Electronic conductivity in anharmonic crystals: phonon dephasing in the electron-phonon interaction

The electron-phonon interaction underpins many material properties, for example the conductiv- ity of metals and the optoelectronic response of semiconductors. First principles calculations of the electron-phonon interaction are a powerful tool to quantitatively describe many of these properties in increasingly complex materials. However, one key assumption of all calculations is that phonons have infinite lifetimes, an approximation that may break down when anharmonic phonon-phonon interactions are strong. In this work, we present a theory for the interaction of electrons with finite- lifetime phonons experiencing dephasing. Using a first principles implementation of the theory, we find that anharmonic dephasing dramatically enhances electron-phonon scattering rates in metallic MgB2. Microscopically, phonon-phonon interactions create new scattering channels that increase the phase space available for electron-phonon scattering. As a result, anharmonic dephasing strongly suppresses conductivity in MgB2, bringing the calculated values substantially closer to experiment within the Boltzmann transport equation framework.This example establishes the importance of finite phonon lifetimes in the evaluation of electron-phonon scattering, and the microscopic mecha- nism suggests that anharmonic dephasing could play an important role in the conductivity of many metals. More broadly, our theory and first principles implementation of anharmonic dephasing in the electron-phonon interaction provides a solid foundation to explore this regime in other materials.