  The Schottky barrier height ($E_{SBH}$) is a crucial factor in determining
the transport properties of semiconductor materials as it directly regulates
the carrier mobility in opto-electronics devices. In principle, van der Waals
(vdW) Janus heterostructures offer an appealing avenue to controlling the ESBH.
However, the underlying atomistic mechanisms are far from understood
conclusively, which prompts for further research in the topic. To this end,
here, we carry out an extensive first principles study of the electronic
properties and $E_{SBH}$ of several vdW Janus MXY/Graphene (M=Mo, W; X, Y=S,
Se, Te) heterostructures. The results of the simulations show that by changing
the composition and geometry of the heterostructure's interface, it is possible
to control its electrical contact, thence electron transport properties, from
Ohmic to Schottky with nearly one order of magnitude variations in the
$E_{SBH}$. Detailed analysis of the simulations enables rationalization of this
highly attractive property on the basis of the interplay between the permanent
dipole moment of the Janus MXY sheet and the induced one due to interfacial
charge redistribution at the MXY/Gr interface. Such an interplay is shown to be
highly effective in altering the electrostatic potential difference across the
vdW Janus heterostructure, determining its ESBH, thence Schottky (Ohmic)
contact type. These computational findings contribute guidelines to control
electrical contacts in Janus heterostructures towards rational design of
electrical contacts in nanoscale devices.
