STATISTICAL THERMODYNAMICS OF HIGH TCTWO BAND SUPERCONDUCTIVITY IN MgB2

Abstract

Thermodynamic properties of the multiband high critical temperature superconductors have been described previously with simple standard BCS expressions corresponding to and bands, but the microscopic mechanisms that allow superconductivity to persist at high temperatures remain unknown. Studies on two band superconductors have previously been described through one band model; this approach has not adequately addressed cases of inter-band scattering for superconductors at high temperature. Research reverted to canonical two band BCS Hamiltonian containing a fermi surface of p- and d- bands, followed byBogoliubov-Valatin transformationequations, to obtain transition temperature, energy gap and specific heat forMgB2 superconductor. A detailed study of phonon-mediated attraction and coulomb repulsion was proposed to act differently on energy band states and stabilizing superconductor phase for MgB2..The results were comparedto the approach of a sum of two independent bands using Bardeen, Cooper and Schrieffer like π- and α- model expressions for the specific heat, entropy and free energy to the solution of Bogoliubov-Valatin transformation for strongly correlated electrons. The research lead todevelopment of electron-phonon interaction model Hamiltonian for superconducting MgB2and its energy, obtaining transition temperature TCfor MgB2 superconducting and expression for variation of thermodynamic properties of high TC superconductors in two-band model system.The researchdemonstrated the physical meaning of the sum over the contribution of the two bands, where band parameters tend to agree with the previous determinations ofband structure calculations and experiments. Informationwas found on the thermodynamic transition by presenting an empirical two bands that fits the experimental data over the whole range of temperature to high TC. A perturbed Hamiltonian was developed from the Bogoliubov-Valatin transformations equations, where thermodynamic variables were derived. Kaleidagraph and Mathcad software were used to calculate values of statistical thermodynamics of high TC variables for high temperature superconductors, which included specific heat capacity = 0.0192729906 eV/K, calculated TC = 47.667720441K, ground state energy = 0.4111340888 eV, total energy = 0.7670001738 eV and entropy = 3.3245572813 eV/k used in data processing and analysis.