  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 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 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.
