Sound attenuation by electrons in metals

Abstract

Rigorous formal transport theory is used to formulate a theory of sound attenuation in the temperature regime where band electrons are the resistive agent. The theory is equivalent to Pippard's, and covers both the hydrodynamic (Ql\ensuremath{\ll}1) and quantum (Ql\ensuremath{\gg}1) regimes where the electron mean free path l is small or large compared with the sound wavelength 2\ensuremath{\pi}/Q. The theory generalizes Pippard's work on sound attenuation in metals with nontrivial band structure by allowing the inclusion of microscopic theories of scattering instead of the phenomenological constant l. In order to formulate the theory it is necessary to make careful use of new results in the theory of deformation potentials. In the regime Ql\ensuremath{\ll}1 the theory reduces to a theory of viscous response of the electrons to a dc shear flow. Variational formulas are given for the elements of the viscosity tensor. In the appendixes parts of the theory are developed microscopically using diagramatic perturbation theory.