Quantum Statistical Theory of Superconductivity in MgB<sub>2</sub>

Abstract

A quantum statistical theory of the superconductivity in MgB2 is developed regarding it as a member of the graphite intercalation compound. The superconducting temperature Tc 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 a 0 while Mg's form a base-hexagonal lattice with the nearest neighbour distance a 0 3 above and below the B-plane distanced by c 0. 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 cp = ε for moving Cooper pairs. The superconducting temperature Tc identified as the Bose-Einstein condensation temperature of the Cooper pairs in two dimensions is given by T cn k 1 2 1 c 0 B 1.954 − = , where n 0 is the Cooper pair density, k B the Boltzmann constant. The lattices of KC8 and CaC6 are clearly specified.

Bulk MgB2 Superconducting Materials: Technology, Properties, and Applications

“…As mentioned in Introduction, for more than 20 years, since the discovery of the superconductivity in MgB 2 , scientists have been exploring the possibility of increasing the pinning and, hence, the critical current density using various additives [ 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 , 90 ,…”

“…Many publications have been devoted to the investigation of the various properties of MgB 2 superconductors and their theoretical considerations (e.g., [ 19 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 ] and the references therein). MgB 2 ’s properties are considered more similar to metal than to those of HTS [ 28 ].…”

“…Among the dozens of studied additions to MgB 2 , the ones that are the most effective from the point of view of an increase in the critical current density are carbon, carbon-containing compounds, silicon carbide, titanium, tantalum, zirconium, and compounds containing these metals [ 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 ]. Relatively recently, in the literature [ …”