One of the keys to the high-temperature superconductivity puzzle is the identification of the energy scales associated with the emergence of a coherent condensate of superconducting electron pairs. These might provide a measure of the pairing strength and of the coherence of the superfluid, and ultimately reveal the nature of the elusive pairing mechanism in the superconducting cuprates. To this end, a great deal of effort has been devoted to investigating the connection between the superconducting transition temperature Tc and the normal-state pseudogap crossover temperature T * . Here we present a review of a large body of experimental data that suggests a coexisting two-gap scenario, i.e. superconducting gap and pseudogap, over the whole superconducting dome.

Library of Congress Cataloging-in-Publication Data. Hiifner, Stefan, 1935-. Photoelectron spectroscopy: principles and applications/Stefan Hiifner. p. em.-(Springer series in solid-state sciences; 82) Includes bibliographical references and index.

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We present a comprehensive theoretical investigation of the electron-phonon contribution to the lifetime broadening of the surface states on Cu(111) and Ag(111), in comparison with high-resolution photoemission results. The calculations, including electron and phonon states of the bulk and the surface, resolve the relative importance of the Rayleigh mode, being dominant for the lifetime at small hole binding energies. Including the electron-electron interaction, the theoretical results are in excellent agreement with the measured binding energy and temperature dependent lifetime broadening. Understanding the temporal evolution of quasi particles (electron and holes) on metal surfaces is of paramount importance to describe many important phenomena such as the dynamics of charge and energy transfer, quantum interference, localization and many others. This temporal evolution is characterized by a finite lifetime, τ , which refers to the time the quasi particle retains its identity. While the lifetime of an excited electron or hole is determined by many-body interactions, namely electron-electron (e-e) and electron-phonon (e-p) scattering processes, the peak width in an experiment might also be influenced by electron-defect scattering on crystal or surface imperfections [1]. However, it was demonstrated in recent STM [2] and photoemission experiments [3] that these defect contributions can be minimized, making it possible to analyze the pure lifetime broadening due to the formation of a hole in the sp surface state band in the L-gap of the (111)-surface of noble metals.These Shockley-type surface states form a twodimensional (2D) electron gas and the e-e contribution to the hole lifetime has been rationalized in terms of a dominant contribution from intraband transitions within the 2D surface state band, screened by the underlying 3D bulk electron system, and in terms of interband transitions (bulk states → surface state) [2]. On the other hand an appropriate calculation of the e-p contribution to the lifetime broadening of surface states is still lacking. The present work is an attempt in this direction.The strength of the e-p coupling is described by the electron mass enhancement parameter λ, which is, in general, energy and momentum dependent. Many properties of metals [4], such as resistivity, specific heat and superconductivity, reflect the e-p coupling and can be expressed in terms of the Fermi surface-averaged λ-value. It also reflects the high temperature behavior of the broadening Γ ep = 2πλk B T , and the e-p contribution to the renormalization of the mass m * = m(1 + λ). The anisotropy of λ is well known [5] and is revealed in e.g. cyclotron resonance measurements [6].Typically, the phonon contribution to the decay of surface states is estimated using the Debye phonon model. Within this model the Eliashberg spectral function of the e-p interaction is proportional to the quadratic density of phonon states α 2 F (ω) = λ(ω/ω D ) 2 , where ω D is the Debye energy, λ is usually obtained from measurements or th...