Theory of Electron‐Phonon Interaction in Metals in the Presence of an External Magnetic Field

Semiclassical treatments of the interaction of conduction electrons in metals with ultrasonic waves in the presence of a magnetic field use two coordinate systems: the laboratory system (LS) and a moving system (MS) which shares the motion of the ionic lattice. In the present work the relationship between these two formulations is studied by a quantummechanical treatment of the problem. It is shown that in the MS the semiclassical representation of the charge and current densities by means of an electron distribution function is essentially correct. In the LS, however, the off‐diagonal elements of the electron density matrix are important, and give rise to the Holstein‐effect, i.e. a component of electron current exactly in phase with the lattice current and originating from the motion of the periodic potential. Generally the formulation of the theory for Bloch electrons is more complex in the LS than in the MS. Only for the free electron model the basic equations obtain their simplest form in the LS.