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Theory of the Superconductivity of MgB2

We consider MgB 2 to be a structure-dependent superconductor, the B 2 plane of the MgB 2 crystal to be superconducting and the Mg plane to be a tunneling junction plane between the B 2 planes. We set up the superconducting interaction within the B 2 plane between two adjacent planes and the coupling pair interactions in the perpendicular direction of the B 2 plane. Using the mean field approximation for the equation of motion of the superconducting electron, we solve the Green function of the electron and obtain the order parameters Δ∥(T) and Δ⊥(T) of the intra B 2 plane and inter B 2 plane electrons, respectively. It is found that these two order parameters have the same T c with an appropriate choice of model parameters. Our gap function in the form Δ∥ + const × Δ⊥ cos q, where q represents the momentum along the c-axis direction, leads to a two-peak structure in the density of states, which explains the experimental measurement of two gaps in MgB 2 . The bulk properties of the specific heat, the NMR and the thermal conductivity are also calculated.