Chaotic effects in electron drag processes in metals

Abstract

We investigate theoretically and experimentally the dependence of the electron drag force on the magnetic field H in normal metals. The conventional theory assumes a linear increase with increasing H. Here we demonstrate that F(H) α H^β . Our experiments with a zinc crystal give β = 2·27. Thoretically, assuming diffusive motion, we obtain 2 ⅓ < β < 2 ½. Unlike the linear theory where the cyclotron motion remains unaffected by the dislocation potential, here we show with numerical simulations that an isolated dislocation gives rise to chaotic scattering. The origin of the nonlinear dependence of the drag force is related to the substantial deviation of a typical electron trajectory from its unperturbed cyclotron motion. Using a topological criterion of chaos, the diffusion coefficient was estimated as D α 1/|K|^½, where K is the Gaussian curvature of the potential energy surface. The diffusive motion is seen to result from the combined effects of deterministic chaotic motion (by a single dislocation) and the scattering by randomly distributed defects in a real sample.