Quantum Statistical Theory of Superconductivity in MgB₂

Abstract

A quantum statistical theory of the superconductivity in MgB 2 is developed regarding it as a member of the graphite intercalation compound. The superconducting temperature T c for MgB 2 , C 8 K ≡ KC 8 , CaC 6 , 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 KC 8 and CaC 6 are clearly specified.