Band-edge quasiparticles from electron phonon coupling and resistivity saturation

We address the problem of resistivity saturation observed in materials such as the A-15 compounds. To do so, we calculate the resistivity for the Hubbard-Holstein model in infinite spatial dimensions to second order in on-site repulsion $U\leq D$ and to first order in (dimensionless) electron-phonon coupling strength $\lambda\leq0.5$, where $D$ is the half-bandwidth. We identify a unique mechanism to obtain two parallel quantum conducting channels: low-energy and band-edge high-energy quasi-particles. We identify the source of the hitherto unremarked high-energy quasi-particles as a positive slope in the frequency-dependence of the real part of the electron self-energy. In the presence of phonons, the self-energy grows linearly with the temperature at high-$T$, causing the resistivity to saturate. As $U$ is increased, the saturation temperature is pushed to higher values, offering a mechanism by which electron-correlations destroy saturation.