Superconductivity via Electron-Phonon and Electron-Exciton Interactions

In this chapter an attempt will be made to present some basic ideas in the theory of conductivity. We start immediately below in Section 16.1 with a discussion of the electron-phonon Hamiltonian in the jellium approximation. The effective electron-electron interaction is derived using a canonical transformation and the “Cooper pair” is then discussed in Section 16.2. The Bardeen-Cooper-Schrieffer ground-state wave function is derived in Section 16.3 while the general theory of the inhomogeneous superconductor is discussed in Section 16.4 on the basis of the Bogoliubov equation. In Section 16.5 this equation is solved for the homogeneous case and, in particular, is used to discuss some aspects of the transition temperature. In Section 16.6 the derivation of the Landau-Ginzburg theory is given. In the last two sections, this background is utilized to give short accounts on the excitonic mechanism and the effects of limited dimensionality.