A theoretical investigation was made of the dependence of the electron drag force, in normal metals, upon the magnetic field strength. Previous theories had assumed a linear increase with increasing magnetic field strength. It was demonstrated here that the force had a power-law dependence upon magnetic field strength. The exponent for Zn crystals was shown experimentally to be 2.27. By assuming diffusive motion, a theoretical value of between 2.33 and 2.25 was obtained. Contrary to the linear theory, where cyclotron motion remained unaffected by the dislocation potential, numerical simulations here showed that an isolated dislocation gave rise to chaotic scattering. The origin of the non-linear dependence of the drag force was attributed to a substantial deviation of the typical electron trajectory from its unperturbed cyclotron motion. By using a topological criterion for chaos, the diffusion coefficient was estimated to be inversely proportional to the square root of the Gaussian curvature of the potential-energy surface. The diffusive motion was seen to result from the combined effects of deterministic chaotic motion (by a single dislocation) and of scattering by randomly distributed defects.

Chaotic Effects in Electron Drag Processes in Metals. J.M.Galligan, L.N.Gumen, I.V.Krivoshey, A.A.Krokhin, G.A.Luna-Acosta: Philosophical Magazine A, 1998, 77[2], 507-21