Quantum chaotic transport in double barrier tunnel structures

Abstract

The transition from regular to chaotic classical electron dynamics in a wide potential well with a high tilted magnetic field is investigated using Poincaré sections. The corresponding quantized energy level spectrum for the well is calculated as a function of the tilt angle π. For values of π where the system exhibits strong classical chaos, the distribution of nearest-neighbor level spacings obeys universal Wigner statistics. Regular long-range fluctuations in the density of levels are identified and related to distinct unstable closed classical orbits in accordance with the Gutzwiller trace formula. These orbits are found to produce regions of high probability density (scars) in the wavefunctions associated with subsets of almost equally-spaced energy levels. The energies of these scarred states can be located using a simple semiclassical quantization rule. This periodic scarring of individual wavefunctions is shown to have a pronounced influence on the tunneling characteristics of double barrier structures. Tunneling transitions into the scarred states dominate the current-voltage curves and generate a series of resonant peaks as observed in recent magnetotunneling experiments. Regimes in which resonant tunneling spectroscopy might provide experimental evidence for the existence of scarred states are identified.