  The p-n junctions dynamics in graphene channel induced by stripe domains
nucleation, motion and reversal in a ferroelectric substrate is explored using
self-consistent approach based on Landau-Ginzburg-Devonshire phenomenology
combined with classical electrostatics. We revealed the extrinsic size effect
in the dependence of the graphene channel conductivity on its length. For the
case of perfect electric contact between the ferroelectric and graphene,
relatively low gate voltages are required to induce the pronounced hysteresis
of ferroelectric polarization and graphene charge in response to the periodic
gate voltage. Pronounced nonlinear hysteresis of graphene conductance with a
wide memory window corresponds to high amplitudes of gate voltage. We predict
that the considered nano-structure "top gate/dielectric layer/graphene
channel/ferroelectric substrate" can be a promising candidate for the
fabrication of new generation of modulators and rectifiers based on the
graphene p-n junctions.
