Statistical Thermodynamics Of High Tctwo Band Superconductivity In Mgb2

ABSTRACT

Thermodynamic properties of the multiband high critical temperature superconductors have

been describedpreviously 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.