Introduction

Rapid advances in the fabrication and transfer techniques of graphene have now provided researchers with a variety of structures that have remarkably distinct electronic properties1,2,3,4,5,6. The two graphene layers with inter-layer dielectric such as boron-nitride and Al2O3, were achieved experimentally to observe the Coulomb drag effect7,8,9. Theoretical studies have predicted the condensation of electron-hole pairs in such a quantum-bilayer system10,11. Graphene heterostructures with atomically thin boron-nitride or molybdenum disulfide as a vertical transport barrier, exhibit remarkably high conductance switching ratios of ~50 and ~104 at room temperature, respectively3. In these devices, an insulating spacer is necessary to separate the graphene monolayers. The structural diversity of the two-stacked graphene monolayers, that is the layers are stacked on top of each other, nourishes hopes for future graphene based electronics12,13,14,15. The two-stacked graphene monolayers can be synthesized by chemical vapor deposition (CVD)16, identifying exfoliated fragments with folds17 or using a polymethyl methacrylate (PMMA)-transfer technique to stack two graphene monolayers18. Sequences of quantum Hall plateaus were formed for two independent graphene monolayers with electronic screening taken into account4,8,12. Independent contributions to the magnetoresistance (MR) from the Landau level spectrum of each layer were demonstrated in the two-stacked graphene monolayers17,18,19. However, for a total filling factor of zero, the inter-layer interaction leads to an insulating state which cannot be explained by completely independent monolayer graphene sheets in parallel conductance18. The coupling and decoupling of the two-stacked graphene monolayers still need further experimental studies.

Here, we develop a new method of mass production of two-stacked graphene monolayers with a clean interface. We perform Raman and electronic transport measurements on our two-stacked graphene monolayers. The Raman spectrum similar to that of a monolayer graphene shows that the two graphene monolayers remain independent. We observe asymmetric transfer curves in the field effect transistors based on the two-stacked graphene monolayers. The position of the maximum resistance of the transfer curves shifts towards higher gate voltage with increasing magnetic field because of the magnetic field induced decoupling of the two graphene monolayers. The system exhibits large positive magnetoresistance for the discrepancy of the carrier mobilities in the two graphene monolayers. The two-stacked graphene monolayers show electronic properties quite different from single-crystal monolayer and bilayer systems.

Results

Monolayer graphene was grown using CVD method on Cu foils20. The monolayer graphene has a Hall mobility ~3900 cm−2/V̇s. Figure 1(a) displays the back-gate voltage (Vg) dependence of the resistivity and Hall conductivity of a typical monolayer graphene device at 1.8 K and 14 T. The Hall plateaus at ±2, 6, 10… are well formed, which show good quality of the monolayer graphene. The MR curves at two back-gate voltages of 0 V and 7 V at 1.8 K are shown in Fig. 1(b). The MR shows clear Shubnikov-de Haas (SdH) oscillations.

Figure 1
figure 1

Low temperature electronic transport in a monolayer graphene grown by CVD.

(a) The longitudinal resistivity ρxx and Hall conductivity σxy as a function of back gate voltage Vg. (b) The magnetoresistance described as Rxx(B)/Rxx(0) as a function of magnetic field at Vg = 0 V, 7 V.

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The as-grown monolayer graphene was used to fabricate the two-stacked graphene monolayers based on our transfer techniques20. A new method was developed to fabricate the stacked graphene monolayers without any PMMA between the graphene layers. Details of the fabrication of the stacked graphene monolayers are shown in Fig. 2(a). First, a PMMA thin layer was spin-coated on a monolayer graphene surface grown on copper foil. The Cu foil was then dissolved by FeCl3 saturated solution for 30 min. The graphene/PMMA film was washed three times by 60°C deionized (DI) water. Another monolayer graphene on copper foil was used to fish out the graphene/PMMA film from deionized water. Because of the face-to-face superposition of clean graphene surfaces, there is no any PMMA between the graphene layers. The two-stacked graphene monolayers/PMMA film was then patterned into microstamps via electron beam lithography (EBL) and O2 plasma etching. After the Cu foil was dissolved and the film was rinsed, the two-stacked graphene monolayers/PMMA microstamps can be transferred onto arbitrary substrate. The optical image of one typical two-stacked graphene monolayers microstamp transferred on SiO2/Si substrate is shown in Fig. 2(b). Figure 2(c) shows the Raman spectrum of the two-stacked graphene monolayers, which is nearly the same as the monolayer graphene. It means that there is no lattice coupling between graphene layers. A weak D band implies a bit of lattice defects in graphene.

Figure 2
figure 2

Fabrication and characterization of two-stacked graphene monolayers.

(a) Details of the fabrication process of the two-stacked graphene monolayers/PMMA microstamps. (b) Optical image of typical two-stacked graphene monolayers transferred on SiO2/Si substrate. (c) Raman spectrum of the two-stacked graphene monolayers.

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As shown in Fig. 3(a), the two-stacked graphene monolayers were patterned into Hall bar configuration with a length of 6 μm and a width of 2 μm. The electrodes were formed by 5 nm/75 nm Ti/Au thin film. The back-gate voltage dependence of the longitudinal resistance (Rxx) at 1.9 K is displayed in Fig. 3(b). The maximum of the resistance locates at Vg = 37.5 V and the transfer curve exhibits asymmetric behavior with respect to 37.5 V. In particular, the two graphene monolayers may have different Dirac points because the bottom graphene contacts with the SiO2 layer while the top graphene is exposed to the atmosphere. Besides, with screening taken into account the carrier density in top graphene will be less sensitive to gate voltage than that of the bottom graphene. The Rxx − Vg curve can be explained by the parallel conduction of the two independent monolayer graphene sheets. The total conductivity can be expressed as σ = σT + σB, where the conductivities of top and bottom graphene are σT = nTeμT and σB = nBeμB, respectively. μT and μB are the carrier mobilities in the top/bottom graphene sheets, respectively. nT = CT|Vg − VD,T| and nB = CB|Vg − VD,B| are carrier densities in the two graphene sheets, where VD,T, VD,B are the Dirac neutral points, CT and CB are the capacitances between the top/bottom graphene sheets and the gate electrode. Then the total conductivity σ = CTeμT|Vg − VD,T| + CBeμB|Vg − VD,B|, where e is the charge element. When Vg is between VD,T and VD,B, the slope for σ − Vg curve is |CBeμB − CTeμT| and is much smaller than CBeμB + CTeμT. So the resistance is less sensitive to the back-gate voltage between VD,T and VD,B. Figure 3(b) shows that the resistance is less sensitive to the back-gate voltage near the Vg = 37.5 V.

Figure 3
figure 3

Devices based on two-stacked graphene monolayers.

(a) Optical image of a two-stacked graphene monolayers patterned into Hall bar configuration. (b) The longitudinal resistance Rxx as a function of back gate voltage Vg at 1.9 K.

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We investigated the magnetotransport at low temperatures, as shown in Fig. 4. Unlike the pristine monolayer graphene (see Fig. 1(b)), the two-stacked graphene monolayers exhibit large positive MR background superimposed with SdH oscillations. This is probably due to the discrepancy of the carrier mobilities in the two graphene monolayers21. In particular, the electrons deflect from the current direction without the Hall voltages balancing the Lorentz force in the two graphene monolayers simultaneously. We estimated the average Hall mobility at Vg = 0 V to be 2500 cm2V−1s−1. It is worth noting that the Hall resistivity increased with increasing the magnetic field and then decreasing above 6 T for a back-gate voltage of 40 V. This is also observed in graphene with electron-hole coexistence in disordered graphene22. In our system, electrons exist in the bottom graphene and holes in the top graphene when applied a back-gate voltage of 40 V.

Figure 4
figure 4

Magnetotransport in two-stacked graphene monolayers.

(a) The magnetoresistance described as Rxx(B)/Rxx(0)-1 at Vg = 0 V, 20 V and 40 V at 1.9 K. (b) Hall resistance at Vg = 0 V, 20 V and 40 V at 1.9 K. (c, d) Longitudinal resistance Rxx as a function of the back-gate voltage at various magnetic fields at (c) 1.9 K and (d) 300 K.

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Discussion

Figures 4(c) and 4(d) display the gate voltage dependence of the resistance at various magnetic fields. As shown in Fig. 4(c), the SdH oscillations are not as clear as that in monolayer graphene (see Fig. 1(a)). At 14 T, the interspace of the two neighboring oscillation valleys near the Dirac point is ΔVg = 40 V, corresponding to the difference of the carrier density Δn = 2.7 × 1012 cm−2 due to the gate efficiency of the SiO2 dialectical layer. The number of carrier states of each Landau level is Δn = geB/h, where g is the degeneration factor of the Landau level, h is the Planck's constant. Therefore, we can calculate that g equals 8 for the two-stacked graphene monolayers. At 300 K, we also clearly observed that the position of the resistance maxima shifts toward higher gate voltage as increasing the magnetic field (Fig. 4(d)), which indicates that the tunability of the carrier density by gate voltage decreases with increasing magnetic field. The weakening tunability of the carrier density by gate voltage may be due to the decoupling between the two-stacked graphene monolayers under high magnetic field, as graphene is of diamagnetic nature.

In summary, we develop a new method of mass production of two-stacked graphene monolayers with a clean interface. We perform Raman and electronic transport measurements on our two-stacked graphene monolayers. The Raman spectrum similar to that of a monolayer graphene shows that the two graphene monolayers remain independent. The electronic transport properties of the two-stacked graphene monolayers are quite different from monolayer and bilayer graphene. We observe the asymmetric resistance-gate voltage curves and the maxima of the resistance-gate voltage curves shift with the magnetic field. The SdH oscillations indicate the 8-folded degeneracy of each Landau level.

Methods

Monolayer graphene was grown on Cu foils in a tube furnace by CVD method. PMMA thin film was used to carry the graphene after etching Cu. Another Cu/graphene was used to stack with the graphene/PMMA. The graphene/graphene/PMMA thin film was then patterned into microstamps using PMMA as resist and EBL technique. The graphene/graphene/PMMA film was then suspended after etching the Cu. The graphene/graphene/PMMA microstamps were transferred and printed onto SiO2/Si substrate using a micromanipulator under an optical microscope. The two-stacked graphene monolayers were then fabricated into Hall bar geometry using EBL and oxygen plasmas etching. Metal electrodes were fabricated to contact with the graphene Hall bar by another round of EBL and metal deposition using electron-beam evaporation. The devices were placed in an Oxford cryostat instrument with temperature ranging from 300 K to 1.5 K and magnetic field up to 14 T. The electrical signals were measured using low frequency lock-in techniques.