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We revealed that 180 degree ferroelectrics domain walls (FDWs) in aferroelectric substrate, which induce p-n junctions in a graphene channel, leadto the nontrivial temperature and gate voltage dependences of the perpendicularand parallel modes of the integer quantum Hall effect. In particular the numberof perpendicular modes v, corresponding to the p-n junction across the graphenechannel varies with gate voltage increase from small integers to higherfractional numbers, e.g.v=1, 1.5, 2, ... 5.1,..9.1, 23 in the vicinity of thetransition from ferroelectric to paraelectric phase.These numbers and theirirregular sequence principally differ from the sequence of fractional numbersv=1.5,2.5,... reported earlier. The origin of the unusual v-numbers issignificantly different numbers of the edge modes, v1 and v2, corresponding tosignificantly different concentration of carriers in the left (n1) and right(n1) domains of p-n junction boundary. The concentrations n1 and n2 aredetermined by the gate voltage and polarization contributions, and so theirdifference originates from the different direction of spontaneous polarizationin different domains of ferroelectric substrate. The difference between n1 andn2 disappears with the vanishing of spontaneous polarization in a paraelectricphase. The phase transition from the ferroelectric to paraelectric phase cantake place either with the temperature increase (temperature-induced phasetransition) or with the decrease of ferroelectric substrate thickness(thickness-induced phase transition).

Integer Quantum Hall Effect in Graphene Channel with p-n Junction at Domain Wall in Ferroelectric Substrate