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