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.[1] 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 T_c = 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.
    Fig.1 shows a typical example of the normalized conductance versus voltage for a Cu-MgB₂ contact at different temperatures. The curves reveal a two-gap structure corresponding to the maxima, placed symmetrically around the zero bias. The spectra of other contacts showed similar two-gap features. These conductance curves could be fitted by the sum of the two BTK conductances ad_S+(1-a)d_Lwith the weight factor a varying from ~60% to ~90% at the small gap depending on the position of the tip. The temperature dependent data can be well fitted by the sum of two BTK contributions as shown by the dotted lines in the figure. The resulting energy gaps D_L@ 7 meV and D_S@2.8 meV for point contacts with different weight values a are shown in figure 2.1b.

Figure 1:
a) Differential conductances of Cu - MgB₂ point-contact measured (full lines) and fitted (dotted lines) for the thermally smeared BTK model with fitting parameters a = 0.71 and Z = 0.52±0.02.
b) Temperature dependence of small and large gap (D_S(T) _and D_L(T))determined from the fitting on three different point-contacts as displayed with three corresponding different symbols.

    Both gaps are closing near the same bulk transition temperature. The obtained very weakly coupled gap with 2D_S/kT_c@1.7 and strongly coupled gap with 2D_L/kT_c@4.1 are in good agreement with the predictions of the multigap superconductivity in MgB₂ (a 3D gap ratio 2D_S/kT_c@1.3 and a 2D gap ratio 2D_L/kT_c@4.0)[1]. 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 T_c [2]. 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.

[1] A.Liu et al., Phys. Rev. Lett. 87 (2001), 87005.
[2] P.Szabó,P. Samuely, J. Kačmarčík et al.,
Phys. Rev. Lett. 87 (2001), 137005.

P. Szabó, P. Samuely, J. Kačmarčík
T.Klein, J. Marcus (LEPES CNRS, Grenoble), D. Fruchart, S. Miraglia (Cristallographie CNRS, Grenoble), A. G. M. Jansen (GHMFL MPI & CNRS Grenoble), C. Marcenat (CEA-DRFMC, Grenoble)

 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 p_x-y orbitals and a smaller gap to three-dimensional p_z bonding and antibonding orbitals. Such a picture indicates a significant anisotropy of the superconducting state. Data reported so far on the anisotropy factor G = H_c2||ab/H_{c2^ 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.
    Here, in Fig. 2 we report on specific heat, high magnetic field transport and ac-susceptibility measurements on magnesium diboride single crystals [1].

Figure 2: H-T phase diagram of the MgB₂ single crystal. Circles - H_c2 from transport measurements. Squares - H_c2 from ac-susceptibility. Triangles - H_c2 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 (moHŁ5 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 m₀H_c2^ab @3.5 T. On the other hand the parallel upper critical field has a different strength and shape: close to T_c, H_c2||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 T_c (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.

[1] 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)