Periodic Orbit theory for Resonant Tunneling Diodes : comparison with quantum and experimental results

Abstract

We investigate whether the quantal and experimental amplitudes of current oscillations of Resonant Tunneling Diodes in tilted fields are obtainable from Periodic Orbit (PO) theories by considering recently proposed PO approaches. We show, for the first time, that accurate amplitudes and frequency shifts for the current oscillations (typically to within a few %) can be obtained from a simple analytical formula both in the stable (torus-quantization) limit and the unstable regimes of the experiments which are dominated by isolated PO's. But we find that the PO approach does not describe quantitatively the dynamically interesting intermediate experimental regimes which appear to be dominated by contributions from complex orbits and multiple non-isolated PO's. We conclude that these regimes will not easily be described by the usual PO approach, even with simple normal forms.