Integer quantum Hall effect in graphene channel with p-n junction at domain wall in a strained ferroelectric film

We revealed that 180° domain walls in a strained ferroelectric film can induce p-n junctions in a graphene channel and lead to the nontrivial temperature and gate voltage dependences of the perpendicular modes of the integer quantum Hall effect (IQHE). In particular, the number of perpendicular modes v⊥, corresponding to the p-n junction across the graphene channel, varies with the gate voltage increase from small integers to higher non-integer numbers, e.g., v⊥ = 1.9, 2, …, 5.1, 6.875, …, 9.1, …, 23,…, 37.4, in the vicinity of the transition temperature from the ferroelectric to paraelectric phase. The non-integer numbers and their irregular sequence principally differ from the sequence of non-integer numbers ν = 3/2, 5/3, … reported earlier. The unusual v⊥-numbers originate from significantly different numbers of the edge modes, ν1 and ν2, corresponding to different concentrations of carriers in the left (n1) and right (n2) domains of the p-n junction boundary. The concentrations n1 and n2 are determined by the gate voltage and spontaneous polarization contributions, and so their difference originates from different directions of the spontaneous polarization in different domains of the strained ferroelectric film. The difference between n1 and n2 disappears with the vanishing of the film spontaneous polarization in a paraelectric phase. The temperature transition from the ferroelectric to paraelectric phase taking place in a strained ferroelectric film can be varied in a wide temperature range by an appropriate choice of misfit strain so that the first plateaus of the predicted IQHE effect can be observed even at room temperatures.We revealed that 180° domain walls in a strained ferroelectric film can induce p-n junctions in a graphene channel and lead to the nontrivial temperature and gate voltage dependences of the perpendicular modes of the integer quantum Hall effect (IQHE). In particular, the number of perpendicular modes v⊥, corresponding to the p-n junction across the graphene channel, varies with the gate voltage increase from small integers to higher non-integer numbers, e.g., v⊥ = 1.9, 2, …, 5.1, 6.875, …, 9.1, …, 23,…, 37.4, in the vicinity of the transition temperature from the ferroelectric to paraelectric phase. The non-integer numbers and their irregular sequence principally differ from the sequence of non-integer numbers ν = 3/2, 5/3, … reported earlier. The unusual v⊥-numbers originate from significantly different numbers of the edge modes, ν1 and ν2, corresponding to different concentrations of carriers in the left (n1) and right (n2) domains of the p-n junction boundary. The concentrations n1 and n2 are determine...