Effects of Andreev scattering on the tunneling conductance in superconducting MgB2

The discovery of superconductivity in MgB2 with a rather high transition temperature of T=39 K has opened up new territory. Recently, single crystals of MgB2 have become available. Based on the available experimental data an anisotropic s-wave superconducting order parameter has been proposed to model the properties of this material. In this contribution, we discuss the effects of Andreev scattering on the tunneling conductance between a normal metal point contact and a sample of superconducting MgB2 within the theoretical framework of Blonder, Tinkham, and Klapwijk (BTK). The issue is to distinguish the response of a multi-gap isotropic s-wave model, suggested for MgB2 by other members of the community, from the single-gap anisotropic s-wave order parameter we are proposing. We can show that for intermediate values of the tunneling matrix element between the normal metal tip and the superconducting sample a two-peak tunneling conductance is obtained, resembling recent measurements by Szabo et al., Phys. Rev. Lett. 87, (2001) 137005. Furthermore, in the Giaever tunneling limit only one sharp cusp should be observable at the frequency of the maximum of the superconducting gap.