Anisotropic s -wave superconductivity: Comparison with experiments on MgB 2 single crystals

The recently discovered superconductivity in MgB 2 has captured world attention due to its simple crystal structure and relatively high superconducting transition temperature T c = 39 K. It appears to be 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 its implications with the predictions of a multi-gap isotropic s -wave model. The quasiparticle density of states, thermodynamic properties, NMR spin-lattice relaxation rate, optical conductivity, and H c2 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 the MgB 2 compound, though more experimental data appear to be necessary from single-crystal MgB 2 .