| In this thesis we investigate the electron-phonon interaction in metals in the superconducting and normal states. A transformed Hamiltonian is derived in the superconducting state which involves realistic electron and phonon spectra obtained from previously published experimental data on de Haas-van Alphen and neutron scattering experiments. In contrast to previous analyses in which the electronic structure of lead was approximated by a free-electron sphere, the full two-band nature of lead is taken into account in our transformed Hamiltonian. A gap equation is derived and solved numerically on the two bands using previous results by Farnworth and Timusk (Farnworth and Timusk, 1974, 1976) who found the superconducting energy gap to be 1.286 meV and 1.379 meV on the two bands. The quasiparticle self-energy and spectral density function are calculated and comparison with recent ARPES data on lead is made. We find no evidence of α2F features in our results contrary to claims by Chainani et al. (2000).; Using a memory function method we derive expressions for the optical conductivity in the superconducting state and compare with data from Farnworth and Timusk (Farnworth and Timusk, 1976). The two band model we employ results in good agreement with their data, improving on previous theoretical studies by Allen and coworkers (Allen, 1971) who neglected the details of the Fermi surface and approximated it by a free electron sphere.; In the last part we study the normal state and effects of the electron-phonon interaction on thermodynamic properties of sodium at temperatures >100 K. We find that the leading temperature dependence of the contribution for the interaction between the electronic and lattice degrees of freedom in the entropy goes as T and is different from what previous authors found. Contact is made between our electron-phonon approach which starts out from low temperatures with an electron-ion approach starting from high temperatures (Zwanzig, 1957). |
