Letter pubs.acs.org/NanoLett
Electronic Transport in Two Stacked Graphene Monolayers Dong-Hun Chae,*,† Ding Zhang, Xuting Huang, and Klaus von Klitzing Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany S Supporting Information *
ABSTRACT: We report on interlayer and lateral electronic transport measurements in two stacked graphene monolayers which have separate electrical contacts. The current−voltage characteristic across the two layers shows linear Ohmic behavior at zero magnetic field. At high magnetic fields, sequences of quantum Hall plateaus of the overlap region with filling factors 4, 8, and 12 are observed which can be explained by equilibration of the edge channel potentials of the individual graphene layers. An anomaly is observed at total filling factors ±2 in the overlap region. The I−V characteristic for interlayer transport turns nonlinear, and the Hall signal vanishes, indicating a magnetic field induced electrical decoupling of the two graphene layers. KEYWORDS: Graphene, non-Bernal stacked graphene bilayer, quantum Hall effect, interlayer transport, electrical coupling
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sequence of quantum Hall plateaus for the overlap region that resembles that of a Bernal-stacked graphene bilayer. However, we also do observe an anomalous magnetic field induced electrical decoupling of the two layers at backgate voltages symmetric with respect to the charge neutrality point for the double layer region. In our unconventional Hall measurement configuration, this leads to a suppression of the Hall voltage close to zero. Interlayer transport experiments require two graphene layers which are stacked on top of each other such that it is possible to make separate contacts. To accomplish this task we have adopted a precision transfer method that has been previously developed for the transfer of carbon nanotubes17 and has also been used in the context of graphene placed on top of boron nitride.18 The details of the fabrication procedure are described in the Supporting Information. Mechanically exfoilated graphene was used as starting material. The geometry of the flakes and the arrangement of the electrical leads for the device used in this Letter are displayed in Figure 1a. A number has been assigned to each lead. The device was annealed in a flow of a H2/N2 gas mixture to remove residues of poly(methyl methacrylate) (PMMA) resist. Figure 1b displays four-terminal measurements of V/I as a function of the back-gate voltage for three different terminal configurations in the absence of an external magnetic field. One configuration includes the region where both graphene flakes overlap, while the other configurations address the resistance of the monolayer regions of the top and bottom layer. Subscripts of V and I denote the lead numbers used in each measurement. Charge neutrality is reached at different back-gate voltages in the three regions. For the monolayer region of the top and
he uncommon electronic properties of graphene stem from the chiral nature of the charge carriers and the linear energy-momentum dispersion relation. Stacking one graphene layer on top of another causes a drastic change in the electronic band structure. In the ubiquitous Bernal stacked bilayer, quasiparticles are massive as they exhibit a quadratic instead of a linear dispersion near the Dirac point.1 Nature also allows for non-Bernal stacked bilayers, where one layer is twisted with respect to the other by an arbitrary angle from the Bernal configuration. This twisted stacking has been observed for instance for multilayer graphene obtained on the C-face of SiC through graphitization.2 It can also be synthesized by chemical vapor deposition 3 and accidentally occurs during the mechanical exfoliation procedure when a graphene layer folds.4,5 Contrary to the Bernal stacked bilayer, in a twisted bilayer the dispersion is back to linear near the Dirac point.6−9 Moreover each Dirac cone splits into two with a separation in k-space determined by the twist angle. The interaction of states belonging to the two cones gives rise to a saddle point in the energy dispersion and a van Hove singularity in the density of states with a twist angle dependent van Hove energy.10 In the presence of a magnetic field, a distinct Landau level spectrum11,12 emerges. It still possesses an 8-fold degenerate zero energy mode as in a Bernal stacked bilayer due to topological protection. This was predicted by theory11 and is consistent with quantum Hall measurements.13 Hence, the twist angle is a powerful additional degree of freedom to tune the electronic properties as considered theoretically, for instance in ref 14. Interest in two stacked layers of graphene has also emerged in the context of exciton condensation.15,16 Here we show interlayer and in-plane transport measurements in two stacked graphene monolayers. By using a precision transfer technique, the two layers are stacked into a cross shape so that it is possible to fabricate separate contacts on each layer. Magnetotransport measurements exhibit a © 2012 American Chemical Society
Received: February 10, 2012 Revised: June 8, 2012 Published: July 23, 2012 3905
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configuration drawn schematically in the lower left inset of Figure 2b. Current is sourced into and sunk out of the bottom layer using two terminals on opposite sides of the overlap region. The Hall voltage is measured using two probes on the top flake on either side of the overlap area. Well-developed quantum Hall plateaus are observed on the hole side (Figure 2b). The Hall plateau sequence 1/i·h/e2 with i = 4, 8, 12, etc. is identical to that of a commensurate Bernal stacked bilayer, despite the arbitrary rotational orientation of the two flakes. A color rendition of the Hall resistance in the back-gate voltage and magnetic field plane is shown in the inset. The slope of the plateau features indeed coincides with the filling factors at which a commensurate Bernal bilayer condenses in a quantum Hall state. Similar results are obtained when the role of the bottom layer and the top layer is exchanged or on the electron side, even though in this case the Hall plateaus are not fully developed. To understand the observed sequence of quantum Hall plateaus, we adapt a model19 of Landau level for two decoupled monolayers. For two fully decoupled monolayers having equal carrier densities, each Landau level has 8-fold degeneracies arising from spin, valley, and which-layer degrees of freedom. The Hall plateau sequence would be consequently 1/i·h/e2 with i = 4, 12, 20, etc. However, an external back-gate voltage can easily lift the layer degeneracy, leading to the potential difference and thereby an imbalance of the carrier density between two layers (Figure 2c), which has also been reported by others.4,20 Figure 2d shows a schematic diagram of Landau level for decoupled bilayer with the layer degeneracy lifted. As the gate voltage is applied, combinations of the filling factor of νB = −2, −6, and −10 for the bottom layer and the filling factor of νT = −2 for the top layer can be accessible due to a screening of the bottom layer. This simple addition of two filling factors can yield the observed sequence. This condition is depicted by a dotted arrow in Figure 2d. We note that this sequence is also consistent with the recent result13 for twisted bilayer obtained from the C-face of a graphitized SiC substrate showing that the quantum Hall sequence is the same as for Bernal bilayer. Apart from this similarity in the quantum Hall sequence, other prominent features are observed in the Hall trace in Figure 2b. The Hall resistance drops nearly to zero symmetrically with respect to the charge neutrality of the overlap bilayer region. We note that the suppression of the Hall voltage does not emerge when the same device is initially highly doped (see the Supporting Information). Figure 2g displays I−V characteristics measured across the interface of the two layers at corresponding back-gate voltages at a magnetic field of 14 T in a four-terminal configuration. Current is injected in the top layer using terminal 8 and extracted from the bottom layer via lead 5, and the voltage difference between lead 4 and lead 10 is measured. These I−V characteristics are nonlinear, as opposed to the I−V characteristic shown in Figure 1c. Temperaturedependent measurements of the differential conductance in insets to Figure 2g show that the transport is thermally activated. Both observations suggest that under these conditions transport between layers is hampered and governed by tunneling effects. We notice that almost linear I−V characteristics are observed at gate voltages corresponding to the quantum Hall plateaus, indicating an efficient mixing of the edge channels of the individual graphene layers (see the Supporting Information). To explain the origin of this tunneling phenomenon under a magnetic field, we consider a following picture of the two
Figure 1. (a) Optical image of the measured device and the arrangement of the electrical leads. For clarity, graphene has been colored. (b) Field effect curves for three different regions: monolayer region of top (red) and bottom (blue) layer and overlap area (black). Subscripts denote the electrical lead numbers used for the four terminal measurements. (c) Current−voltage characteristic when driving a current from the top layer to the bottom layer measured at back-gate voltages of 50 and −3 V.
bottom flake, the charge neutral point is at −3 and +12 V, respectively. A measurement across the overlap region is dominated by the high resistance near charge neutrality (−3 V) of the monolayer portions of the top flake but also exhibits a shoulder structure around 6 V, which we attribute to the approach of the charge neutral point in the overlap region. Panel c shows I−V characteristics obtained when current is sourced into one layer and sunk from the second layer. Here too, additional voltage probes are used to avoid contact resistance contributions. These and all other measurements in this work are acquired at a temperature of 1.4 K. The I−V characteristic for interlayer transport at zero magnetic field is linear. To estimate the interlayer resistances for the overlap region, the resistance contributions of the monolayer areas included in the measurement need to be subtracted. These contributions are estimated from the four terminal field effect measurements on these areas. After this subtraction, we find that the interlayer resistances are about 100 Ω at a back-gate voltage of −3 V (blue) and 50 Ω for 50 V back-gate voltage (green). Figure 2a displays the Hall resistance and the longitudinal resistance probed in the monolayer region of the transferred top layer as a function of the back-gate voltage at a magnetic field of 12 T. The νtop,mono = 2, 6, 10, etc. sequence of quantum Hall plateaus is the hallmark of monolayer graphene. The inset to Figure 2a is a color rendition of the longitudinal resistance as a function of back-gate voltage and perpendicular magnetic field. It illustrates the quality of the transferred graphene. To investigate quantum Hall states in the stacked bilayer region, Hall measurements were performed in the unconventional 3906
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Figure 2. (a) Quantum Hall effect in the monolayer region of the transferred top layer at a magnetic field of 12 T. Black (gray) curve depicts the Hall (longitudinal) resistance. The inset shows the color rendition of longitudinal resistance as a function of gate voltage and perpendicular magnetic field. (b) Corresponding behavior in the bilayer region. The Hall voltage is measured as illustrated in lower left inset, and its value is divided by driving current. Blue, green, and red traces measured at magnetic fields of 12 T, 14.5 T, and 17 T are plotted. The upper right inset shows a color map of the Hall resistance as a function of gate voltage and magnetic field. Anomalous suppression of the Hall voltage occurs almost symmetrically with respect to the charge neutrality point marked by A and B. (c) Landau level (LL) spectrum of two decoupled monolayers. Red (blue) lines represent LL of top (bottom) layer. If the layer degeneracy is lifted, the degeneracy of each level becomes from 8 fold to 4 fold (left schematic). (d) LL crossing as a function of a potential difference between the layers. A dotted arrow depicts a possible condition to achieve the filling factor sequence of −4, −8, −12 on hole side. (e) Charge configuration near the suppression of the Hall voltage. The hole type carrier is considered for the bottom layer, while the top layer is near the charge neutrality with the applied magnetic field pointed out of page. (f) Edge channel mixing far away from the charge neutrality of the overlap region. The hole side is conceived. (g) Current−voltage characteristics when the Hall resistance is suppressed at gate voltages of −8 V and 20 V in magnetic field of 14 T. The upper left inset shows measured differential conductance as a function of voltage for four different temperatures. The lower right inset depicts the temperature dependence of differential conductance at a gate voltage of −8 V and at zero bias voltage.
stays at a dissipationless edge channel in the bottom layer, and hence the Hall voltage measured across the bottom layer drops to zero. On the other hand, far away from the charge neutral condition, for example, holes are induced at negative gate voltages (Figure 2f). Consequently, edge channels in monolayer regions of both layers can lead to an efficient mixing of the edge channels at positions marked by four circles. This mixing leads to the strong coupling of the two layers. We note that if both layers are initially undoped the mentioned Hall drop would not occur. One of the intriguing issues in graphene bilayer system is an expected interlayer supercurrent phenomenon arising from a formation of excitonic condensate. Even though an individual tunability of the carrier densities in the bilayer region is limited in the present device geometry, a bipolar carrier configuration with a similar density may be realizable at a gate voltage between the charge neutrality points for each layer. However, we did not have any chance to observe the interlayer
stacked monolayers as illustrated in Figure 2e. The suppression of the Hall voltage occurs nearly at the total filling factor of 2. This implies that the top or bottom layer regions may condense into the 2 or −2 integer quantum Hall state while the other layer remains compressible in the formation of electron−hole puddles near the charge neutrality, and hence edge channels are not developed well. The suppression of the tunneling from an incompressible layer to a compressible layer has also been observed in the GaAs bilayer system (see the Supporting Information). However, rather than having two electrically decoupled layers as in the GaAs bilayer case, here in the two stacked graphene monolayers we have seen strong coupling between the two layers at zero B-field (Figure 1c) as well as at other quantum Hall states (Figure S4 of the Supporting Information). The decoupling only occurs at the total filling factor of 2. At νtot = ±2 with the measurement configuration of Figure 2b, current injected in the bottom layer no longer spreads between the two layers in the overlap region, that is, it 3907
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supercurrent in our experiments at zero magnetic field. No signature of supercurrent was observed either in differential conductance maps as a function of magnetic field and gate voltage in the four-probe configuration. To pursue an experimental realization, a more controllable device geometry would be necessary including a clean substrate like boron nitride, a thin spacing layer between two graphene layers, and a top gate for an individual tunability of the carrier densities for each layer. In summary, we have observed an anomalous nonlinear current−voltage characteristic for interlayer transport of a stacked graphene bilayer at a total filling factor of ±2. We ascribe it to a discrepancy of the charge neutrality for two layers. This decoupling at the corresponding filling factors leads to a suppression of Hall voltage of the overlap region in our measurement geometry. We have also observed a similarity between two stacked graphene monolayers and the Bernal stacked graphene bilayer. Sequences of quantum Hall plateaus in the overlap region are 4, 8, and 12. This behavior can be explained by two independent graphene monolayers with screening taken into account.
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ASSOCIATED CONTENT
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AUTHOR INFORMATION
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S Supporting Information *
Device fabrication procedure, field effect and Hall measurements for highly doped case, current−voltage characteristics at total filling factors (−4, −8, and −12), and interlayer tunneling in a GaAs bilayer sample. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author
*E-mail:
[email protected]. Present Address †
Korea Research Institute of Standards and Science, 267 Gajeong-ro, Yuseong-gu, Daejeon 305-340, Republic of Korea. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank Werner Dietsche for kindly providing GaAs bilayer wafer for supporting experiments. We also acknowledge Jürgen Smet and DongSu Lee for motivation of this work, insightful discussions, and careful reading of the manuscript.
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REFERENCES
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