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

In standard treatments of electron transport, momentum relaxation in a perfect, defect-free crystal is linked with phonon creation or annihilation. In this work, we reconsider this problem for a finite, isolated crystal, retaining the lattice center-of-mass (recoil) degree of freedom and enforcing conservation of total mechanical momentum together with discrete crystal pseudomomentum. Starting from the density-density form of the electron-lattice interaction, we show that an electron in the interior of a perfect crystal admits elastic momentum-transfer channels in which total momentum is conserved by recoil of the lattice background without phonon excitation. These elastic channels can provide the leading contribution to momentum relaxation. We further identify mixed quasi-elastic and superelastic processes in which phonon occupations change but do not account entirely for the electron's momentum transfer. The elastic channels arise within the standard microscopic Hamiltonian and do not require additional disorder or defects. The resulting framework provides a complementary microscopic perspective on momentum relaxation in clean crystals and is consistent with experimental phenomena such as weak localization, quantum oscillations, ultrasonic attenuation, and the observed separation of momentum and energy relaxation times.