Introduction

The electronic properties of graphene are very sensitive to applied magnetic fields (B) and are ideally suited for the investigation of the quantum Hall effect (QHE). This is exemplified by plateaus in the Hall resistance due to the quantization of the two-dimensional electron motion into Landau levels (LL)1,2,3,4,5,6,7,8,9. The QHE, first discovered in Si metal–oxide–semiconductor field-effect transistors10, exhibits important differences in graphene due to the electron–hole degeneracy near the charge neutrality point, which leads to a distinctive half-integer QHE and a non-zero Berry’s phase of the electron wavefunction4,5,7,8,9.

Of particular significance for the QHE in graphene is the effect of dopant impurities near its surface. Screening effects in graphene11,12 tend to be weakened by a magnetic field and can facilitate the localization of charge carriers in the disordered potential of the graphene layer13,14. For example, for epitaxial graphene on a Si-terminated SiC substrate15,16,17,18, donors reside in the SiC layer adjacent to the graphene layer. These dopants act as a reservoir of electrons for graphene, maintaining the Hall voltage on the ν = 2 QH plateau over a wide range of magnetic fields19. An extended quantum Hall plateau was also observed in graphene-based field effect transistors (FETs) in which graphene is capped by a thin layer of the van der Waals crystal InSe20,21. These examples of “giant” QH plateaus in graphene have been reported at low temperatures (T < 200 K) and have been assigned to the magnetic field and electric field induced transfer of charge carriers between the degenerate LLs of graphene and the localized states in its proximity. A full microscopic model for the QHE in these hybrid systems does not yet exist. However, recent work has modeled the interaction between free carriers and localized charges near the surface of graphene22, showing that when the chemical potential is in the gap between LLs, these charges can form stable bound states over a distance of the order of the magnetic length \({l}_{B}=\sqrt{\hslash /{eB}}\) and with binding energy \({E}_{B}{\approx } \hslash {\upsilon }_{F}/{l}_{B}\), where\(\,{\upsilon }_{F}\,\)≈ 106 m/s is the Fermi velocity and e is the elementary charge. This phenomenon can persist well beyond cryogenic temperatures, opening possibilities for the manipulation of the QHE at room temperature. To date, a room temperature resistance quantum has been reported only in high mobility graphene at large magnetic fields that are available only in a few high field magnet laboratories5,23.

Here, we report on the QHE in FETs based on a single layer graphene channel capped with the insulating ferroelectric van der Waals crystal CuInP2S6 (CIPS). The CIPS layer acts as a source of localized charge carriers in proximity to graphene. We report a hysteretic behavior in the longitudinal and transverse magnetoresistance of graphene over a range of applied magnetic fields and temperatures. Similar hysteretic phenomena in the resistivity of graphene have been reported in zero magnetic field and assigned to charge trapping24,25,26,27,28,29 and/or ferroelectric polarization30,31,32,33,34. In this work, we report on the dynamic exchange of charge carriers at the CIPS/graphene interface and its influence on the QHE and its hysteretic behavior. The QHE is found to be weakly dependent on temperature over a range of easily accessible magnetic fields.

Results

Transport characteristics in zero magnetic field

The CIPS/graphene heterostructure was prepared by exfoliation and visco-elastic stamping of a CIPS flake on a Hall bar based on high-quality graphene grown by CVD (chemical vapor deposition). Figure 1a shows the optical image of a ten-terminal Hall bar, half of which is based on graphene (G) and the other half on CIPS/graphene (CG), mounted on a 285 nm-thick SiO2/n-Si substrate. The morphology of the layers was probed by atomic force microscopy (AFM) and single pass amplitude-modulated Kelvin probe force microscopy (AM-KPFM)35. The CIPS layer has a non-uniform thickness ranging from 20 to 50 nm and a uniform work function potential at the graphene/CIPS interface (Fig. 1b). Details of the fabrication and of the characterization of the CIPS flakes by AFM and piezoresponse force microscopy (PFM) are presented in the experimental section, Supplementary Note 1 and Supplementary Fig. 1.

Fig. 1: Gated Hall bar based on graphene capped with CuInP2S6.
figure 1

a Optical image of a Hall bar based on CuInP2S6/graphene (CG) on a SiO2/n-Si substrate and Ni-Au contacts. One section of the graphene layer is covered by a CIPS layer. The white dotted lines mark the edges of pristine graphene. b Amplitude-modulated Kelvin probe force microscopy (AM-KPFM) contact potential difference (CPD) map and CPD profile of CIPS/graphene measured with a Multi75E cantilever at a voltage amplitude of VAC = 4 V and frequency fAC = 17 kHz. The CPD-profile is obtained along the length of the CIPS-flake, as indicated by the white arrow in the map. c Resistance-gate voltage RXX(VG) curves for CG at T = 300 K (I = 1 μA, B = 0 T). The sweep up/down branches are shown in blue and red arrows, respectively. Curves are displaced along the vertical axis for clarity. Inset: RXX(VG) curve for a reference sample based on pristine graphene at T = 300 K (I = 1 μA, B = 0 T). This sample corresponds to the uncapped section of the graphene Hall bar shown in part (a). A sweep rate ΔVG/Δt = 0.3 V/s was used for the measurements.

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The longitudinal resistance RXX was measured at a constant current (I = 1 μA). The voltage drop VXX across different pairs of terminals along the graphene channel was measured over a range of gate voltages VG applied between the graphene and Si-gate electrodes. As can be seen in the inset of Fig. 1c, for pristine graphene the RXX(VG) curve at T = 300 K is peaked at the neutrality point VNP = +10 V. Using a capacitance model of the graphene FET, we estimate a hole density p = 7 × 1011 cm-2 at VG = 0 and a hole (electron) mobility μ = 9 × 103 cm2/Vs (1 × 104 cm2/Vs) for carrier concentrations in the range 1011–1012 cm-2 at T = 300 K.

In contrast to pristine graphene, the RXX(VG) curves for CIPS/graphene (CG) show a pronounced hysteresis and are asymmetric (Fig. 1c): The amplitude of the hysteresis increases with increasing the sweep range of VG from ΔVG = ± 10 V to ±50 V. For ΔVG = ±10 V, the RXX(VG) curves shift to lower VG compared to pristine graphene; also, the field effect (and Hall) mobility for holes and electrons is reduced from μ ~ 104 cm2/Vs to μ ~ 2 × 103 cm2/Vs. In general, the RXX(VG) curve consists of multiple peaks, suggestive of a channel with a non-uniform distribution of dopants; also, the temporal response of RXX is slow (with rise and decay times τ > 100 s). Thus, the RXX(VG) curve depends on the sweep range of VG and sweep rate ΔVG/Δt. A value of ΔVG/Δt = 0.3 V/s was used for the data presented in this work.

Hysteresis in the transport characteristics of graphene can arise from a gate-induced polarization at the interface of graphene with a ferroelectric layer33. For our CG, the hysteresis is not dominated by this phenomenon as a gate-induced ferroelectricity would produce a shift of the neutrality point VNP in the direction of the gate sweep, i.e., VNP would shift to higher voltages when VG is swept from negative to positive values compared to when VG is swept from positive to negative values. On the other hand, a hysteresis can also originate from a slow charge transfer at the CIPS/graphene interface, as reported earlier in a similar device structure25. The gate voltage induces charges in the graphene layer, which then redistribute between the graphene and CIPS layers. In the first part of the sweep of VG to positive gate voltages (VG > 0 V), electrons are transferred from graphene onto CIPS; during the reverse sweep with VG < 0 V, the CIPS layer discharges its electrons onto graphene. A non-homogeneous distribution of localized states in CIPS can create areas of graphene with different carrier densities, thus causing the multiple peaks in RXX(VG) shown in Fig. 1c.

We model the hysteresis in RXX(VG) using a classical capacitance model of the FET that takes into account a charge transfer across the CIPS/graphene interface (Supplementary Note 2 and Supplementary Fig. 2). We estimate that a charge ΔQ redistributes slowly between the graphene (Qg) and CIPS (QCIPS) layers with a characteristic time constant τ > 100 s; different regions of CG tend to charge/discharge with similar temporal dynamics; also, the value of ΔQ/e = nQ is dependent on VG and reaches values of up to nQ ~ 1012 cm-2 at large VG (VG = +50 V) and T = 300 K.

The hysteresis in RXX(VG) weakens with decreasing T (Fig. 2a) or under excitation of the sample with photons of energy (hv = 3.06 eV) larger than the band gap of CIPS (Supplementary Note 3 and Supplementary Fig. 3). Light of increasing intensity induces a shift of the neutrality point to larger positive VG and a narrowing of the RXX(VG) curve. This indicates that carriers photocreated in the CIPS layer can screen the disordered potential created by localized charges. In summary, the transport characteristics of graphene are very sensitive to charges transferred from/to the CIPS layer. This effect is observed in all our CG devices and is used to probe the role of localized charges on the QHE.

Fig. 2: Longitudinal magnetoresistance for CuInP2S6/graphene.
figure 2

a, b Resistance-gate voltage RXX(VG) curves for CuInP2S6 (CIPS)/graphene at different temperatures T (I = 1 μA) and for magnetic fields (a) B = 0 T and (b) B = 16 T. The sweep up/down branches are shown in blue and red, respectively. For clarity, curves are displaced along the vertical axis. Color plots of RXX versus B and gate voltage VG at (c) T = 4 K, (d) T = 200 K and (e) T = 300 K and different sweeps (I = 1 μA). Dashed white lines represent the calculated Landau level (LL) charts using a conventional model, as described in the text. Dashed black lines in part (e) show the calculated LL charts assuming a B-dependent charge transfer.

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Magneto-transport and quantum Hall effect

Figure 2a, b show the temperature dependence of the RXX(VG) curves for CG at B = 0 T and 16 T, respectively. At low temperatures (T ≤ 200 K), the hysteresis in RXX(VG) is weak, as also observed in the pristine graphene. However, it becomes pronounced for T > 200 K. In particular, in a magnetic field (B = 16 T in Fig. 2b), the RXX(VG) curves exhibit additional maxima and minima. To illustrate this behavior more clearly, we plot in Fig. 2c–e the color maps of RXX versus VG and B at different T and for different (up/down) sweeps of VG. For T up to 200 K (Fig. 2c, d), the bright red region in RXX(B, VG) centered at VNP ~ +30 V corresponds to the neutrality point of graphene represented by the zeroth Landau level, LL (n = 0). For both sweep up/down branches, secondary peaks in RXX(B, VG) emerge for B > 5 T at around VG = +20 V and +40 V. As VG increases from negative to positive values, first holes (VG < VNP) and then electrons (VG > VNP) fill successive LLs.

The energy-level spectrum of Dirac fermions in a magnetic field is described by the relation En = \({{{{\mathrm{sgn}}}}}(n)\sqrt{2e\hslash {v}_{F}^{2}B{{{{{\rm{| }}}}}}n{{{{{\rm{| }}}}}}}\), where n = 0\(,{{{{{\rm{\pm }}}}}}1,\,{{{{{\rm{\pm }}}}}}2\)… The spectrum comprises electron and hole LLs, as well as a LL (n = 0) at the neutrality point. We use the capacitance equation \(C=e[{{dn}}_{{{{{{\rm{g}}}}}}}/d{V}_{{{{{{\rm{G}}}}}}}]\) to calculate the voltage separation \(\Delta {V}_{G}\) of the maxima in RXX(VG) at different B. Here \(C=\varepsilon {\varepsilon }_{0}/t\) is the “classical” capacitance per unit area of the graphene/SiO2/Si heterostructure, t = 285 nm is the SiO2 layer thickness, \(\varepsilon\) = 3.9 is the relative dielectric constant of SiO2, \({\varepsilon }_{0}\) is the permittivity of free space, and ng is the carrier density in the graphene layer. We express the separation between the two maxima in RXX(VG) corresponding to the alignment of the Fermi level with the n = 0 and n = \({{{{{\rm{\pm }}}}}}1\) LLs as \(\Delta {V}_{G}\) = eg/C, where g = 4eB/h. This model reproduces the data at low T for both sweep up and down of VG (T = 4 K and 200 K in Fig. 2c, d, white dashed lines), but fails to describe the data at T > 200 K (T = 300 K in Fig. 2e, white dashed lines). At T = 300 K, the LL quantization is obscured by a large hysteresis; in particular, the neutrality point VNP shifts to larger positive VG with increasing B. The black lines in Fig. 2e describe the deviation of the LL features in RXX(B, VG) from a conventional LL chart model. The measured deviation is reproduced by considering a B-dependent charge transfer and the capacitance equation \(C=e[{{dn}}_{{{{{{\rm{g}}}}}}}/d{V}_{{{{{{\rm{G}}}}}}}]\). The magnetic field tends to reduce the density of electrons transferred from CIPS to graphene by \({{\Delta }n}_{{{{{{\rm{g}}}}}}}\,\)= 4 × 1010 cm-2 at B = 10 T and \({{\Delta }n}_{{{{{{\rm{g}}}}}}}\) = 4 × 1011 cm-2 at B = 16 T. This phenomenon can also be seen in the dependence of the Hall resistance RXY on B, VG and T, as discussed below.

Figure 3a shows the VG-dependence of RXY over a range of temperatures (T = 4–300 K) and magnetic fields from B = 0 T to 16 T. Figure 3b compares the RXY(VG) and RXX(VG) curves at B = 16 T for different T. At T = 4 K (Fig. 3a,b, i), the RXY(VG) curve shows QH plateaus centered at VG ≈ + 20 V and VG ≈ + 40 V, corresponding to the LL filling factor ν = 2 for holes and electrons, respectively. Here, ν is derived from the relation ν = ±4(∣n∣+1/2), where n is the LL index16. Plateaus corresponding to lower value of RXY can also be seen at VG ≈ −2 V (ν = 6) and VG ≈ −25 V (ν = 10). As the temperature increases to T = 100 K (Fig. 3a, b-ii) and 200 K (Fig. 3a, b-iii), the QH plateaus tend to narrow. A further increase of temperature to T ≥ 300 K (Fig. 3a, b-iv) induces a large hysteresis in the RXY (VG) curves (see also Supplementary Notes 4, 5, 6 and Supplementary Figs. 4, 5, 6). Figure 4 shows the color plots of RXY versus VG and B at T = 300 K for different (up/down) sweeps of VG. These data illustrate the sign of the ν = 2 QH plateau and its evolution with increasing values of B and VG. It can be seen that the neutrality point VNP shifts to larger positive VG with increasing B.

Fig. 3: Hall resistance for CuInP2S6/graphene.
figure 3

a Hall resistance-gate voltage RXY(VG) curves for CuInP2S6/graphene at different temperatures: (i) T = 4 K, (ii) T = 100 K, (iii) T = 200 K, (iv) T = 300 K, and magnetic field B ranging from B = 0 T to 16 T in 1 T steps (I = 1 μA). b Longitudinal resistance RXX and Hall resistance RXY versus gate voltage VG at B = 16 T and (i) T = 4 K, (ii) T = 100 K, (iii) T = 200 K, (iv) T = 300 K. Dashed lines correspond to the quantized values of RXY.

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Fig. 4: Room temperature Hall resistance for CuInP2S6/graphene.
figure 4

Color plots of the Hall resistance RXY for CuInP2S6/graphene versus magnetic field B and gate voltage VG at temperature T = 300 K (current I = 1 μA) for (a) sweep down and (b) sweep up of VG. The color bar indicates the value of RXY and its quantized value (h/2e2).

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From Fig. 3 it can be seen that the ν = 2 QH plateau is accompanied by a hysteresis that depends on T and B. This behavior is shown in more detail in Fig. 5a where the RXY(VG) curves are plotted at B = 16 T for different T. Increasing T above T = 100 K causes a shift of the neutrality point VNP to lower VG, corresponding to an increasing density of electrons in the graphene layer. This behavior is not observed in pristine graphene and is assigned to the thermal excitation of electrons from CIPS into the graphene layer. For lower T (T = 4.2 and 100 K), the shift of VNP is towards higher values of VG with increasing T, indicative of a thermal excitation of carriers near the Dirac point.

Fig. 5: Hysteresis in the Hall resistance of CuInP2S6/graphene.
figure 5

a Hall resistance RXY(VG) for CuInP2S6/graphene at magnetic field B = 16 T and different temperatures T. The sweep up/down branches are shown in blue and red, respectively. For clarity, curves are displaced along the vertical axis (current I = 1 μA). ΔVGH is the amplitude of the hysteresis in RXY(VG). b Amplitude of the hysteresis \(\left|\Delta {V}_{{{{{{\rm{GH}}}}}}}\right|\) versus T at different B. Lines are guides to the eye. For T = 4.2 K and B ≤ 5 T, \(\left|\Delta {V}_{{{{{{\rm{GH}}}}}}}\right|\,\)≈ 0. Inset: Arrhenius plot of \(\,\left|\Delta {V}_{{{{{{\rm{GH}}}}}}}\right|\) versus 1/T at B = 16 T. The dashed line is an exponential fit to the data.

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To quantify the hysteresis in RXY(VG), we consider the gate voltage at which RXY (VG) goes to zero (i.e., the charge neutrality point) on the sweep up (\({V}_{{{{{{\rm{Gu}}}}}}}\)) and sweep down (\({V}_{{{{{{\rm{Gd}}}}}}}\)) branches of RXY(VG). The difference, \(\left|\Delta {V}_{{{{{{\rm{GH}}}}}}}\right|=\left|{V}_{{{{{{\rm{Gu}}}}}}}-{V}_{{{{{{\rm{Gd}}}}}}}\right|\), is shown in Fig. 5b. For T < 200 K, \(\left|\Delta {V}_{{{{{{\rm{GH}}}}}}}\right|\) is weakly dependent on T and increases with B. For T > 200 K, the hysteresis is more pronounced and is described by the relation \(\left|\Delta {V}_{{{{{{\rm{GH}}}}}}}\right|{{\propto }}{{\exp }}(-{E}_{a}/{kT})\), where Ea is an activation energy (Ea ≈ 0.16 eV for B = 16 T, Arrhenius plot in the inset of Fig. 5b). Also, from the T-dependence of RXX(VG) on the v = 2 QH plateau, we extract an activation energy Ea-v2 = 0.05 eV and 0.09 eV for the sweep up and down branches of RXX(VG) (see Supplementary Fig. 6).

Due to the hysteresis and slow charge transfer in CG, the measurement of RXX and RXY versus B at a given VG require special consideration. For each measurement of the RXY(B) and RXX(B) curves, the value of VG was increased by small increments (ΔVG/Δt = 0.1 V/s) starting from VG = 0 V until reaching the required value of VG. The temporal dependence of RXY and RXX at B = 0 T was then followed over intervals of several minutes, as required for RXY and RXX to reach stable values. The magnetic field was then swept from B = 0 T to 16 T (sweep rate of 5 mT/s). The values of VG were selected according to the RXY(VG) curves in Figs. 3 and 4, showing plateaus on each side of the neutrality point (between the n = 0 and n = ±1 LLs) due to holes (VG ≈ + 20 V) or electrons (VG ≈ + 40 V).

Figure 6a shows the RXY(B) curves of CG for VG = +20 V at T = 4 K and 300 K. It can be seen that the RXY(B) curves exhibit a weak T-dependence; in particular, the approach to the ν = 2 QH plateau shifts to lower B-fields at T = 300 K. We have observed similar behaviors in other CG devices (Supplementary Note 7 and Supplementary Figs. 7, 8, 9), although the threshold in B for the ν = 2 QH plateau may differ depending on the quality of the graphene layer, which can contain defects introduced during the CVD-growth and/or the transfer of graphene from the Cu onto the SiO2/Si substrate. The behavior of CIPS/graphene contrasts with the strong temperature dependence of the ν = 2 QH plateau in pristine graphene (Fig. 6b, Supplementary Note 8, and Supplementary Fig. 10).

Fig. 6: Quantum Hall plateau in CuInP2S6/graphene.
figure 6

Hall resistance RXY versus magnetic field B at temperatures T = 4 K and 300 K in (a) CuInP2S6/graphene (gate voltage VG = +20 V and current I = 1 μA) and (b) pristine graphene (VG = +3 V, I = 1 μA). c Top: Schematic of bound states in CuInP2S6/graphene. Bottom: Landau levels (LLs) in graphene with Fermi level aligned between the n = 0 and n = \({{{{{\rm{\pm }}}}}}1\) LLs corresponding to the v = 2 quantum Hall plateau. d RXY versus B for CuInP2S6/graphene at different VG and T = 300 K (I = 1 μA). Negative and positive values of RXY refer to hole and electron resistivity, respectively. e RXX versus B for CuInP2S6/graphene at different VG and T = 300 K (I = 1 μA). f Deviation of RXY from the quantized value (RXY = h/2e2) versus RXX, as derived from measurements at different T, B and VG: (i) T = 4.2 K, B = 16 T, VG = 42–28 V and 16–22 V; (ii) T = 300 K, B = 14–16 T, VG = 20 V. Dashed lines are guides to the eye.

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As shown in Figs. 4,  6c, d, we can select gate voltages at which a QH plateau is observed in CG for both holes and electrons. The plateau in RXY(B) is accompanied by a corresponding decrease in RXX(B) (Fig. 6e, Supplementary Note 9, and Supplementary Figs. 11–12). However, RXX does not go to zero at values of B corresponding to the v = 2 QH plateau; also, RXY deviates from its nominal quantized value (h/2e2). As shown in Fig. 6f(i), (ii), this deviation (ΔRXY) tends to zero for decreasing RXX. Here, values of RXX and RXY are obtained from measurements of the same device at different T, B and/or VG after the onset of the v = 2 QH plateau in RXY(B). These data indicate a coupling between RXX and RXY that could be accounted for by disorder. A non-uniform channel can exhibit regions that do not have minimal resistance at the same value of B, leading to an effective misalignment of the Hall probes so that RXY is influenced by RXX36. In particular, disorder can play an important role on the ν =  2 QH plateau due to the contribution to the transport of both electrons and holes37. Using the data in Fig. 6f, we estimate the coupling parameter s = ∆RXY/RXX. A linear fit of ∆RXY versus RXX gives s = 0.04 (0.05) at T = 300 K (4.2 K), similar to the value (s = 0.038) reported for graphene/SiC devices in the literature38, although our values of ∆RXY and RXX are larger.

Discussion

The room temperature QHE was first reported in graphene and explained in terms of the magnetic field quantization of Dirac fermions in graphene5. The LL quantization energy of fermions in magnetic field is \({E}_{n}={\upsilon }_{F}\sqrt{2e\hslash B| n| }\) . For n = ±1 and B = 45 T, \({E}_{n} \sim\)250 meV, which greatly exceeds the thermal energy (~26 meV) of charge carriers at T = 300 K. However, the measured thermal activation energy \({E}_{a}\) for the quenching of the ν = 2 QH plateau in graphene corresponds to the cyclotron energy gap \({E}_{1}={\upsilon }_{F}\sqrt{2e\hslash B}\) only at high magnetic fields (B ≈ 30 T), but it is smaller at lower B39. At high B, the number of states with zero energy (n = 0 LL) is determined by the total magnetic flux and does not depend on disorder. Thus, the n = 0 LL is well separated from its neighboring (n = ±1) LLs; in contrast, for lower B, LL mixing due to disorder broadens the LLs, leading to \({E}_{a} < {E}_{1}\)39. Thus, the observation of the ν = 2 QH plateau at room temperature in graphene requires a large B accessible only in a few high field facilities. In our CIPS/graphene sample the ν = 2 QH plateau is observed at relatively small B over a wide range of temperatures, yet it is not seen in pristine graphene in the same range of B. This observation merits further consideration.

First, we note that the CIPS layer is a dielectric that acts as a source of disorder for graphene via charge transfer across the CIPS/graphene interface, which is tuneable by gating and is temperature dependent. Regions of CIPS with different densities of localized states tend to charge and discharge with a similar slow (~100 s) time constant at room temperature, thus accounting for the gate-induced hysteresis in the transport characteristics (Fig. 1c). The hysteresis is significant at T > 200 K (Fig. 2), symptomatic of a thermally activated transfer of charges from/to the CIPS layer onto graphene. A comparison of the transfer characteristics and the hysteresis for CG at B = 0 and 16 T indicates that the charge transfer across the CIPS/graphene interface is influenced by magnetic field. The magnetic field acts to enhance the hysteretic behavior and distorts the VG-dependence of RXX and RXY around the charge neutrality point. As shown in Figs. 2e and 4, for B ≥ 10 T the color regions in RXX and RXY corresponding to the zeroth LL tend to shift to larger VG with increasing B, consistent with a reduced transfer of electrons from the CIPS layer onto graphene due to an increased localization of charges in the quantizing magnetic field. This can also be seen in Fig. 5b, where the hysteresis, as measured by \(\left|\Delta {V}_{{GH}}\right|\), increases with B.

Reference 22 offers an insight into the role of localized charges near the surface of graphene: For a range of chemical potentials inside the gap between the zeroth and first LLs, charged impurities can form stable “molecules” bound by free carriers of opposite sign within graphene22. The optimal distance between charges in the bound state is of the order of the magnetic length \({l}_{B}=\sqrt{\hslash /{eB}}\) and their binding energy scales as \({E}_{B}= \hslash {\upsilon }_{F}/{l}_{B}\). For B = 16 T, this gives \({l}_{B}=\)6.4 nm and EB = 0.10 eV. This binding energy is comparable to the activation energy of the T-dependent hysteresis in RXY (Fig. 5b) and to the effective LL activation energy gap obtained from the T-dependence of RXX (Supplementary Fig. 6). We note that a strongly disordered system cannot show the QHE because no LL quantization can occur. However, it is well established that the standard picture of the QHE requires the existence of disorder and localized states. This enables the Fermi level to be pinned at energies between the extended states of adjacent LLs. The presence of disorder is a key feature of the QHE and its thermal stability: it acts to pin the Fermi level at the localized states between the LLs and maintains the Hall voltage on the plateaus. The charge transfer between CIPS and graphene is reversible, leading to the ν = 2 QH plateau for both electrons and holes, as shown in Figs. 4 and 6.

We now consider our findings in the context of ongoing research on other hybrid systems based on graphene. For example, the use of a conducting layer, such as the relatively small band gap semiconductor InSe (~1.3 eV at T = 300 K) to form an InSe/graphene FET, facilitates the observation of a giant QH plateau, but its observation at room temperature is prevented by parallel conduction in the InSe layer20,21. The use of a high-resistance dielectric poses other challenges. A giant QH plateau has been reported in graphene grown epitaxially by thermal annealing of a SiC dielectric substrate. In this case, the charge transfer across the SiC/graphene interface involves defects in SiC with a high densities of states (1014 cm−2 eV−1) in close proximity to graphene15,16,17,18,19. These states arise from atomic-scale defects within the top few SiC layers, which are created during the formation of the graphene layer by Si-sublimation. For graphene on SiC, the giant QH effect was reported at temperatures of up to

T ~ 100–200 K, suggesting that the bound states in SiC/graphene have a relatively small binding energy even at high B (>20 T). Alternatively, hexagonal boron nitride (hBN) represents an ideal dielectric for graphene-based FETs40. Charge and surface fluctuations in hBN tend to be weaker than in other substrates, such as SiO2. Thus, graphene on hBN has a high-mobility and is well suited for observations of integer and fractional QHE41,42. In particular, the formation of moiré superlattices in rotationally misaligned graphene/hBN layers can promote interfacial charge transfer and new quantum transport regimes43,44,45,46. More recently, a hybrid system based on CrOCl-graphene revealed an exotic QH effect phase due to the formation of a long-wavelength charge ordering47. In all these different hybrid systems, the band structure of graphene is modified around the Dirac cone as a result of an interfacial charge transfer involving a semiconductor or an insulator. However, for all these systems the observation of quantum effects at high temperatures has proven to be challenging. Our choice of CIPS provides an effective layer for charge transfer as CIPS is a dielectric and its defect states are not only sufficiently dense (~1012 cm−2 eV−1), but also they form bound states that are sufficiently deep to be resilient to thermal ionization. The high temperatures (T > 200 K) for charge transfer and hysteresis in the transport curves corresponds to that required for activating the thermal motion of the Cu-ions48,49 out of the CIPS layer planes. The slow motion of localized ionic charges could be responsible for the slow dynamics of charge transfer at the graphene/CIPS interface, leading to the hysteretic transport observed in this system. Since CIPS is a dielectric and electrons remain bound onto its localized states, the QH voltage in graphene is not short-circuited by a significant parallel conduction in CIPS.

In conclusion, the controlled transfer of charges between graphene and localized states in its proximity provides a route for the observation of the QHE over a wide range of temperatures and in readily accessible magnetic fields. The electric field-induced transfer of charge between the CIPS and graphene layers acts to increase or decrease the carrier density in graphene, causing a change in its resistance that is gate-tuneable. The charge transfer causes hysteretic behavior in the electrical characteristics due a slow dynamic exchange of electrons between graphene and localized states in its proximity. Prospects for further research include a more accurate resistance quantization, which will require progress in both material growth and fabrication processes. This requires high-mobility homogenous graphene, a homogenous charge transfer at the graphene/CIPS interface, and the fabrication of low-resistance contacts. A more uniform CIPS/graphene heterostructure could be achieved by the development of scalable growth techniques (for example using epitaxial graphene grown with intrinsic structural alignment on SiC) together with the fabrication of high-quality electrical contacts, such as electrodes with the edge-contact geometry50. Thus, there are prospects for further studies and for engineering interfacial charge transfer in hybrid systems based on graphene for the observation of quantum effects over a wide parameter space beyond the current state-of-the-art for future applications, such as graphene-based resistance standards51.

Methods

Materials and device fabrication

The CuInP2S6 crystal was purchased from HQ Graphene. Graphene Hall bars were fabricated at the NEST laboratories at the Istituto Italiano di Tecnologia, Pisa, Italy. The fabrication of high-mobility CVD-grown graphene Hall bars before the deposition of CIPS is crucial for the observation of the QHE. Single-crystal graphene used in this work was grown on Cu foil by CVD in a cold-wall reactor (Aixtron BM Pro) using chromium nucleation seeds52. Graphene crystals were electrochemically delaminated from the growth substrate in 1 M NaOH and deposited on SiO2/n-doped Si wafers using semi-dry transfer53. The fabrication of the Hall bars was carried out using e-beam lithography (20 kV, Raith Multibeam on Zeiss Ultra Plus scanning electron microscope). The graphene Hall bars were prepared using reactive ion etching (gas flow 80 sccm O2 and 5 sccm Ar, RF power 35 W) and electrical contacts were deposited by thermal evaporation of 7 nm of Ni and 60 nm of Au. A Poly(methyl methacrylate) (PMMA) resist (950 K, 4.5% in anisole, Allresist) was used for lithography, followed by 2-step cleaning in acetone and removal of AR600-71 (Allresist) to ensure a polymer-free surface of graphene54. The wafer containing the graphene Hall bar devices was covered with a protective coating of PMMA for dicing and storage. The processed wafers were diced into ~4 × 4 mm2 chips and then cleaned in hot acetone (T ∼ 65 °C) for 1 h, rinsed with isopropyl alcohol (IPA) and dried with pressurized nitrogen gas to remove the protective PMMA coating. These devices were then annealed in a tube furnace at T = 300 °C for 3 h in a 5% H2 and 95% Ar flowing gas atmosphere to remove surface impurities and residues on the graphene surface. The graphene was then used for stamping the CIPS layer to form the CIPS/graphene heterostructure. The interface between graphene and CIPS after stamping was not further cleaned. The heterostructure was fabricated by exfoliating a CIPS flake onto polydimethylsiloxane (PDMS) from a low-residue tape and identified using optical microscopy. By using a micromanipulator stage, an exfoliated flake of CIPS on PDMS was aligned to one section of the graphene Hall bar and brought into contact with it. The PDMS was then slowly retracted in order to deposit CIPS. The graphene Hall bar capped with CIPS was bonded into non-magnetic chip carriers for electrical measurements.

Optical, electrical and microscopy studies

The surface topography of the flakes was acquired by atomic force microscopy (AFM, Park NX20) in non-contact mode under ambient conditions. The KPFM study was conducted using an additional lock-in amplifier connected to the same AFM system. Transport measurements in the dark and under light illumination were conducted in vacuum (2 × 10-6 mbar) using Keithley-2400 source-meters and Keithley-2010 multi-meters. A temperature controller from Lakeshore Cryotronics was used to control and probe the temperature. A solid-state laser (λ = 405 nm) and a He-Ne laser (λ = 632.8 nm) were used for the optical studies. The position of the laser spot was adjusted on the device and measurements were taken at different powers. A cryogen free magnet (Cryogenic Limited) was used to perform the magneto-transport studies over a range of temperatures.