Coherent branched flow in a two-dimensional electron gas

Semiconductor nanostructures based on two-dimensional electron gases (2DEGs ) could form the basis of future devices for sensing, information processin g and quantum computation. Although electron transport in 2DEG nanostructur es has been well studied, and many remarkable phenomena have already been d iscovered (for example, weak localization, quantum chaos, universal conduct ance fluctuations(1,2)), fundamental aspects of the electron flow through t hese structures have so far not been clarified. However, it has recently be come possible to image current directly through 2DEG devices using scanning probe microscope techniques(3-13). Here, we use such a technique to observ e electron flow through a narrow constriction in a 2DEG-a quantum point con tact. The images show that the electron flow from the point contact forms n arrow, branching strands instead of smoothly spreading fans. Our theoretica l study of this flow indicates that this branching of current flux is due t o focusing of the electron paths by ripples in the background potential. Th e strands are decorated by interference fringes separated by half the Fermi wavelength, indicating the persistence of quantum mechanical phase coheren ce in the electron flow. These findings may have important implications for a better understanding of electron transport in 2DEGs and for the design o f future nanostructure devices.