Breakdown of Pippard ineffectiveness condition for phonon-electron scattering in micro and nanostructures

The Pippard ineffectiveness condition - that electrons strongly scattering from impurities and defects are ineffective in scattering phonons - is based on the assumption that electron scatterers vibrate in the same way as the host lattice. Then the relaxation rate of a low-energy phonon with the wave vector q is 1/τ_ph-e ∼ u²q²l/v_F (u and v_F are the sound velocity and Fermi velocity, l is the electron mean free path). Boundaries and defects moving differently from host lattice drastically change the character of the interference between scattering processes and increase the phonon-electron coupling. In the presence of the quasistatic potential the phonon relaxation is (q²lL)^-1 times faster: 1/τ_ph-e ∼ u²/(v_F L) (L is the electron mean free path with respect to scattering from the quasistatic potential). Analogous effect is expected for phonons with ω ∼ 0.01ω_D (ω_D is the Debye frequency) in conductors with substitutional disorder.