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Abstract

The recently discovered superconductivity in MgB2 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 man aspects of the unusual superconducting properties of the MgB2 compound, though more experimental data appear to be necessary from single- crystal MgB2.