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We study a plasma instability in semiconductor superlattices irradiated by amonochromatic, pure AC electric field. The instability leads to sustainedoscillations at a frequency \omega 2 that is either incommensurate to thedrive, or frequency-locked to it, \omega 2 = (p/q) \omega. A spontaneouslygenerated DC bias is found when either p or q in the locking ratio are evenintegers. Frequency locked regions form Arnol'd tongues in parameter space andthe ratio \omega 2 / \omega\ exhibits a Devil's staircase. A transition tochaotic motion is observed as resonances overlap.

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