ELECTRONS IN ANHARMONIC PHONON FIELDS OF LOW-DIMENSIONAL HIGH-T-C SUPERCONDUCTORS

A general Mathematical formulation is developed for calculating the el ectron response function of layered superconductors. A model Hamiltoni an for the low-dimensional superconducting system is developed which i ncludes (i) bare electron interactions, (ii) harmonic phonon fields, ( iii) electron-phonon interactions, (iv) anharmonic phonons and (v) eff ects of localized phonon fields. Quantum dynamics of electrons is stud ied adopting the Green's function theory via this advanced Hamiltonian in order to describe the many-body problem. This work remarkably desc ribes that the electron-phonon coupling coefficient shows its inevitab le presence in all sectors of phonon fields, namely, the Fields of (i) anharmonic phonons (ii) localized phonons and (iii) the impurity-anha rmonicity interaction. The expressions for electron density of states and electron heat capacity are also obtained in the new framework.