Systematic characterization of upper critical fields for MgB$_2$ thin films using the two-band superconducting theory
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 $D_π/D_σ>1$, where $D_π$ and $D_σ$ are the intraband electron diffusivities for $π$ and $σ$ 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.