The microwave properties of polycrystalline MgB 2 thin films prepared by the so-called in-situ method are investigated. The characterization of the films at microwave frequencies was obtained by a coplanar resonator technique. The analysis of the experimental data results in the determination of penetration depth, surface impedance and complex conductivity. The aim of this work is to set the experimental results in a consistent framework, involving the two-band model in the presence of impurity scattering. The energy gaps are calculated and the contribution of intra-and inter-band scattering is considered. From the comparison between the calculated gap values and the experimental data it turns out that the temperature dependence of the penetration depth 1 can be accounted for by an effective mean energy gap, in agreement with the predictions of Kogan et al. [Phys. Rev. B 69, 132506 (2004)]. On the other hand, the temperature dependence of the real part of the microwave conductivity and of the surface resistance is accounted for by the single smaller gap, in agreement with the work of Jin et al. [Phys. Rev. Lett. 91, 127006 (2003)]. Since these findings rely on the same calculated gap structure, the required consistency is fulfilled.74.70. Ad, 74.25.Nf
IntroductionSince the discovery of its superconducting properties, magnesium diboride (MgB 2 ) has generated a great deal of interest because of its simple structure, relatively high critical temperature and two-gap nature. The Fermi surface of MgB 2 consists of two threedimensional sheets, from the π bonding and antibonding bands, and two nearly cilindrical sheets from the two-dimensional σ bands. 1 Many physical properties of MgB 2 are reasonably described within a model with two separated energy gaps, ∆ π and ∆ σ . 2,3 Nevertheless, the role of interband and intraband scattering has to be considered: 2,3 it is still not completely clear, also due to the wide spread quality of samples used in different experiments. In fact, a significant scattering between the different Fermi sheets may reduce the effective gap structure to a single isotropic gap. Recently, the expected 2 observation of single-gap superconductivity at high impurity level has been observed in C-substituted MgB 2 single crystals by point-contact spectroscopy. 4 When the level of impurities is high enough, the two gaps merge into a single gap with a ratio 2∆/k B T c close to the standard BCS value.The role of the two bands in determining the microwave conductivity in MgB 2 thin films is controversial as well. The temperature dependence of the microwave conductivity in caxis oriented films was interpreted by Jin et al. 5 in terms of a dominant contribution of the π band. They deduced this argument from the observation of a single anomalous peak around t=T/T c =0.6. The presence of such a peak can be explained in the framework of the BCS theory. When the superconducting state is entered and the gap opens, a singularity appears in the density of states at the gap edges, increasing the microwave ...