We investigate how fractals evolve into nonfractal behavior as the generation process is gradually suppressed. Fractals observed in the conductance of semiconductor billiards are of particular interest because the generation process is semiclassical and can be suppressed by transitions towards either fully classical or fully quantum-mechanical conduction. Investigating a range of billiards, we identify a "universal" behavior in the changeover from fractal to nonfractal conductance, which is described by a smooth evolution rather than deterioration in the fractal scaling properties.

Recent investigations of fractal conductance fluctuations (FCF) in electron billiardsreveal crucial discrepancies between experimental behavior and the semiclassical Landauer-Buttiker (SLB) theory that predicted their existence. In particular, the roles played by the billiard's geometry, potential profile and the resulting electron trajectory distribution are not well understood. We present new measurements on two custom-made devices -a 'disrupted' billiard device and a 'bilayer' billiard device -designed to directly probe these three characteristics. Our results demonstrate that intricate processes beyond those proposed in the SLB theory are required to explain FCF.

We present a low-temperature ͑mK͒ magnetotransport study, using intense pulsed magnetic fields to 50 T, of two double GaAs quantum well, triple AlAs barrier resonant tunneling structures, which demonstrates the critical influence of the second quantum well on the tunneling behavior. We show that charge accumulation in the first well, and thus the overall tunneling characteristic, is controlled by the position of the lowest bound state in the second well, and identify tunneling transitions that are unique to triple-barrier structures. We also demonstrate that the tunneling current is sensitive to integer and fractional quantum Hall effect states, and find that the voltage-tunable accumulation of charge in one of the samples provides an unusual environment for the study of ground states of a two-dimensional electron system. ͓S0163-1829͑96͒06431-4͔

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