We study the impact of the ferroelectric domain wall on the ballistic conductance of the single-layer graphene channel in the heterostructure graphene / physical gap / ferroelectric film using Wentzel-Kramers-Brillouin approximation. Both self-consistent numerical modeling of the electric field and space charge dynamics in the heterostructure and approximate analytical theory show that the domain wall contact with the surface creates p-n junction in graphene channel. We calculated that the carriers' concentration induced in graphene by uncompensated ferroelectric dipoles originated from the spontaneous polarization abrupt near the surface can reach the values of 10 19 m -2 order, which is in two orders higher than it can be obtained for the gate doped graphene on non-ferroelectric substrates. Therefore we predict that graphene channel with the pn junction caused by ferroelectric domain wall would be characterized by rather high ballistic conductivity.

P-N junctions in graphene on ferroelectric have been actively studied, but the impact of piezoelectric effect in ferroelectric substrate with ferroelectric domain walls (FDWs) on graphene characteristics was not considered. Due to the piezo-effect ferroelectric domain stripes with opposite spontaneous polarizations elongate or contract depending on the polarity of voltage applied to the substrate. We show that the alternating piezoelectric displacement of the ferroelectric domain surfaces can lead to the alternate stretching and separation of graphene areas at the steps between elongated and contracted domains. Graphene separation at FDWs induced by piezo-effect can cause unusual effects. In particular, the conductance of graphene channel in a field effect transistor increases essentially, because electrons in the stretched section scatter on acoustic phonons. At the same time the graphene conductance is determined by ferroelectric spontaneous polarization and varies greatly in the presence of FDWs. The revealed piezo-mechanism of graphene conductance control is promising for next generations of graphene-based field effect transistors, modulators, electrical transducers and piezo-resistive elements.Also our results propose the method of suspended graphene fabrication based on piezo-effect in a ferroelectric substrate that does not require any additional technological procedures.