Energy Stability of Branching in the Scanning Gate Response of Two-Dimensional Electron Gases with Smooth Disorder

Keith R. Fratus, Rodolfo A. Jalabert, Dietmar Weinmann

Published 2019-04-16Version 1

Recent experimental and theoretical investigation into the subject of electron flow through two dimensional electron gases (2DEGs) has revealed that the presence of weak, smooth disorder results in "branched flow," a phenomenon in which electron trajectories form thinly collimated branches, rather than filling space uniformly, despite the ballistic propagation of the electrons. Previous work has identified local features of the disorder potential as being responsible for the formation of these branches, understood to be a largely classical phenomenon, through the mechanism of caustic formation. Recently this phenomenon has been found to be robust against a very large shift in the Fermi energy of the electron gas. Here we study a toy model of branch formation which allows us to understand the origin and extent of this stability with respect to energy.