Date of Award
Doctor of Philosophy (PhD)
Professor J.P. Carbotte
We study the effects of energy dependence in the electronic density of states (EDOS) on the electron quasi-particle properties in the normal state, the single particle tunneling characteristics into superconductors and the superconducting thermodynamic properties. The Migdal-Eliashberg equations generalized to include nonconstant EDOS are derived in detail in the isotropic approximation. By numerical solution of the electron self-energy equations in the normal state we assess the effect of the interplay of the energy dependence in EDOS, the electron-phonon interaction and/or elastic impurity scattering on the electron quasiparticle properties. The frequency dependence of the inverse life-time due to the electron-phonon interaction is significantly affected by energy dependence in EDOS on the scale of several Debye energies around the Fermi level EF. The analysis of single-particle tunneling density of states into superconductor with nonconstant EDOS via solution of the three generalized Eliashberg equations and inversion of the calculated tunneling conductances shows that the effects of the peaks in EDOS, on a scale of several Debye energies, are important and cannot necessarily be reproduced within the usual Eliashberg theory, by working with some effective values of α²F and/or μ* without introducing unphysical features of these parameters. We derive the expression for the free energy difference between the normal state and superconducting state for a symmetric Lorentzian model of EDOS starting from Eliashberg's expression for the grand thermodynamic potential of an interacting electron-phonon system. From the solution of the generalized Eliashberg equations on the imaginary frequency axis we calculate the superconducting critical field deviation function D(t). Also, by analytical continuation of the imaginary axis solutions via N-point Padé approximants we calculate the corresponding ratios (2Δօ)/(kʙTⅽ). We show that for a peak in EDOS near EF with a half-width less than the Debye energy one can describe the effect of this peak on the above mentioned thermodynamic quantities only within the full Eliashberg theory modified to include the energy dependence in EDOS. However for a peak half-width greater than the Debye energy, the influence of the structure in EDOS on D(t), Tc and (2Δօ)/(kʙTⅽ) is small.
Mirtrović, Božidar, "Effects of Energy Dependence in the Electronic Density of States on Some Normal State and Superconducting Properties" (1981). Open Access Dissertations and Theses. Paper 568.