Coherent Branched Flow in a Two-Dimensional Electron Gas
  Semiconductor nanostructures based on two dimensional electron gases (2DEGs) have the potential to provide new approaches to sensing, information processing, and quantum computation. Much is known about electron transport in 2DEG nanostructures and many remarkable phenomena have been discovered (e.g. weak localization, quantum chaos, universal conductance fluctuations)1,2 - yet a fundamental aspect of these devices, namely how electrons move through them, has never been clarified. Important details about the actual pattern of electron flow are not specified by statistical measures such as the mean free path. Scanned probe microscope (SPM) measurements allow spatial investigations of nanostructures, and it has recently become possible to directly image electron flow through 2DEG devices using newly developed SPM techniques3-13. Here we present SPM images of electron flow from a quantum point contact (QPC) which show unexpected dynamical channeling - the electron flow forms persistent, narrow, branching channels rather than smoothly spreading fans. Theoretical study of this flow, including electron scattering by impurities and donor atoms, shows that the channels are not due to deep valleys in the potential, but rather are caused by the indirect cumulative effect of small angle scattering. Surprisingly, the channels are decorated by interference fringes well beyond where the simplest thermal averaging arguments suggest they should be found. These findings may have important implications for 2DEG physics and for the design of future nanostructure devices. 
M.A.Topinka, B.J.LeRoy, R.M.Westervelt, S.E.J.Shaw, R.Fleischmann,   E.J.Heller, K.D.Maranowski, A.C.Gossard