Elastic, Quasielastic, and Superelastic Electron Scattering from Thermal Lattice Distortions in Perfect Crystals

Abstract: In conventional treatments of electron transport, momentum relaxation within a perfect, defect free crystal is commonly assumed to require phonon creation or annihilation. Here we treat the crystal as finite and isolated, retaining the lattice center of mass (recoil) degree of freedom and enforcing conservation of total mechanical momentum alongside discrete crystal pseudomomentum. Starting from the density density form of the electron lattice interaction, we find that an electron in the interior of a perfect crystal admits strong, and in some regimes dominant, elastic momentum relaxing scattering channels, in which momentum is conserved by recoil of the lattice background without phonon excitation. In addition, we identify mixed quasielastic and superelastic channels in which phonon occupations change but do not account fully for the electron's momentum transfer. These results provide a microscopic basis for momentum relaxation that does not rely on local energy dissipation. They naturally reconcile a wide range of experimental observations, including weak localization, quantum oscillations, ultrasonic attenuation, and the separation of momentum and energy relaxation times, with predominantly elastic scattering in clean crystals. The framework clarifies how diffusive transport, including Planckian scale diffusion, can emerge from elastic dynamics in a time dependent lattice background.