Devil's staircase, spontaneous-DC bias, and chaos via quasiperiodic plasma oscillations in semiconductor superlattices

Abstract

We study a plasma instability in semiconductor superlattices irradiated by a monochromatic, pure ac electric field. The instability leads to sustained oscillations at a frequency ω2 that is either incommensurate to the drive, or frequency-locked to it, ω2 = (p/q)•ω. A spontaneously generated dc bias is found when either p or q in the locking ratio are even integers. Frequency locked regions form Arnol'd tongues in parameter space and the ratio ω2/ω exhibits a Devil's staircase. A transition to chaotic motion is observed as resonances overlap.

Beyond the ordinary acoustoelectric effect: Superluminal phenomena in the acoustic realm and phonon-mediated Bloch gain

“…To characterize the kinetic properties the electrons bunches, we introduce the average momentum p a = p φ h/d, where p φ = arg(m 1 ) is a circular mean angle. Here m 1 = exp(ip x (t )d/ h) x i is the first trigonometric moment m 1 of the distribution function [51,52]. The operator .…”

“…This method relies on superlattice balance equations[51] and their connection to rotationally symmetric distributions in directional statistics[52].…”

Beyond the ordinary acoustoelectric effect: superluminal phenomena in the acoustic realm and phonon-mediated Bloch gain

“…To characterize the kinetic properties the electrons bunches, we introduce the average momentum p a = p φ /d, where p φ = arg(m 1 ) is a circular mean angle. Here m 1 = exp(ip x (t)d/ ) xi is the first trigonometric moment m 1 of the distribution function [51,52]. The operator .…”