  Ultra-thin planar heterostructures of graphene and other two-dimensional
crystals have recently attracted much interest. Very high carrier mobility in a
graphene-on-boron nitride assembly is now well-established, but it has been
anticipated that appropriately designed hybrids could perform other tasks as
well. A heterostructure of graphene and molybdenum disulphide (MoS$_2$) is
expected to be sensitive to photo illumination due to the optical bandgap in
MoS$_2$. Despite significant advances in device architectures with both
graphene and MoS$_2$, binary graphene-MoS$_2$ hybrids have not been realized so
far, and the promising opto-electronic properties of such structures remain
elusive. Here we demonstrate experimentally that graphene-on-MoS$_2$ binary
heterostructures display an unexpected and remarkable persistent
photoconductivity under illumination of white light. The photoconductivity can
not only be tuned independently with both light intensity and back gate
voltage, but in response to a suitable combination of light and gate voltage
pulses the device functions as a re-writable optoelectronic switch or memory.
The persistent, or `ON', state shows virtually no relaxation or decay within
the the experimental time scales for low and moderate photoexcitation
intensity, indicating a near-perfect charge retention. A microscopic model
associates the persistence with strong localization of carriers in MoS$_2$.
These effects are also observable at room temperature, and with chemical vapour
deposited graphene, and hence are naturally scalable for large area
applications.
