Discrete lattice model for the large polaron

Abstract

The energy states of a polaron in the weak-coupling limit were first obtained by Fröhlich and co-workers, assuming that the polarization of the lattice due to the electron is continuous. If the polaron radius is comparable to the lattice constant then the assumption is inappropriate. A model based on the discrete nature of the lattice is more suitable. Such a model, based on the semiclassical zero-point energy, is proposed. We have calculated the ground-state energy of the polaron and the energy of the polaron near the bottom of the conduction band. The first discussion of the effect of lattice discreteness on the polaron energy was presented by Lepine and Frongillo who used for their calculations, a method based on the "kq" representation. Our method differs from the method of these earlier authors but the results of the two approaches are similar. Some differences exist nevertheless. The main aim of this paper is, therefore, to provide an alternate method for calculating the effect of discreteness on the polaron energy. The differences arising between the results of the two methods are discussed.