Surface effects in two-band superconductors: Application to MgB2

Recent experiments report the existence of superconductivity at nearly 40 K in MgB2. Its origin is not completely elucidated. The material shows a pronounced isotope effect, and the density of states is well approximated by the BCS theory. Tunneling experiments suggest that the superconducting properties at the surface of the material differ from the expected bulk behavior. In addition, photoemission results suggest the existence of an s-like gap, D , such that D<3kBTc . A possible explanation of this result is that the measured D is the average of different gaps. The present work is motivated by the persistent discrepancy between the gap values measured in different experiments, and, particularly, the excellent fit to a BCS gap too low to explain the value of the critical temperature observed in tunneling experiments reported in Ref. 3. Band structure calculations suggest that there are, at least, two types of bands at the Fermi surface: a hole band, built up of boron s orbitals, with a weak dispersion in the direction perpendicular to the boron planes, and a broader band, built up mainly of p boron orbitals, which shows a significant dispersion in the direction perpendicular to the boron planes. Theoretical arguments favor, as the origin of the superconductivity, the holelike s band, or the p band. The existence of two bands with different physical properties is assumed in other models for the superconducting properties of MgB2. 11,12 It has been argued that the upper critical field can be best modeled if the superconducting properties depend on the specific band at the Fermi level. On general grounds, it is reasonable to assume that the s and p bands in MgB2 will have different contributions to the superconducting properties, and that the superconducting gap needs not be the same in the two bands. The existence of many bands at the Fermi level, with very different physical properties, is probably a generic feature of intermetallic superconductors. In these materials, it can be expected that the pairing interaction which gives rise to the superconductivity will depend on the details of each band. If this is the case, there is not a uniform gap at the Fermi level. The superconducting state resembles, in this respect, that of an anisotropic superconductor. The effects of interband scattering on the bulk properties of a superconductor with two different bands at the Fermi level was studied in Ref. 17. Those results were extended in Ref. 18. Interband scattering can be induced by any defect which breaks the translational symmetry of the lattice, including