Limit cycle theory of self-sustained current oscillations in sequential tunneling of superlattices

A unified theory of self-sustained current oscillations (SSCOs) is presented. We establish these oscillations as the manifestations of limit cycles, around unstable steady-state solutions caused by the negative differential conductance. This theory implies that both the generation and the motion of an electric field domain boundary are universal in the sense that they do not depend on the initial conditions. Under an extra, weak ac bias with a frequency ωac, the frequency must be either ωac or an integer fractional of ωac if the tunneling current oscillates periodically in time, indicating the periodic doubling for this nonlinear dynamical system.