Abstract:
We present the results of point-contact spectroscopy measurements on High-quality epitaxial MgB2 thin films with injected current along the c-axis. The temperature and field dependences of π-band properties with the field parallel to (H⊥) or perpendicular to (H|| the c-axis are investigated in detail. When a magnetic field is applied, either parallel or perpendicular to the c-axis, the density of the quasiparticle state (DOS) of the π-band proliferates quickly with increasing field, while the gap amplitude of the π-band decreases slowly, which is different from the recent theoretical calculations, showing a field dependent competition between the interband scattering and the pair-breaking effects.

Abstract:
We have studied the structure of the superconducting gap in MgB2 thin films by means of point-contact spectroscopy using a gold tip. The films were produced by depositing pure boron on a sapphire substrate, using e-beam evaporation, followed by reaction with magnesium vapour. The films have a Tc of 38.6 +- 0.3 K and resistivity of about 20 microOhm cm at 40 K. The point-contact spectra prove directly the existence of a multi-valued order parameter in MgB2, with two distinct values of the gap, DELTA1=2.3+-0.3 meV and DELTA2=6.2+-0.7 meV at 4.2 K. Analysis of the spectra in terms of the Blonder-Tinkham-Klapwijk model reveals that both gaps close simultaneously at the Tc of the film. Possible mechanisms that can explain the intrinsic co-existence of two values of the gap are discussed.

Abstract:
We demonstrate that the variation of the Andreev reflection with applied magnetic field provides a direct means of comparing the properties of MgB2 with the theory for a dirty two-band superconductor, and we find good agreement between the two. The ratio of electron diffusivities in the s and p bands can be inferred from this experiment. We find that the field dependence of the density of states at the Fermi level in the p band is independent of the field direction, and that the anisotropic upper critical field is determined by the anisotropic diffusivity in the s band.

Abstract:
The progress in investigation of two-band superconductor MgB$_2$ by the point-contact spectroscopy (PCS) is given. Results of study of superconducting gap temperature and magnetic field dependence for two-dimensional $\sigma$ and three-dimensional $\pi$ band and electron-phonon-interaction spectral function are presented. Correlation between the gap value and the intensity of the high T$_c$ driving force -- $E_{2g}$ boron vibration mode, is provided. PCS data on some nonsuperconducting transition metal diborides are surveyed for comparison.

Abstract:
Analysis of the point-contact spectroscopy (PCS) data on the new dramatic high-T$_c$ superconductor MgB$_2$ reveals quite different behavior of two disconnected $\sigma$ and $\pi$ electronic bands, deriving from their anisotropy, different dimensionality, and electron-phonon interaction. PCS allows direct registration of both the superconducting gaps and electron-phonon-interaction spectral function of the two-dimensional $\sigma$ and three-dimensional $\pi$ band, establishing correlation between the gap value and intensity of the high-T$_c$ driving force -- the $E_{2g}$ boron vibration mode. PCS data on some nonsuperconducting transition-metal diborides are surveyed for comparison.

Abstract:
The two-band/two-gap superconductivity in aluminium and carbon doped MgB$_2$ has been addressed by the point-contact spectroscopy. Two gaps are preserved in all samples with $T_c's$ down to 22 K. The evolution of two gaps as a function of the critical temperature in the doped systems suggest the dominance of the band-filling effects but for the increased Al-doping the enhanced interband scattering approaching two gaps must be considered. The magnetic field dependences of the Andreev reflection excess currents as well as zero-energy density of states determined from the experimental data are used to analyze the intraband scattering. It is shown, that while the C-doping increases the intraband scattering in the $\pi$-band more rapidly then in the $\sigma$ band, the Al-doping does not change their relative weight.

Abstract:
Experimental support is found for the multiband model of the superconductivity in the recently discovered system MgB2 with the transition temperature Tc = 39 K. By means of Andreev reflection evidence is obtained for two distinct superconducting energy gaps. The sizes of the two gaps (Delta_S = 2.8 meV and Delta_L = 7 meV) are respectively smaller and larger than the expected weak coupling value. Due to the temperature smearing of the spectra the two gaps are hardly distinguishable at elevated temperatures but when a magnetic field is applied the presence of two gaps can be demonstrated close to the bulk T_c in the raw data.

Abstract:
Point-contact measurements on the carbon-substituted Mg(B$_{1-x}$C$_x$)$_2$ filament/powder samples directly reveal a retention of the two superconducting energy gaps in the whole doping range from $x = 0$ to $x \approx 0.1$. The large gap on the $\sigma$-band is decreased in an essentially linear fashion with increasing the carbon concentrations. The changes in the the small gap $\Delta_{\pi}$ up to 3.8 % C are proportionally smaller and are more difficult to detect but for the heavily doped sample with $x \approx 0.1$ and $T_c = 22$ K both gaps are still present, and significantly reduced, consistent with a strong essentially linear, reduction of each gap with the transition temperature.

Abstract:
We formulate a minimal model of point contact Andreev reflection spectroscopy of a normal- metal/multiband superconductor interface. The theory generalizes the Blonder-Tinkham-Klapwijk (BTK) formulation to a multiband superconductor and it is based on the quantum waveguides theory. The proposed approach allows an analytic evaluation of the Andreev and normal reflection coefficients and thus is suitable for a data fitting of point contact experiments. The obtained differential conductance curves present distinctive features similar to the ones measured in the experiments on multiband systems, like the iron-based pnictides and the MgB2.

Abstract:
The history is described of how one of the most commonly used electric circuit components, an ordinary electric contact, has become a powerful tool for the physicists to study various mechanisms of electron scattering in metals. The physical principles of spectroscopy of quasi-particle excitations in metals by means of point contacts (PCs) whose dimensions range from only a few to tens of nanometers are presented in a popular form.