Electron coherence effects in the coherent state picture for electron-phonon interactions

Bloch-Grüneisen formalism of electrical resistivity is an approximation that is built upon incoherent Boltzmann transport theory, treating electron-phonon interactions as uncorrelated successive first order events. Any effects of electron coherence cannot be captured within this picture. Here we present a new framework for electron-phonon interaction. We treat the lattice vibrations as coherent states where the deformation potential becomes a real field acting on electrons. Phonons create a disordered landscape in which conduction electrons can quasi-elastically scatter. This approach is inherently nonperturbative and allows one to take the coherence of electrons into account. Coherent state representation can be seen as the wave-limit of lattice vibrations as opposed to the particle-limit which is utilized in the second quantization formalism. Direct analogs of these are the wave (former) and particle (latter) limits in quantum optics. We do full quantum propagation of electron wave packets under the deformation potential and find that electron coherence causes Anderson localization as a function of temperature and doping. We construct a novel phase diagram of metal-insulator transition where the localized region is V-shaped and occurs at the high temperature regime and around a critical level of doping. This fresh perspective represents the neglected half of the wave-particle duality for the lattice and might have a potential to shed light on the unexplained phenomena in the metallic resistivity such as linear-in-temperature dependence in strange metals.