Directional point-contact spectroscopy of MgB$_{2}$ single crystals in magnetic fields: two-band superconductivity and critical fields

The results of the first directional point-contact measurements in MgB2 single crystals, in the presence of magnetic fields up to 9 T either parallel or perpendicular to the ab planes, are presented. By applying suitable magnetic fields, we separated the partial contributions of the sigma and pi bands to the total Andreev-reflection conductance. Their fit with the BTK model allowed a very accurate determination of the temperature dependency of the gaps (Delta_sigma and Delta_pi), that resulted in close agreement with the predictions of the two-band models for MgB2. We also obtained, for the first time with point-contact spectroscopy, the temperature dependence of the (anisotropic) upper critical field of the sigma band and of the (isotropic) upper critical field of the pi band.