Disorder induced evolution of two energy gaps in MgB2

We study disorder effect on MgB2 superconductivity using the two band model by Suhl, Matthias, and Walker. We stress the importance of the Cooper pair size effect in the response of the BCS superconductor to the perturbation: the bounded Cooper pairs see the impurities within the range of the coherence length. This effect will undermine the initial decrease of the Tc and the big energy gap due to disorder, until the resistance ratio reaches about $\sim $3. For the resistance ratio less than 3, weak localization starts to decouple electrons and phonons, leading to the significant decrease of both the Tc and the big gap. In particular, we trace the evolution of two energy gaps of MgB2 as a function of disorder. Estimating the inter-band scattering rate from the experimental data, we compare our calculations with experiments. We also calculate the transition temperature, Tc as a function of the resistance ratio.