  Electron transport in nanoscale devices can often result in nontrivial
spatial patterns of voltage and current that reflect a variety of physical
phenomena, particularly in nonlocal transport regimes. While numerous
techniques have been devised to image electron flows, the need remains for a
nanoscale probe capable of simultaneously imaging current and voltage
distributions with high sensitivity and minimal invasiveness, in magnetic
field, across a broad range of temperatures, and beneath an insulating surface.
Here we present such a technique for spatially mapping electron flows based on
a nanotube single-electron transistor, which achieves high sensitivity for both
voltage and current imaging. In a series of experiments using high-mobility
graphene devices, we demonstrate the ability of our technique to visualize
local aspects of intrinsically nonlocal transport, as in ballistic flows, which
are not easily resolvable via existing methods. This technique should both aid
in understanding the physics of two-dimensional electronic devices, as well as
enable new classes of experiments that image electron flow through buried
nanostructures in the quantum and interaction-dominated regimes.
