Evidence for quantum states corresponding to families of stable and chaotic classical orbits in a wide potential well

Abstract

The quantized energy-level spectrum corresponding to stable and chaotic classical electron motion in a wide 60-nm potential well with a strong tilted magnetic field is studied by magnetotunneling spectroscopy. At low bias voltages (V\ensuremath{\lesssim}1 V) and for tilt angles \ensuremath{\theta} of the magnetic field within the domain of hard classical chaos, the current-voltage characteristic I(V) reveals several distinct series of resonances which evolve rapidly with V and \ensuremath{\theta}. In this regime, a hierarchy of unstable but periodic orbits is identified and related to fluctuations in the density of levels in the well and to the observed magnetotunneling characteristics. Widely spaced resonances in I(V) observed for V\ensuremath{\gtrsim}1 V originate from the appearance of stable orbits in regions of the classical phase space accessible to the tunneling electrons.