A two band model for Superconductivity: Probing interband pair formation

We propose a two band model for superconductivity. It turns out that the simplest nontrivial case considers solely interband scattering, and both bands can be modeled as symmetric (around the Fermi level) and flat, thus each band is completely characterized by its half-band width $W_{n}$ (n=1,2). A useful dimensionless parameter is $\delta $, proportional to $W_{2}-W_{1}$. The case $\delta =0$ retrieves the conventional BCS model. We probe the specific heat, the ratio gap over critical temperature, the thermodynamic critical field and tunneling conductance as functions of $\delta $ and temperature (from zero to $T_{c}$). We compare our results with experimental results for $MgB_{2}$ and good quantitative agreement is obtained, indicating the relevance of interband coupling. Work in progress also considers the inclusion of band hybridization and general interband as well as intra-band scattering mechanisms.