1. Two-gap superconductivity in MgB2
In the months following the surprising discovery of superconductivity in MgB2
early 2001, most of its superconducting properties have been investigated
extensively. We report here on experimental support for the two-band/two-gap
model proposed by Liu et al. thus showing that MgB2 belongs
to an original class of superconductors in which two distinct 2D and 3D
Fermi surfaces contribute to superconductivity very differently. In order
to get direct spectroscopic information about the superconducting energy
gap, point-contact measurements have been performed on polycrystalline
MgB2 samples with critical temperature Tc
= 39.3K by pressing a copper tip on the freshly polished surface of the
superconductor. The electrical transport in such contacts between a normal
(N) and a superconducting (S) electrode can be described by the Blonder,
Tinkham and Klapwijk (BTK) theory for interfaces ranging from a pure conducting
interface where ballistic transport with Andreev reflection dominates up
to an insulating barrier where Giaever tunnelling dominates.
Both gaps are closing near the same bulk transition temperature. The obtained very weakly coupled gap with 2DS/kTc@1.7 and strongly coupled gap with 2DL/kTc@4.1 are in good agreement with the predictions of the multigap superconductivity in MgB2 (a 3D gap ratio 2DS/kTc@1.3 and a 2D gap ratio 2DL/kTc@4.0). Our point-contact experiments in a magnetic field have shown that the small-gap structure disappears in fields of 1-2Twhereas the large-gap structure is only suppressed in fields around 15 T. These field-dependent data reveal directly in the raw data the presence of two superconducting gaps up to temperatures close to Tc . The regular observation of the two-gap structure in our spectra and the support found for it by other techniques, like Raman scattering and specific heat, indicate that this is an inherent property of MgB2.
 A.Liu et al., Phys. Rev. Lett. 87 (2001), 87005.
P. Szabó, P. Samuely, J. Kaèmarèík
2. Anisotropy of the upper critical field in single crystal MgB2
The two-band/two-gap superconductivity in
MgB2 has already been experimentally evidenced by different
techniques like for instance specific heat measurements or Andreev reflection
(see previous paragraph). A larger gap is attributed to two-dimensional
px-y orbitals and a smaller gap to three-dimensional
pz bonding and antibonding orbitals. Such a picture indicates a significant anisotropy of the superconducting state. Data reported so far on the anisotropy factor G = Hc2||ab/Hc2^
ab scatter from 1.1 to 13 depending on the form of material (polycrystals,
thin films, single crystals) and method of evaluation. The problem remains
to be clarified on high quality single crystals.
Figure 2: H-T phase diagram of the MgB2 single crystal. Circles - Hc2 from transport measurements. Squares - Hc2 from ac-susceptibility. Triangles - Hc2 from specific heat. In the insert : temperature dependence of the anisotropy.
One can see that all three presented methods reveal the same results in the common range of applied fields (moH£5 T). The upper critical field perpendicular to the basal plane has a typical temperature dependence for a type-II superconductor with a linear shape near the zero-field transition temperature and a saturation at the lowest temperatures with m0Hc2^ab @3.5 T. On the other hand the parallel upper critical field has a different strength and shape: close to Tc, Hc2||ab reveals a positive curvature which changes to negative below 20 K and saturates to about 17 Tesla at the lowest temperatures. It has been suggested that the positive curvature observed here for H||ab is a consequence of the two-gap structure. However, it is worth mentioning that a very similar behavior has also been observed in conventional superconductors. The origin of this effect thus still has to be clarified A direct consequence of the different forms of the temperature dependencies of these two critical fields is a temperature dependent anisotropy factor G. Then, G~ 5 is found at low temperatures but it is about 2 near Tc (see inset of Fig. 2. The angular dependence of the upper critical field measured at 5.4 K and 26 K show an elliptic form as predicted by a one-band Ginzburg-Landau theory, but obviously this theory can not account for the temperature dependent G parameter.
 L. Lyard, P. Samuely, P. Szabó et al., Phys. Rev. B 66 (2002), 180502(R).
P. Samuely, P. Szabó
T.Klein et al.(University Joseph Fourier, Grenoble), C. Marcenat (Commissariat l'Energie Atomique, Grenoble), A.G.M. Jansen (GHMFL MPI & CNRS Grenoble), S.-I. Lee et al. (Pohang University of Science and Technology), U. Welp et al. (Argonne National Laboratory)