which gives rise to the well-known pseudopotential effect.

Electron - Phonon Superconductivity

A fairly sophisticated description of electron-phonon superconductivity has existed since the early 1960’s, following the work of Eliashberg [1], Nambu [2], Morel and Anderson [3], and Schrieffer et al. [4]. All of this work extended the original ideas of Bardeen, Cooper, and Schrieffer [5] on superconductivity, to include dynamical phonon exchange as the root cause of the effective attractive interaction between electrons in a metal. For certain superconducting materials, Eliashberg theory (as this description is generally called) provides a very accurate description of the superconducting state. Nonetheless, as B.T. Matthias was fond of iterating [6], this description was never considered (by him and others) particularly helpful for discovering new, high temperature superconductors [7]. Part of the problem remains that a truly accurate description of the normal state has not been forthcoming. Part of that problem is the “curse” of Fermi Liquid Theory. To the extent that the electron-phonon coupling causes relatively innocuous corrections to most normal state properties, its underlying characteristics remain undetectable (indeed, as will be reviewed here, the characteristics of the electron-phonon interaction are made more apparent in the superconducting state). An exception may be the A15 compounds, whose anomalous normal state properties might help us achieve further understanding of the electron-phonon interaction in these materials [10].

Optical sum rule violation, superfluid weight and condensation energy in the cuprates

The model of hole superconductivity predicts that the superfluid weight in the zero-frequency δ-function in the optical conductivity has an anomalous contribution from high frequencies, due to lowering of the system’s kinetic energy upon entering the superconducting state. The lowering of kinetic energy, mainly in-plane in origin, accounts for both the condensation energy of the superconductor as well as an increased potential energy due to larger Coulomb repulsion in the paired state. It leads to an apparent violation of the conductivity sum rule, which in the clean limit we predict to be substantially larger for in-plane than for c-axis conductivity. However, because cuprates are in the dirty limit for c-axis transport, the sum rule violation is found to be greatly enhanced in the c-direction. The model predicts the sum rule violation to be largest in the underdoped regime and to decrease with doping, more rapidly in the c-direction that in the plane. So far, experiments have detected sum rule violation in c-axis transport in several cuprates, as well as a decrease and disappearance of this violation for increasing doping, but no violation in-plane. We explore the predictions of the model for a wide range of parameters, both in the absence and in the presence of disorder, and the relation with current experimental knowledge.

INVERSION OF K3C60 REFLECTANCE DATA

Abstract We outline a procedure for obtaining the electron-phonon spectral density by inversion of optical conductivity data, a process very similar in spirit to the McMillan-Rowell inversion of tunelling data. We assume both electron-impurity (elastic) and electron-phonon (inelastic) scattering processes. This procedure has the advantage that it can be utilized in the normal state. Furthermore, a very good qualitative result can be obtained explicitly , without iteration. We illustrate this technique on recently acquired far-infrared data in K 3 C 60 . We show that the electron-phonon interaction is most likely responsible for superconductivity in these materials.

On the dependence of superconducting Tc on carrier concentration

Abstract A striking similarity exists between the dependence of T c on carrier concentration in transition metal alloys and in oxide superconductors. Such a dependence follows naturally from a mechanism of superconductivity based on pairing of hole carriers through Coulomb interactions.

Modification of ensemble emission rates and luminescence spectra for inhomogeneously broadened distributions of quantum dots coupled to optical microcavities

We investigate the spontaneous emission modifications when ensembles of quantum dots (QDs) with differing emission frequencies and finite Lorentzian linewidths are coupled to a microcavity. Using contour integrals we develop a general expression for the rate enhancement when neither the emitter nor the cavity resonance can be treated as a delta function. We show that the ensemble cavity-coupled luminescence lifetimes are generally suppressed in the case of spherical cavities and that the spontaneous emission dynamics of the cavity coupled component becomes increasingly stretched as the coupling factor increases. The Q-factor measured from the luminescence spectrum can be much lower than the intrinsic cavity Q-factor, and is in many practical situations limited by the QD spectral width. The mode spectrum observed in the photoluminescence (PL) spectrum can be largely determined by the QD emission linewidth, permitting this parameter to be extracted without requiring single-particle spectroscopy. In the case of Si-QDs, the linewidth cannot be significantly greater than 10 meV in order to observe spherical cavity resonances in the PL spectrum.

Optical study of electronic structure and electron-phonon coupling in ZrB12

We report optical (6 meV - 4 eV) properties of a boride superconductor ZrB

Hole superconductivity: Review and some new results

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Doping dependence of the redistribution of optical spectral weight in Bi2Sr2CaCu2O8+δ

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Tunneling asymmetry: A test of superconductivity mechanisms

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