Order and chaos in semiconductor microstructures

The semiclassical theory of ballistic electron transport in semiconductor microstructures provides a description of the quantum conductance fluctuations in terms of the classical distributions for the lengths and directed areas of the scattering trajectories. Because the classical dynamics differs for integrable (circular) and chaotic (stadium) scattering domains, experimental measurements of the conductance of these microstructures provide a unique probe of the quantum properties of classically regular and chaotic systems. To advance these theoretical and experimental studies we compare geometrical formulas for the classical distributions of lengths and areas with numerical simulations for microstructures examined in recent experiments, we assess the effects of lead size and placement, and we provide a critical analysis of the role of scattering "noise" on the classical and semiclassical predictions. Finally, we present a detailed comparison of the semiclassical theory with recent experimental measurements of the conductance fluctuations in circular- and stadium-shaped microstructures.