Transport Equations Treating Phonon Drag Effect in a Strong Magnetic Field

Abstract

The first theoretical work on the phonon drag transport in quantizing magnetic fields was made by GUREVICH and NEDLIN [1] who derived a set of coupled transport equations for electron and phonon distribution functions by using a diagramatic method proposed by KONSTANTINOV and PEREL′ [2]. Similar equations were derived by FISCHER [3] using a truncation approximation for the equation of motion of Green’s functions and by SUGIHARA [4] with a phenomenological argument. These authors all neglected the renormalization of phonon frequency due to the electron-phonon interaction. On the other hand, recent theoretical investigations [5–7] indicate that the electronic density correlation function in strong magnetic fields has singularities as a function of the wave vector because of the one-dimensional character of the electronic motion. This fact means that a phonon with a particular wave vector is expected to be softened due to the electron-phonon interaction. Such a softening of the phonon frequency will lead to an anomalous dependence of the phonon-drag thermopower on the magnetic field and temperature.