  Correlated electron states in high mobility two-dimensional electron systems
(2DESs), including charge density waves and microemulsion phases intermediate
between a Fermi liquid and Wigner crystal, are predicted to exhibit complex
local charge order. Existing experimental studies, however, have mainly probed
these systems at micron to millimeter scales rather than directly mapping
spatial organization. Scanning probes should be well-suited to study the
spatial structure of these states, but high mobility 2DESs are found at buried
semiconductor interfaces, beyond the reach of conventional scanning tunneling
microscopy. Scanning techniques based on electrostatic coupling to the 2DES
deliver important insights, but generally with resolution limited by the depth
of the 2DES. In this Letter, we present our progress in developing a technique
called "virtual scanning tunneling microscopy" that allows local tunneling into
a high mobility 2DES. Using a specially-designed bilayer GaAs/AlGaAs
heterostructure where the tunnel coupling between two separate 2DESs is tunable
via electrostatic gating, combined with a scanning gate, we show that the local
tunneling can be controlled with sub-200 nm resolution.
