Scanning Gate Microscopy
Contact Michael Jura (jura@) or Mark Topinka (mtopinka@) for more information.
Until recently, most research on mesoscopic systems relied on electrical transport measurements to understand how electrons flow and organize themselves. While a great deal has been learned from these transport measurements, they are in some sense blind to direct spatial information. Scanning gate microscopy (SGM) instead gives direct spatial information about the locations of electrons.
While scanning tunneling microscopy (STM) is often used to spatially investigate electronic properties of surfaces, STM is not an option for studying mesoscopic systems located in a GaAs/AlGaAs two-dimensional electron gas (2DEG) because the 2DEG is typically around 100 nm below the surface of the sample. Instead of measuring tunneling from a tip to the sample of interest, SGM relies on the capacitive gating effect of a scanned metallic tip.
GaAs-based 2DEGs display a wide variety of amazing electronic states, such as the fractional quantum hall effect, and serve as the basis for fast transistors, research on electrons in nanostructures, and prototypes of quantum computing schemes. All these uses depend on GaAs 2DEGs' extremely low levels of disorder. We have been particularly interested in using SGM to understand how disorder in 2DEGs affects electron flow and conversely to use features in images of electron flow to understand the disorder potential.
Figure 1: Electron flow in three samples with different mean free paths. Electrons originate from a 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
Figure 1 shows branched flow through three different 2DEGs, with mean free paths ranging by over an order of magnitude. There is an amazing branching structure to the flow patterns, even on length scales much shorter than the mean free path. Electrons flowing over many small-angle scattering sites are focused into these branches , and we have investigated various properties of these branches. The flow varies from twisted and diffusive in the lowest mean free path sample to straight, smooth branches of flow in the highest mobility sample .
We have also investigated how stable the positions of these branches are to changes in the initial conditions of electrons injected into the 2DEG . We have found the positions of these branches are quite stable to significant changes in initial conditions even though the disorder potential they are moving through is classically chaotic. The stability of these branches is an interesting feature of quantum mechanical flow through a chaotic potential.
 Topinka, M. A. et al. Coherent branched flow in a two-dimensional electron gas. Nature 410 183–186 (2001).
Goldhaber-Gordon Lab References
 M.P. Jura, M.A. Topinka, L. Urban, A. Yazdani, H. Shtrikman, L.N.
Pfeifer, K.W.West, and D. Goldhaber-Gordon, "Unexpected features of
branched flow through high mobility two-dimensional electron gases", to
be published in Nature Physics (2007).