Coherent state representation of lattice vibrations and its application to electron-phonon interaction

Since the introduction of the deformation potential model to describe electron-phonon interaction, the mechanism of the scattering of the electron by the lattice vibrations was described by phonon creation and annihilation using second quantization for the lattice vibrations. Furthermore, an incoherent concatenation of first-order scattering events using Boltzmann transport theory was used to calculate resistivity.

However, as the lattice vibrations can be treated as a classical field, it is natural to choose a coherent state, instead of a phonon Fock state, to describe lattice vibrations. In this picture, the electron scattering by the lattice vibrations can be explained without phonon creation and annihilation like an impurity scattering. It turned out that the calculated resistivity in this way gives the same result to the conventional theory up to a factor of order unity. Also, Anderson localization of an electron by the deformation potential was observed. Using the coherent state representation helps understanding electron coherence effects such as Anderson localization and Shubnikov-de Haas effect, which was not naturally described in the incoherent Boltzmann transport theory.