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Using Scanning Tunneling Microscope at low temperature we explore the superconducting phase diagram in the $pi$-band of the two-band superconductor MgB$_2$. In this band the peculiar shape of the local tunneling spectra and their dynamics in the magnetic field reveal the complex character of the quasiparticle density of states (DOS). The gap in the DOS is first rapidly filled with states in raising the magnetic field up to 0.5 T and then slowly approaches the normal state value : The gap is observed up to 2 T. Such a change in the DOS dynamics suggests the existence of two terms in the DOS of the $pi$-band: a first one, reflecting an intrinsic superconductivity in the band and a second one, originating from an inter-band coupling to the $sigma$-band. Our findings allow a deeper understanding of the unique phase diagram of MgB$_2$.
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The optical response of the two-band superconductor MgB$_2$ has been studied in the 0.7-4 THz range on films with very low impurity level. The effect of the high-energy $sigma$-gap is observed in the ratio $R_S/R_N$ between the normal and superconducting state reflectance, while in a neutron irradiated film with a slightly higher impurity level mainly the effect of the $pi$-gap is evident as reported in previous experiments. At terahertz frequencies, the electrodynamic of MgB$_2$ can be well described by the two-band parallel conductivity model and is dominated by the $pi$-bands when the impurity level is only slightly higher than that of an ultra-clean sample.
We present experimental results of the upper critical fields $H_{rm c2}$ of various MgB$_2$ thin films prepared by the molecular beam epitaxy, multiple-targets sputtering, and co-evaporation deposition apparatus. Experimental data of the $H_{rm c2}(T)$ are successfully analyzed by applying the Gurevich theory of dirty two-band superconductivity in the case of $D_{pi}/D_{sigma}>1$, where $D_{pi}$ and $D_{sigma}$ are the intraband electron diffusivities for $pi$ and $sigma$ bands, respectively. We find that the parameters obtained from the analysis are strongly correlated to the superconducting transition temperature $T_{rm c}$ of the films. We also discuss the anormalous narrowing of the transition width at intermediate temperatures confirmed by the magnetoresistance measurements.
We report a detailed study of the electronic and structural properties of the 39K superconductor mgbtwo and of several related systems of the same family, namely mgalbtwo, bebtwo, casitwo and cabesi. Our calculations, which include zone-center phonon frequencies and transport properties, are performed within the local density approximation to the density functional theory, using the full-potential linearized augmented plane wave (FLAPW) and the norm-conserving pseudopotential methods. Our results indicate essentially three-dimensional properties for these compounds; however, strongly two-dimensional $sigma$-bonding bands contribute significantly at the Fermi level. Similarities and differences between mgbtwo and bebtwo (whose superconducting properties have not been yet investigated) are analyzed in detail. Our calculations for mgalbtwo show that metal substitution cannot be fully described in a rigid band model. casitwo is studied as a function of pressure, and Be substitution in the Si planes leads to a stable compound similar in many aspects to diborides.
The magnetic field dependence of the spin-susceptibility, $chi_{s}$ was measured in the superconducting state of high purity MgB$_{2}$ fine powders below 1.3 T. $chi_{s}$ was determined from the intensity of the conduction electron spin resonance spectra at 3.8, 9.4, and 35 GHz. At the lowest magnetic fields (0.14 T), a gap opens in the density of states at the Fermi energy and, accordingly, $chi_{s}(T)$ is small at low temperatures. Fields above 0.2 T (about 15 % of $H^{c}_{c2}$, the minimum upper critical field), destroy the gap. The field induced $chi_{s}$ is much larger than expected from current superconductor models of MgB$_{2}$.
A study of the pressure effect on the magnetic penetration depth $lambda$ in polycrystalline MgB$_{2}$ was performed by measuring the temperature dependence of the magnetization under an applied pressure of 0.15 and 1.13 GPa. We found that $lambda^{-2}$ at low temperature is only slightly affected by pressure [$frac{Delta lambda^{-2}}{lambda^{-2}} = 1.5(9)%$], in contrast to cuprate superconductors, where, in the same range of pressure, a very large effect on $lambda^{-2}$ was found. Theoretical estimates indicate that most of the pressure effect on $lambda^{-2}$ in MgB$_2$ arises from the electron-phonon interaction.
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