One-Electron Theory of Crystalline Solids in a Homogenous Electric Field

摘要

Assuming that the one-electron states of a perfect crystalline solid are known, a method for calculation of the one-electron states in the presence of external force fields and/or the other divergences from the periodic potential of the perfect crystal is suggested. The calculation is accomplished by means of solving the equation of motion in Wannier representation. In the framework of the approximation of the one-band Wannier equation an exact solution of the problem for electron states of the crystals in a homogeneous external electric field is given. The obtained final results in a tight-binding electron approximation for cubical crystals show that the electron motion parallel to the electrical field is always finite one and the degree of its localization for a given intensity of the field is so much greater as smaller the width of the considered initial energy band is. Always the energy spectrum of electrons has a character of the Stark ladder. Also it is shown that, if there is a non-additivity in the initial dispersion law with respect to motions of electrons along the co-ordinate axes, it leads to an influence of the quasifree motion, perpendicular to the electrical field, on the character of the finite motion, parallel to the field. (Atomindex citation 13:712231)