Electrons in anharmonic phonon fields of low-dimensional high- Tc superconductors

Abstract

A general Mathematical formulation is developed for calculating the electron response function of layered superconductors. A model Hamiltonian for the low-dimensional superconducting system is developed which includes (i) bare electron interactions, (ii) harmonic phonon fields, (iii) electron-phonon interactions, (iv) anharmonic phonons and (v) effects of localized phonon fields. Quantum dynamics of electrons is studied adopting the Green's function theory via this advanced Hamiltonian in order to describe the many-body problem. This work remarkably describes that the electron-phonon coupling coefficient shows its inevitable presence in all sectors of phonon fields, namely, the fields of (i) anharmonic phonons (ii) localized phonons and (iii) the impurity-anharmonicity interaction. The expressions for electron density of states and electron heat capacity are also obtained in the new framework.