Electrons and Phonons in High Temperature Superconductors

The defect-induced anharmonic phonon-electron problem in high-temperature superconductors has been investigated with the help of double time thermodynamic electron and phonon Green’s function theory using a comprehensive Hamiltonian which includes the contribution due to unperturbed electrons and phonons, anharmonic phonons, impurities, and interactions of electrons and phonons. This formulation enables one to resolve the problem of electronic heat transport and equilibrium phenomenon in high-temperature superconductors in an amicable way. The problem of electronic heat capacity and electron-phonon problem has been taken up with special reference to the anharmonicity, defect concentration electron-phonon coupling, and temperature dependence. 1. Introduction With the remarkable discovery of high-temperature superconductivity (HTSC) in the Ba-La-Cu-O system with ？K by Bednorz and Mullers there begins a new exciting era in condensed matter physics because of their variety of applications in science and technology. The pairing mechanism in high temperature superconductors (HTS), however, being an unresolved problem, there are large number of experimental evidences that the electron-phonon (e-p) interaction together with strong electronic correlations plays a decisive role in understanding the phenomenon of superconductivity [1]. In the literature, it is reported that e-p coupling plays a crucial role in determining the electron density of states (EDOS) and electronic heat capacity (EHC). The specific heat which can be determined from temperature dependence and the spectrum of electrons and phonons has always been a central one in view of its importance in understanding the low-temperature phenomenon in solids. The total heat capacity of HTS is contributed by lattice heat capacity (LHC) and EHC [2]. The EHC (~ ) is only appreciable at low-temperatures and changes dramatically at the superconducting transition, whereas the phonon contribution dominates at room temperature and is generally undisturbed by the transition at . The Sommerfeld constant provides an important test for proposed theories [3–5], where is the EDOS evaluated at Fermi energy . In the present work, the expressions for EDOS and EHC have been obtained with the help of many body Green's function theory which uses an almost complete Hamiltonian via quantum dynamics of electrons and phonons. 2. The Hamiltonian and Green’s Functions In order to formulate the problem with special reference to HTS, we consider an almost complete (without BCS type) Hamiltonian [6, 7] in the form: where , , , , and