MgB2: superconductivity and pressure effects

The Ginzburg-Landau theory is presented for a two-band superconductor with emphasis on MgB2. Experiments are proposed which lead to identification of the possible scenarios: whether both σand π-bands superconduct or σ-alone. According to the second scenario a microscopic theory of superconducting MgB2 is proposed based on the strongly interacting σ-electrons and non-correlated π-electrons of boron ions. The kinematic and Coulomb interactions of σ-electrons provide the superconducting state with an anisotropic gap of s*-wave symmetry. The critical temperature Tc has a non-monotonic dependence on the distance r between the centers of gravity of σand πbands. The position of MgB2 on a bell-shaped curve Tc (r) is identified in the overdoped region. The derived superconducting density of electronic states is in agreement with available experimental and theoretical data. It is argued that the effects of pressure are crucial to identify the microscopic origin of superconductivity in MgB2. Possibilities for Tc increase are discussed. The discovery of superconductivity in MgB2 [1] poses many interesting and fundamental questions regarding the nature of the superconducting state as well as the possibility of multi-band superconductivity. The crystal belongs to the space group P6/mmm or AlB2-structure where borons are packed in honeycomb layers alternating with hexagonal layers of magnesium ions. The ions Mg are positioned above the centers of hexagons formed by boron sites and donate their electrons to the boron planes. The electronic structure is organized by the narrow energy bands with near two-fold degenerate σ-electrons and the wide-band π-electrons. Without any of the lattice strain, the σ dispersion relations are slightly splitted due to the two boron atoms per unit cell. The corresponding portions of the Fermi surface consist of coaxial cylinders along the Γ A symmetry direction of the Brillouin zone (BZ), whereas the πbands are strongly dispersive. In the following sections we present a Ginzburg-Landau (GL) analysis of the two-band superconductor with emphasis on MgB2, we apply it in pressure experiments which potentially distinguish the different superconducting bands [2], then we provide a microscopic model.