We study the quantum “branched flow” pattern of electron flux from a quantum point contact (QPC) traveling over a random background potential in two-dimensional electron gases (2DEGs) as well as in the depths of the ocean leading to freak wave development.
For instance, we have studied how disorder affects the spatial structure of electron transport by imaging electron flow in three different GaAs/AlGaAs 2DEGs, whose mobilities range over an order of magnitude. As expected, electrons flow along narrow branches that we found remain straight over a distance roughly proportional to the mean free path. We also observed two unanticipated phenomena in high-mobility samples. In our highest-mobility sample we observed an almost complete absence of sharp impurity or defect scattering, indicated by the complete suppression of quantum coherent interference fringes. Also, branched flow through the chaotic potential of a high-mobility sample remains stable to significant changes to the initial conditions of injected electrons. (Nature Physics 3, 841 - 845 (2007))
a–c, Electron flow originates from the QPC formed between the two depletion regions, schematically indicated in black below each image. The length over which branches remain straight depends on the sample's mean free path. a, Sample A, with mean free path 1.5 m, has branches that quickly change direction or are hard to assign a direction. b, Sample B, with mean free path 13 m, has branches that remain straight over moderate length scales. The average distance along a branch of flow between observable branch points is 480 nm. c, Sample C, with mean free path 28 m, has branches that remain straight over the longest length scales. The average distance along a branch of flow between branch points is 740 nm. b,c, Red arrows denote two neighbouring, observable branch points where one branch splits into two. d, Schematic diagram showing metallic gates and tip (orange) creating depletion regions (black) in the 2DEG (green) buried below the surface of the sample.