ROLE OF LONG – RANGE ELECTRON - PHONON AND COULOMB INTERACTIONS IN HIGH - TC CUPRATE SUPERCONDUCTORS

Abstract

Superconductivity is the disappearance of the electrical resistance of certain materials at certain critical temperatures called transition temperatures. This phenomenon was discovered in 1911 and is one of the most interesting and sophisticated discoveries in condensed matter physics. Superconducting materials have long been classified into two categories, viz low temperature (conventional) and high temperature ( unconventional) supercunductors and the current work deals with the later type. High temperature superconductors have transition temperatures above 30 K (-243.150C) and are further grouped into pnictides and cuprates. Cuprates are copper oxide superconductors. This study investigated the role of long – range electron phonon and Coulomb interactions in high - Tc cuprate superconductors. In the study, the electron – phonon and Coulomb Hamiltonian was derived using frozen phonon method. The expectation value of the Hepc was calculated using second quantization and many body techniques. The equation for the energy of the system at ground state was obtained from the product of the expectation value of Hepc and the thermal activation factor, exp (-E1/kT). The equation relating specific heat and absolute temperature was obtained from the first derivative of the energy of the system at ground state with respect to absolute temperature. The equation relating entropy and absolute temperature was obtained from the specific heat equation, using integral calculus. From the equations relating specific heat and entropy with absolute temperature, values of specific heat and entropy against absolute temperature were calculated. In these calculations, the onsite energy of copper (Ed) was fixed at 2.0 x 10-6 eV. The onsite energy of oxygen (Ep), hybridization energy of oxygen and copper bands (tpd), the electron – phonon interaction energy, (gep) and energy due to repulsion of copper holes occupying the same orbital (ud), were varied. From the results, it was found out that increase in the parameters Ed, tpd, gep and ud leads to increase in the transition temperature from 30 K to 90 K. It was further found that entropy and specific heat decrease with increase in the parameters. It can therefore be concluded that long range electron – phonon and Coulomb interactions increase the transition temperature of superconducting cuprates.