Is it the boundaries or disorder that dominates electron transport in semiconductor `billiards'?

TL;DR

This paper challenges the traditional view that boundary shape solely determines electron transport in semiconductor billiards, providing evidence that small-angle disorder scattering at sub-100 nm scales plays a dominant role.

Contribution

The study presents strong evidence that small-angle scattering, rather than boundary shape, primarily influences electron transport in semiconductor billiards, impacting their use in quantum chaos experiments.

Findings

Magnetoconductance measurements are highly sample-dependent.

Boundary shape has limited influence on electron dynamics.

Small-angle scattering dominates transport at sub-100 nm scales.

Abstract

Semiconductor billiards are often considered as ideal systems for studying dynamical chaos in the quantum mechanical limit. In the traditional picture, once the electron's mean free path, as determined by the mobility, becomes larger than the device, disorder is negligible and electron trajectories are shaped by specular reflection from the billiard walls alone. Experimental insight into the electron dynamics is normally obtained by magnetoconductance measurements. A number of recent experimental studies have shown these measurements to be largely independent of the billiards exact shape, and highly dependent on sample-to-sample variations in disorder. In this paper, we discuss these more recent findings within the full historical context of work on semiconductor billiards, and offer strong evidence that small-angle scattering at the sub-100 nm length-scale dominates transport in these devices, with important implications for the role these devices can play for experimental tests of ideas in quantum chaos.