Browsing by Author "Aynajian, Pegor"

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Electron-phonon interaction in conventional and unconventional superconductors
(2009) Aynajian, Pegor; Keimer, Bernhard (Prof. Dr.)
Asking most scientists if it is worth to have a closer look at the phonon spectra of conventional superconductors like niobium and lead using inelastic neutron scattering, the answers would be quite discouraging. First of all, there exists the famous microscopic theory of Bardeen, Cooper, and Schrieffer (1957) known as the BCS theory, which explains nearly all aspects of conventional superconductivity. Second, the worldwide interest is oriented towards high temperature superconductivity in cuprates and heavy fermion systems. Thus the first experiments of this thesis, which addressed the phonon linewidths of superconducting niobium and lead, were only intended as a short testbed of the resolution properties of a new high-resolution neutron spectrometer at the research reactor FRM II. This new generation spectrometer, TRISP (triple axis spin echo), allows us to measure phonon linewidths over large parts of the momentum space, with a resolution in the sub micro-eV range, i.e., two orders of magnitude better than what is achieved by conventional triple-axis neutron spectrometers. It was pointed out by Philip Allen that the phonon linewidth is proportional to the electron-phonon coupling parameter, which is an essential parameter describing the formation of Cooper pairs in phonon mediated superconductors. The superconducting energy gap, whose magnitude, symmetry, and temperature dependence are intimately related to Cooper pairing, can also be directly determined in phonon linewidth measurements. The opening of the gap results in a redistribution of electronic states and excitations in the immediate vicinity of the Fermi surface. Electron-phonon scattering is suppressed for phonon energies below the gap 2D due to the stability of the Cooper pairs below Tc. Discontinuities in the phonon linewidths are thus expected when the phonon energy exceeds 2D. Consequently, the gap and its momentum dependent anisotropy (and also the pairing symmetry) can be accurately resolved from a map of these discontinuities in different crystallographic directions. While phonon energies are highly sensitive to the superconducting energy gap, their momenta can serve as a similarly comprehensive probe of the geometry of the Fermi surface, which also leaves an imprint on the phonon linewidth. Phonons which connect nearly parallel segments of the Fermi surface exhibit an enhanced electron-phonon scattering probability, and thus linewidth extrema (termed Kohn anomalies) are expected. A full image of the underlying Fermi surface is contained in a map of these Kohn anomalies. The phonon-linewidth spectra of these long-known superconductors presented in this thesis showed new and unexpected features that were not visible in previous low resolution experiments. Anomalies were observed at phonon energies corresponding to the magnitude of the superconducting gap, 2D, in the electron spectrum. These features were not only visible, as expected, below the superconducting transition temperature Tc, but persist to much higher temperatures. A detailed analysis showed that these features originate from previously unknown Kohn anomalies. As these anomalies were observed both in niobium and lead, which have different crystal structures (BCC and FCC), Fermi surfaces, and energy gaps, it is likely that this link between 2D and the Kohn anomalies is more a general phenomenon. Thus the question arose whether the Kohn anomalies impose a limit on the magnitude of the 2D gap. The major part of this thesis was accordingly concentrated on the relation between Kohn anomalies and 2D. First, similar measurements were carried out along different high symmetry directions. Yet in all cases, the 2D gap was found to coincide with the lowest-energy Kohn anomaly indicating that this phenomenon can not be attributed to an accident. Since the energies of the Kohn anomalies vary (within 10%) for different crystallographic directions, this "locking" of 2D to the Kohn anomaly provides a simple explanation to the long quest for the origin of the gap anisotropy, which was already inferred from tunneling experiments in the 1960's and intensively discussed in the following decades. To shed more light on this lock-in mechanism, other metallic superconductors were explored. A key candidate was the Pb-Bi alloy. Bi adds electrons and increases the radius of the Fermi surface. It was known from previous tunneling experiments that both the gap magnitude 2D and Tc increase with Bi concentration. Inelastic neutron spectroscopy on different Pb-Bi alloys revealed a shift of the Kohn anomalies to higher energies with increasing Bi content in lockstep with 2D, supporting the lock-in hypothesis. Phonon linewidth experiments were also performed on the high temperature superconductor LSCO, whose understanding is still in its infancy. The electron-phonon linewidths of transverse acoustic phonon branches in underdoped, optimally doped, and overdoped samples were extracted from the data.