Anisotropic s-wave superconductivity: comparison with experiments on MgB2 single crystals

– The recently discovered superconductivity in MgB2 has captured world attention due to its simple crystal structure and relatively high superconducting transition temperature Tc = 39K. It is generally accepted that it is phonon-mediated s-wave BCS-like superconductivity. Surprisingly, the strongly temperature dependent anisotropy of the upper critical field, observed experimentally in magnesium diboride single crystals, is still lacking a consistent theoretical explanation. We propose a simple single-gap anisotropic s-wave order parameter in order to compare with the prediction of a multi-gap isotropic s-wave model. The quasiparticle density of states, thermodynamic properties, NMR spin-lattice relaxation rate, optical conductivity, and Hc2 anisotropy have been analyzed within this anisotropic s-wave model. We show that the present model can capture many aspects of the unusual superconducting properties of MgB2 compound, though more experimental data appear to be necessary from single crystal MgB2. Introduction. – The moderately high temperature superconductivity with Tc ≃ 40K, discovered about one year ago in MgB2 [1, 2] has stimulated an intense research activity all over the world. Superconductivity in this binary compound appears to be due to an electronphonon interaction and compatible with BCS s-wave superconductivity. Thermodynamics and contact tunneling data as well as some theoretical studies indicate that superconductivity in MgB2 is one of the rare examples of two band superconductivity with two energy gaps, attached to different sheets of the Fermi surface [3–10]. On the other hand, the two gap model appears not to be able to cope with a strongly anisotropic upper critical field in caxis oriented MgB2 films and more recently in single crystals of MgB2 [11–16]. Indeed, the