Supplementary information for“Insulating behavior at the neutrality point in single-layer graphene”

F. Amet,1 J. R. Williams,2 K.Watanabe,3 T.Taniguchi,3 and D. Goldhaber-Gordon2

1Department of Applied Physics, Stanford University, Stanford, CA 94305, USA2Department of Physics, Stanford University, Stanford, CA 94305, USA

3Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan

DEVICE FABRICATION

Polyvinyl alcohol (2% in water) is spun at 6000 rpmon bare silicon and baked at 160 C for 5 mins, resultingin a 40 nm thick layer. Then, a layer of PMMA (5% inanisole) is spun at 2400 rpm and baked 5 mins at 160 C.The total polymer thickness is on the order of 450 nm.Graphene is then exfoliated on this stack using Nittotape, located using optical microscopy, and character-ized with Raman spectroscopy. Boron nitride flakes areexfoliated on a silicon wafer piece with a 300 nm thickthermal oxide, then baked in flowing Ar/O2 at 500 Cfor 8 hours to remove organic contamination such as taperesidue [S1]. The cleanliness and thickness of the flakesare characterized with atomic force microscopy and Ra-man spectroscopy.

The PVA layer is dissolved in deionized water at 90 C,which lifts-off the PMMA membrane with the grapheneattached to it. The membrane is then adhered across ahole in a glass slide [S2] and baked at 110 C. We then usea home-made probe-station to align the graphene flakeon top of the boron nitride substrate. Once both flakesare in contact, the stack is baked at 120 C to promoteadhesion. The PMMA layer is dissolved in hot acetone,then rinsed in IPA, which leaves the graphene flake ontop of the boron nitride flake. This stack is annealedin flowing Ar/O2 at 500 C for 4 hours, which removesprocess residue and leaves the graphene flake pristine, aschecked by Raman spectroscopy.

We use regular electron beam lithography combinedwith oxygen plasma etching to pattern a graphene Hallbar. In order to fabricate a suspended top gate above thedevice [S3-6], the samples are spin-coated at 6000 rpmwith a solution of polymethyl-methacrylate (950k), 3%in anisole, then baked at 160 C for 5 minutes. An ad-ditional layer of methyl-methacrylate (8.5% in ethyl lac-tate) is spin-coated at 6000 rpm and baked 5 minutes at160 C. The MMA layer is 50% more sensitive to elec-tron irradiation than the PMMA layer and it is thereforepossible to develop the top resist layer without exposingthe bottom layer. The e-beam writing system we usedis a JEOL 6300, with an acceleration voltage of 100 keV.The contacts and the feet of the suspended bridge areexposed with 1000µC/cm

2, which is enough to dissolve

both resist layers upon development in MIBK/IPA (1:3)for 45 sec. The span of the suspended bridge is only ex-

FIG. S1: Scanning electron micrograph of a graphene on boronnitride device with suspended top gates. Scale bar=1 µm.

posed with a base dose of 650µC/cm2, which only devel-

ops the top resist layer. After development, the deviceis cleaned for 2 minutes with UV ozone, then metallizedwith 1nm of chromium and 200 nm of gold.

Fig. S1 is a scanning electron micrograph of a grapheneon boron-nitride device with a suspended top-gate thathas been fabricated using the same recipe. Suspendedgates as long as 7 microns have been fabricated usingthis recipe. These usually resist further heat treatmentas well as cryogenic temperatures. We found that gatevoltages as high as 40 V can be applied to the top-gatewithout damaging it.

RAMAN SPECTRA

We check the cleanliness of every boron nitride flakewe use with atomic force microscopy and Raman spec-troscopy. Fig. S2(a) shows the Raman spectrum of theboron nitride flake used in the device studied in the pa-per, prior to transferring the graphene flake. The absenceof a broad background signal [S2] is a very clear indica-tion that the flake is free of any kind of organic contam-ination. The Raman spectrum of the transferred devicebefore the last lithographic step -when the suspendedgate is patterned, is shown on Fig. S2(b). The ratio ofthe amplitudes of the 2D and G peak is I2D/IG = 5.5, andthe full half width of the 2D peak is 19 cm−1, indicatingwith no ambiguity that the flake studied here is single-layer graphene [S7]. The absence of a broad background

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Wave number k (cm )

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FIG. S2: (a) Raman spectrum of the boron nitride flake used forthe device described in the main paper, prior to transferring thegraphene flake. The boron nitride Raman peak is labelled GBN .(b) Raman spectrum of the whole graphene on boron nitride deviceafter oxygen annealing and before contacts were made to the flake.The peaks labelled G and 2D are attributed to graphene.

signal attests for the cleanliness of the device.

RESISTANCE OF A NON TOP-GATED SAMPLE

A typical resistivity of a non top-gated part of the sam-ple described in the main paper is shown on Fig. S3,measured at T=4 K. The peak resistivity is ∼10kΩ anddoes not diverge as the temperature is lowered.

QUANTUM HALL CONDUCTANCE OF A NONTOP-GATED DEVICE

The two-terminal quantum Hall conductance of agraphene on boron nitride device with no top-gate isshown on Fig. S4, the mobility for this sample is 45000cm2/Vs. The conductance is measured at T=2 K ina two-probe configuration. Most of the measurementsin this paper use this geometry, as voltage-biased mea-surements of the conductance are more convenient thancurrent-biased ones when the device is insulating, aroundthe charge neutrality point. Quantum Hall plateaus arebetter resolved on the hole side than on the electron side,which we found to be common for two-terminal quantum

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FIG. S3: Resistivity as a function of the VBG for the control device

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FIG. S4: (a) Two terminal inductance as a function of the per-pendicular magnetic field and the back-gate voltage. (b) Cuts ofthe conductance as a function of the back gate voltage at B=2 T(black line) and B=4 T (red line). Inset: gCNP (B) for this sample.

Hall conductance measurements on other graphene on

3

boron nitride devices.

As the magnetic field increases, the degeneracy ofeach Landau level splits and we observe new quantizedplateaux. In particular, the ν=0 phase slowly appearsaround B=3 T, as seen on the inset Fig. S4. This isin sharp contrast with the abrupt transition seen in fig-ure 4b of the main paper, which occurs at a much lowerfield. Fig. S4(b) shows two sections of the fan diagramat B=2 T and B=4 T. The conductance at 2 T shows thestandard sequence of plateaux, as seen in other two ter-minal devices with no splitting of the Landau levels [S8].We stress that the small dip in conductance at the neu-trality point at 2 T is only an artifact from the two ter-minal geometry, as shown in Ref. [S8], and is not relatedto the opening of the ν=0 gap. At 4 T, the device startsbeing insulating around the charge neutrality point, asthe ν=0 gap opens up, and the other plateaus becomefurther resolved.

TABLE OF PEAK RESISTANCES

We show in Tables I and II the peak resistivities underthe top-gate ρTG

CNP and mobilities of the devices includedin this study. ρCNP was always significantly smaller thanh/e2 for non top-gated devices. The insulating behaviorat the CNP is most pronounced for the three devices withthe highest top-gate capacitance, with ρTG

CNP >> h/e2.The two devices marked with a star were patterned inthe same graphene flake.

TABLE I: Measured properties of top-gated devices

Carrier Mobility

(cm2/Vs) ρTGCNP (kΩ/sq) CTG (nF/cm2)

70,000* 2250 12.8

80,000 47.1 10.1

6,000 44.4 12.8

120,000 20.2 9.8

45,000 20.1 3.3

35,000 8.9 3.3

15,000 11.2 2.8

FABRY-PEROT OSCILLATIONS IN THEBIPOLAR REGIME

While the main focus of our work is to study the con-ductance at the neutrality point, we show on Fig. S5the differential conductance of one of our devices in thebipolar regime, at T=250mK, as another proof of theircleanliness. In ballistic top-gated devices, carriers arepartially reflected at each PN interface which can cause

TABLE II: Measured properties of non-top-gated devices.

Carrier Mobility

(cm2/Vs) ρCNP (kΩ/sq)

85,000 16

70,000* 11

70,000 12

62,000 8.8

45,000 8.9

45,000 8.8

40,000 6.8

40,000 5.2

Fabry-Perot oscillations of the conductance. This phe-nomenon was observed in Ref. [S9] using a very narrowtop-gate, on order 50nm. In our work, however, the ef-fective width of the top-gated region is larger than a mi-cron, which gives a lower-bound for the mean-free pathof charge carriers under the gate. In particular, such be-havior would be impossible to observe in the presence ofdisorder under the top-gate.

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FIG. S5: Differential conductance dg/dnTG as a function of the densities under and outside the top-gate, nTG and nBG. Inset: Schematicof the potential profile across the flake.

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