Measurement of the magnetic penetration depth of a superconducting   MgB$_{2}$ thin film with a large intraband diffusivity
  We report the temperature dependent magnetic penetration depth $\lambda(T)$ and the superconducting critical field $H_{c2}(T)$ in a 500-nm MgB$_{2}$ film. Our analysis of the experimental results takes into account the two gap nature of the superconducting state and indicates larger intraband diffusivity in the three-dimensional (3D) $\pi$ band compared to that in the two-dimensional (2D) $\sigma$ band. Direct comparison of our results with those reported previously for single crystals indicates that larger intraband scattering in the 3D $\pi$ band leads to an increase of $\lambda$. We calculated $\lambda$ and the thermodynamic critical field $H_{c}\approx$2000 Oe employing the gap equations for two-band superconductors. Good agreement between the measured and calculated $\lambda$ value indicates the two independent measurements, such as magnetic force microscopy and transport, provide a venue for investigating superconducting properties in multi-band superconductors. 
Jeehoon Kim, N. Haberkorn, Shi-Zeng Lin, L. Civale, E. Nazaretski, B.   H. Moeckly, C. S. Yung, J. D. Thompson, and R. Movsh...
cond-mat.supr-con