Two-band soliton-like polaron model for MgB 2 superconductivity

Abstract

Using a two-band soliton-like polaron model of a deformable continuum, the critical temperature, energy gap and other parameters in MgB 2 superconductor are studied in the framework of finite temperature Green's function technique. Two group of equations for the two energy gaps and two transition temperatures are derived by taking into account the different dimensionality of the relevant bands involved. Based on the ratio between the quasi-2D σ-band energy gap Δ 1 and the quasi-particle ground-state energy | E g1 |, we find, in agreement with recent findings, that the conventional ratio 2 Δ 1/ k B T c1 for the 2D σ-band can take a value ∼4.4. Based on the ratio of the quasi-particle kinetic energy and quasi-3D energy gap Δ 2, we find instead for the smaller π-band ratio 2 Δ 2/ k B T c2 the value ∼2.3. Both these estimates are in quantitative agreement with experimental measurements. The calculated transition temperatures, energy gaps, coherence length and Fermi velocity, are also in agreement with recent experimental data and ab initio calculations.