Chaotic electron dynamics in a semiconductor superlattice

A theory for electron dynamics in a semiconductor superlattice in the presence of external electric and magnetic fields is presented. A semiclassical non-linear equation of motion for a single electron in the combined external electric and magnetic fields and self-field induced by current density of electrons is then derived. The elastic and inelastic (dissipative) electron scatterings are taken into account. A fourth-order Runge-Kutta method with adaptive step size is used to integrate non-linear equation of motion. To determine chaotic electron motion in a semiconductor superlattice Liapunov exponents are calculated. It is shown that for external magnetic field perpendicular to the external electric field the electron motion becomes non-chaotic and regular.