Tunneling spectroscopy of mixed stable-chaotic electron dynamics in a quantum well

Experimental and theoretical studies of mixed stable-chaotic electron dynamics in the quantum well of a resonant tunneling diode are reported. The classical orbits of electrons injected into the well from an emitter accumulation layer change from regular to chaotic when an applied magnetic field is tilted away from the normal to the well walls. In the regime of mixed stable-chaotic electron dynamics, we identify a period-tripling bifurcation, which, in contrast to previous experiments, is directly accessible to the tunneling electrons. Stable classical orbits associated with this bifurcation are related directly to the wave functions of the quantum well using a Wigner function analysis. There is a striking similarity between the form of the electron Wigner functions and the corresponding classical Poincare sections. This allows us to identify subsets of quantum well states associated with stable orbits around the period-tripling bifurcation. These states control the flow of electrons through the device and produce a series of strong resonant peaks in the measured current-voltage characteristics. We also identify resonant features associated with "scarred" quantum well states in which the probability density is concentrated along an unstable but periodic classical path.