  The integration of graphene with complex-oxide heterostructures such as
LaAlO$_3$/SrTiO$_3$ offers the opportunity to combine the multifunctional
properties of an oxide interface with the electronic properties of graphene.
The ability to control interface conduction through graphene and understanding
how it affects the intrinsic properties of an oxide interface are critical to
the technological development of novel multifunctional devices. Here we
demonstrate several device archetypes in which electron transport at an oxide
interface is modulated using a patterned graphene top gate. Nanoscale devices
are fabricated at the oxide interface by conductive atomic force microscope
(c-AFM) lithography, and transport measurements are performed as a function of
the graphene gate voltage. Experiments are performed with devices written
adjacent to or directly underneath the graphene gate. Unique capabilities of
this approach include the ability to create highly flexible device
configurations, the ability to modulate carrier density at the oxide interface,
and the ability to control electron transport up to the
single-electron-tunneling regime, while maintaining intrinsic transport
properties of the oxide interface. Our results facilitate the design of a
variety of nanoscale devices that combine unique transport properties of these
two intimately coupled two-dimensional electron systems.
