the external perpendicular magnetic field as the longitudinal or diagonal voltages obtain a Hall like component. Such electrostatic modification of the substrate can be exploited to create an abrupt p-n junction, which can be useful for engineering planar electronic Veselago lenses and focused beam splitters using controllable transistors based on graphene 21 . These results help to understand the intrinsic behavior of double neutrality points and p-n junctions in graphene field effect transistors, while contributing to a better awareness of the charge carrier characteristics in graphene p-n junctions.

Chemical vapor deposition (CVD) graphene 22,23 films were fabricated into millimeter-scale Hall effect devices using wet transfer techniques and photolithography, and four-terminal DC electrical measurements were carried out in vacuum. Color contrast of graphene on 300 nm thick SiO 2 on p-Si confirmed monolayers, which was consistent with height profile ( ∼ 1 nm) observed in atomic force microscope (AFM) measurements, see Fig. 1a and b, respectively. A sketch of the fabricated Hall bar device with the pin configuration is shown in Fig. 1c and the reported measurements are as labelled in this figure. Figure 1d shows a photograph of the device. Here, the p-Si-substrate layer served as a back-gate to control carrier density in the graphene layer and the back gate voltage sweep range was limited to -50 ≤ V G ≤ +50 V . Under ambient conditions, the gate voltage dependence of the diagonal resistance, R xx , on freshly prepared graphene Hall bar sample at the room temperature exhibited strong hysteretic behavior. The observed behavior of the sample is partly attributed to dipolar adsorbates such as water, oxygen and poly-methyl-methacrylate (PMMA), which act as charge carrier traps. Charge carrier trapping by water is a dynamic process that depends on the sweep conditions of the back gate voltage 8 , as also observed in our measurements.

In order to reduce trapped charge due to adsorbates on the surface, we stored the freshly prepared sample under vacuum at room temperature overnight. Such storage reduced the hysteretic behavior significantly and the charge neutrality point fell within the swept V G span. To introduce the second charge neutrality point, we applied electrical-stressing-voltages to the samples at room temperature with the sample in vacuum. As indicated in the literature, the electrical stressing method involves applying a large source drain voltage, together with a gate voltage on the specimen 17,18 . Here, instead of a large source-drain voltage, we applied a large current. Figure 2a illustrates traces obtained through a typical stressing procedure. Curve (1) in panel Fig. 2a displays R xx1 as a function of gate voltage V G under ambient conditions. After the sample space was evacuated, the first neutrality point appeared here around V G = +33 V , as depicted by curve (2) in panel Fig. 2a. Curve (3) illustrates R xx1 vs. V G after the sample was annealed with I DC = 1 mA for 30 min at room temperature in vacuum. This treatment shifted the first charge neutrality point to + 23 V, and indications of a second neutrality point emerged at the higher end of the gate voltage range. Subsequently, the sample underwent another annealing with 1 mA current for 60 min, with V G = -40 V . This process moved the first neutrality point closer to V G = +8 V , and the second neutrality point appeared around V G = +45 V , as shown in curve (4) in panel Fig. 2a. Finally, the sample was cooled to approximately 15 K with a gate voltage of -30 V, without applying an annealing current. Then, trace (5) in Fig. 2a was collected, which shows double neutrality points in the graphene device. We note that the second charge neutrality point disappeared when the device was exposed to ambient conditions for roughly two hours. Then, the specimen reverted to its initial state, but the p-n junction could be reestablished easily by reapplying the electrical stressing procedure. These repeatable and reversible features confirmed that the applied electrical stressing voltage did not irreversibly damage the device.

The double neutrality points observed in the R xx vs. the gate voltage traces are a signature of the formation of a p-n junction in the graphene channel. The schematic in Fig. 2b depicts the realization of the p-n junction in the graphene channel over a span that includes -4 ≤ V G ≤ 17 V. Two cones represent the graphene dispersion in two regions, and yellow plane represent the Fermi level of the system. When gate voltage is equal to -50 V, the Fermi level lies below the both neutrality points, and the entire channel is p-type as in Fig. 2b. When the gate voltage is swept towards postive voltages from -50 V , the Fermi level is shifted up and crosses the first neutrality point at V G ≈ -4 V, as R xx1 (see Fig. 2a, trace ( 5)) increases and crosses its first maximum with the gate voltage increment. A further increase in V G progressively moves up the Fermi level and, when V G ≈ +17 V, the Fermi level crosses the second neutrality point and this is reflected as the second peak in R xx1 (see Fig. 2a, trace (5)). Hence, over the gate voltage span -4 < V G < +17 V, the sample includes a p-n junction. For V G > 17 V, the entire channel is n-type because the Fermi level lies in the conduction band throughout the channel.

To extract further information, we applied Eq. ( 1), the extended fitting equation for double neutrality points 24 , which assumes the existence of multiple parallel channels contributing to the current, with each channel characterized by its own value of the neutrality point.

Here, (= 0.63) is a parameter related to a geometrical factor in the graphene channel and that depends on the physical locations of the neutrality points. Also, r s is the resistance due to short range scatters, assumed to be gate independent 24 . We found that the r s can be neglected from the fittings of our results. The µ 1 and µ 2 are charge carrier mobilities and n 1 and n 2 are residual charge concentrations in the unperturbed-and perturbed-regions, respectively, in the graphene channel. The carrier densities in these two regions are determined by electrostatic potentials. Data fits indicated that the mobility values are 6148 cm 2 /Vs and 1388 cm 2 /Vs in unperturbed and perturbed regions of the graphene, respectively. Also, the extracted values for the residual carrier concentrations are 1.59 × 10 11 cm -2 and 1.11 × 10 12 cm -2 in unperturbed and perturbed regions of the graphene, respectively.

Since it is known that as the carrier density increases, the mobility decreases for single layer graphene 25 , the high density of residual carriers in perturbed region could be responsible for a corresponding lower mobility. The application of a small perpendicular magnetic field, within the range -0.2 < B < +0.2 T produced a small change in the v , where v is the difference of the back gate voltage between resistance peaks. Further, v is associated with a trapped charge concentration n t = α�v with α = 7.2 × 10 10 cm -2 V -1 . The Fig. 3a shows the longitudinal resistance ( R xx1 ) as a function of magnetic field and gate voltage. The R xx1 color map shows maxima at the charge neutrality points. An asymmetry between hole side and electron side of the characteristic curve is observable relative to the first charge neutrality point. The second charge neutrality point on the side of positive gate voltage may lead to this R xx1 asymmetry around the original neutral point. Also, there was no significant difference in longitudinal voltage measurements V xx1 and V xx2 (see Fig. 1c) from two parallel sides of the Hall bar. The Fig. 3b represents the Hall resistance R xy1 in the unperturbed region of the graphene channel, which is physically away from the second charge neutrality point. Figure 3c depicts the Hall resistance R xy2 in the perturbed area of the graphene sample, which is physically close to the second neutrality point. Here, "unperturbed" and "perturbed" refer to the effect of the stress-voltage on neutrality point.

Figure 4 shows the �R xx = R xx(B� =0) -R xx(B=0) as a function of magnetic field and gate voltage, obtained from the two parallel sides of the Hall bar. The R xx values are close to zero over a large fraction of the color maps except where V G corresponds to gate voltages between two neutrality points. At the same time, the non- vanishing response depends on both the magnitude and the polarity of external magnetic field, with the two sides of the device showing similar behavior at opposite B field polarities. The latter feature can be understood from the observation that a non uniform Hall voltage between the perturbed and unperturbed regions must lead to an antisymmetric in B component in the longitudinal voltages, with polarity reversal on the two sides. The color plots also show a small response just beyond the two neutrality points to the opposite polarity of magnetic field in each side as shown in Fig. 4a and b.

Figure 5a shows the Hall voltage with positive and negative slopes in the perturbed region of the graphene channel for selected back gate voltage values. Figure 5b presents the non-monotonic behavior in the slope of Hall voltages across the perturbed and unperturbed region of graphene channel, as it summarizes the slope of Hall resistances ( dR xy /dB ) as a function of gate voltage. Blue spheres shows the Hall slope variation across the unperturbed region of the graphene channel. From -50< V G <-5 V, the slope remains positive and increase in magnitude, then it starts decreasing from positive values to negative values within the gate voltage range -5< V G < 0 V. From 0 < V G <+ 50 V, Hall slope remains negative but decrease in magnitude with increasing gate voltage. In Fig. 5b, the red spheres show the Hall slope in the perturbed region of the graphene, which stays positive over the span -50< V G <+ 17 V, with a small ripple within the span -5< V G < 0 V. From + 12< V G < + 25 V, slope changes from positive to negative. Above the gate voltage + 25 V, the slope remains negative but decreases in magnitude. Here, the crossover band for the unperturbed region is narrower than the band for perturbed area. This suggests that the perturbed region could also have become more inhomogeneous after the perturbation.

As a supplementary result, the current related Hall sensitivity ( S I ) of the unperturbed device as a function of gate voltage and magnetic field is shown in Fig. 6. The current related sensitivity is defined as S I = V xy /IB = ρ xy /B 26 . Both types of carriers play an important role near to the charge neutrality points of graphene, not as in unipolar type conventional semiconductors. Thus, we utilized ambipolar transport model to describe the experimental data as suggested in a previous study 27 . The current related sensitivity can be written as Eq. ( 2).

Where, e is the electron charge, r H is the Hall coefficient, n h and µ h are density and mobility of hole carriers, and n e and µ e are density and mobility of electrons. By assuming µ e = µ h close to neutrality point, we can derive Eq. ( 3).