Author(s)

S. Fujita¹, A. Suzuki², Y. Takato³

¹Department of Physics, University at Buffalo, State University of New York, Buffalo, NY, USA.
²Department of Physics, Faculty of Science, Tokyo University of Science, Tokyo, Japan.
³Okinawa Institute of Science and Technology Graduate University, Okinawa, Japan.

A quantum statistical theory of the superconductivity in MgB₂ is developed regarding it as a member of the graphite intercalation compound. The superconducting temperature T_c for MgB₂, C₈K ≡ KC₈, CaC₆, are 39 K, 0.6 K, 11.5 K, respectively. The differences arise from the lattice structures. In the plane perpendicular to the c-axis, B’s form a honeycomb lattice with the nearest neighbour distance while Mg’s form a base-hexagonal lattice with the nearest neighbour distance above and below the B-plane distanced by . The more compact B-plane becomes superconducting due to the electron-phonon attraction. Starting with the generalized Bardeen- Cooper-Schrieffer (BCS) Hamiltonian and solving the generalized Cooper equation, we obtain a linear dispersion relation for moving Cooper pairs. The superconducting temperature T_c identified as the Bose-Einstein condensation temperature of the Cooper pairs in two dimensions is given by , where is the Cooper pair density, the Boltzmann constant. The lattices of KC₈ and CaC₆ are clearly specified.

Crystal Structure, BCS Hamiltonian, Electron-Phonon Interaction, Cooper Pairs, Bose-Einstein Condensation, Superconductivity

Fujita, S. , Suzuki, A. and Takato, Y. (2016) Quantum Statistical Theory of Superconductivity in MgB₂. Journal of Modern Physics, 7, 1546-1557. doi: 10.4236/jmp.2016.712141.