Strongly interacting $σ$-electrons and MgB$_2$ superconductivity

Abstract

MgB$(p^{n_σ}p^{n_π})_{2}$ is classified as a system with strongly interacting $σ$-electrons and non-correlated $π$-electrons of boron ions. The kinematic and Coulomb interaction V between the orbitally degenerated $σ$-electrons provide the superconducting state with an anisotropic gap of s*-wave symmetry. The critical temperature $T_c$ has a non-monotonic dependence on the distance r between the centers of gravity of $σ$- and $π$-bands. MgB$_2$ corresponds to r=0.085 eV and V=0.45 eV in our model with flat bands. The derived superconducting density of electronic states is in good agreement with available experimental and theoretical data. The possibilities for increasing $T_c$ are discussed.