  Using continuous approximation we study the static and high-frequency heat
dissipation in multi-layer graphene on a ferroelectric. We demonstrate that the
Joule heating effect, caused by a high-frequency ac electric current in
graphene, creates a pronounced temperature gradient in a ferroelectric
substrate. The pyroelectric effect transforms the gradient into the spontaneous
polarization gradient.. Therefore, the high-frequency depolarizing electric
field occurs and penetrates in the multi-layer graphene. Free charges in
graphene immediately screen the electric field and thus their density
oscillates at high-frequency. Performed calculations had proved that the
pyroelectric effect can modify essentially the free carrier density at the
graphene-ferroelectric interface and consequently the conductivity of
multi-layer graphene channel. So, pyroelectric mechanism can be critical for
understanding of the complex physical thermal and electrical processes taking
place across and along graphene-ferroelectric interfaces at terahertz
frequencies.
