Insulating behavior at the neutrality point in dual-gated, single-layer graphene

5.6 MB·English

by  F. Amet

Insulating behavior at the neutrality point in dual-gated, 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, USA
2Department of Physics, Stanford University, Stanford, CA 94305, USA
3Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
The fate of the low-temperature conductance at the charge-neutrality (Dirac) point in a single
sheet of graphene is investigated down to 20mK. The potential fluctuations in graphene are made
artificially small by using a dual top- and back-gate geometry such that screening reduces the
intrinsic disorder potential. As the temperature is lowered, the peak resistivity diverges with a
2 power-lawbehaviorandbecomesashighasseveralMegaohmspersquareatthelowesttemperature,
1 in contrast with the commonly observed saturation of the conductivity. As a transverse magnetic
0 fieldisapplied,ourdeviceremainsinsulatinganddirectlytransitionstotheν=0quantumHallstate
2 at a field of 100mT.

p
e Theabilitytocreateelectronicdevicesingraphenehas pendence results from a “disorder by order” effect in
S
made it possible to study 2D Dirac fermions in the solid graphene, where increasing order causes the sample to

7 state [1–3]. Transport measurements in a large magnetic become more insulating at low density. Here σ ∝ Tα
NP
2
field display quantum Hall plateaus with unconventional naturallyemergesasthetemperaturedependenceofcon-

values of conductance, a signature of the Dirac equa- duction through a landscape of electron and hole pud-
]
l tion describing electrons in graphene [1]. Such behavior dles. To distinguish between the two competing scenar-
l
a emerges as the cyclotron gap opens in a magnetic field: ios,lower-temperaturetransport,wheretheelectronicco-
h
whenthisgapbecomeslargerthandisorder-inducedfluc- herence important in localization is more prominent, is
-
s tuations in the surrounding potential, the effect of the needed.
e
m linear Dirac band structure becomes evident. At zero In this Letter, we report on electronic transport in
magnetic field, the disorder landscape dominates [4, 30], dual-gated, single-layer graphene devices, in which the
.
t blurring the interesting phenomena that might occur at back gate is used to control the global carrier density,
a
m the Dirac point. Recently, the influence of disorder has andthetopgateisprimarilyusedtoscreentheCoulomb
been reduced by either suspending a sheet [5] or placing disorder potential, not to locally control the carrier den-
-
d itonatomically-flatboronnitride[6],andmanydiscover- sity. At the charge neutrality point (CNP), the de-
n iesintransporthavebeenmadeduetothemorereadily- pendence of the conductance g on temperature (T)
NP
o accessible Dirac point in these cleaner systems [7–10]. and magnetic field (B) is investigated down to temper-
c
[ Thenatureoftheconductivityatthecharge-neutrality atures of 20mK. The temperature dependence is strong
v1 pbaosinetd σdNePvicheasswbeereen fdaebbraictaetdeds.inceTthheeorfiyrsftorgrbapalhliesnteic- dgNowPn∝toTTα=w40it0hmαK≈a0n.4d8±ca0n.05b.e fiTthteedlotwo-fiaelpdowmearg-lnaew-
4 graphene predicts a value of 4e2/πh for σNP [11, 12]. toresistance shows an uncommon behavior around B=0
6 However, early experiments on graphene measured σ thatisinconsistentwithweaklocalization. Thequantum
NP
3 in the range of 2-12e2/h [2, 13, 14]. It was soon re- Hall regime is entered at just 0.1T, but instead of show-
6 alized that σ was sample-dependent and determined ingaconductanceplateauat2e2/haroundtheCNP,the
. NP
9 by the density of carriers in electron and hole puddles device is insulating, indicating that the spin and valley
0 due to disorder from static charges on or near the sheet SU(4) symmetry is broken at very low fields. A peak
2 of graphene [13, 15, 16]. In suspended graphene de- in gNP(B) marks a transition between the zero field in-
1
vices [15] the conductivity showed a more pronounced sulating state and the ν=0 insulator at a field on order
:
v temperature dependence, but still saturated at low tem- 100mT,about20timeslowerthanforournontop-gated
Xi perature and remained higher than 4e2/πh. Recently it devices. Fromthelow-temperaturesaturationofgNP(T)
hasbeenshownthatthepotentiallandscapeingraphene and the field at which the ν=0 quantum Hall plateau
r
a canbemadeartificiallycleanbyscreeningpotentialfluc- emerges, we estimate that the potential fluctuations are
tuationswithasecondnearby,dopedgraphenesheet[17]. less than 100µeV, an order of magnitude lower than re-
In that work, instead of saturating at values near e2/h, ported for the suspended devices.
σ dropped with a power-law temperature dependence We fabricated our devices using hexagonal-boron ni-
NP
Tα, whereα=2forthemostinsulatingsamples, downto tride (h-BN) as a substrate for graphene, with good
T=4K. Further, the authors observed a strong magne- electronic properties [6, 19] resulting from the extreme
toresistance in the temperature regime above 10K and flatness and cleanliness of h-BN flakes. Single-layer
attributed it to weak localization, inferring that ultra- graphene flakes were exfoliated on a stack of polyvinyl
clean graphene may be an Anderson insulator. However, alcohol (PVA) and polymethyl-methacrylate (PMMA).
a recent theory [18] postulates that this temperature de- Separately, h-BN was exfoliated on a silicon wafer with
2
(a) i patterned by electron-beam lithography, was suspended
D
70 nm above the flake [23–26]. For a last cleaning step,
we could not anneal the device in oxygen, as we found it
v
ac damages the metallic contacts [21]. Instead, the device
~
wasannealedat325◦CinAr/H for4hours. Additional
2
details on the fabrication and characterization are avail-
able in Ref. [20]. A schematic of the completed device
h-BN V
TG geometry is shown in Fig. 1(a). Another device, called
the control device, was fabricated with no top-gate on
SiO V
2 BG
the same sheet of graphene but electrically isolated from
0 g (mS) 1.5 the top-gated device. The control device showed none of
the distinct transport properties of the top-gated device
8 (b)
attheCNP,helpingdiscernwhichtransportfeaturesare
solely due to the presence of the suspended gate.
Graphene devices were measured in two differ-
4 ent cryostats: a variable-temperature insert enabling
temperature-dependent transport measurements from
300Kdownto1.7K,andadilutionfridgewheresamples
were measured at lower temperatures, down to 20mK.
0
) The conductance g is determined in a standard voltage-
V
V (BG biasedlock-inmeasurementwithanexcitationvoltageof
4 µV at 92.3Hz. The resistance r is defined as 1/g. DC
-4
voltagesareappliedtothetop-gate(V )andback-gate
TG
(V ).
BG
g is shown on Figure 1(b) as a function of V and
TG
-8 VBG at T=4K. The carrier density can be controlled
independently and with opposite polarities underneath
and outside the top-gated region. As in previous work
-10 -5 0 5 10
on dual-gated graphene [3, 27, 28], g exhibits local min-
V (V)
TG
ima along two intersecting lines corresponding to each
FIG. 1: (a) Schematic of the device in voltage biased mode. A region being tuned through the CNP. However, unlike
biasvAC isappliedtothesample,thecurrentiD isthencollected in typical dual-gated graphene devices, gNP is near zero
atthedrainandmeasuredwithalock-inamplifier. AvoltageVBG along these lines. g was also measured in a 4-probe ge-
is applied to the degenerately doped piece of wafer to control the
ometry, from which we extracted the resistance of the
carrier density in the whole sheet. VTG is applied to a suspended
metallic gate, 70nm away from the graphene sheet, which varies cryostat’s wiring, 2.5 kΩ. Underneath the top-gate,
thecarrierdensityunderneathit. (b)Conductivityσasafunction C V + C V = 0 at the CNP, yielding a top-
TG TG BG BG
ofbothgatevoltages,measuredatatemperatureT=4K. gate-to-back-gate capacitance ratio of 1.3 from the slope
of the diagonal line in the (V ,V ) plane. C is
BG TG BG
5.94(±0.5)×1010cm−2V−1,asextractedfromtheperiod-
a 300nm-thick thermal oxide, then exposed to flowing icity of Shubnikov-de-Haas oscillations. Using a parallel-
Ar/O at500◦Cfor8hours,whichremovesorganiccon- plate capacitance model, we estimate that the top gate
2
tamination from tape residue [21, 22]. Each flake was is 70nm away from the flake, which was confirmed by
characterized by atomic force microscopy and Raman atomicforcemicroscopy. Thedeviceexhibitslittleintrin-
spectroscopy prior to transfer [20]. The PVA layer was sicdoping,withaCNPvoltageof-2.2Vontheback-gate,
dissolved in deionized water, which lifted off the PMMA andamobilityof60,000cm2/Vs,asextractedfromalin-
membrane with the attached graphene flake [6]. The ear fit to g(V ) at the CNP. We note that the mobility
BG
graphene flake was then aligned to the h-BN, pressed of top-gated and non top-gated regions was comparable,
on top and baked at 110◦C to promote adhesion be- whichshowsthatthesuspendedgatedoesnotdeteriorate
tween the two flakes. The PMMA membrane was dis- the electronic properties of our device.
solvedinacetone/IPAandthegraphene/h-BNstackwas Unlike typical graphene samples, r as a function of
again treated in Ar/O at 500◦C for 4 hours [21]. The V has a strong temperature dependence in our device
2 BG
cleanlinessofthewholestackwasconfirmedwithRaman (all measurements from here on are taken with V =0).
TG
spectroscopy [20]. Successive electron-beam lithography The resistance at the CNP r dramatically increases
NP
steps were used to oxygen-etch the graphene flake into atlowtemperature,from13kΩatT=300Kto300kΩat
a Hall-bar and to make electrical contact to the device T=4K [inset, Fig. 2(a)]. By contrast, the peak in r of
(1nmCr,200nmAu). Finally,a1µmwidetopgate,also the control device is only 10kΩ at 4K [20], comparable
3
(a)
300 T=300K T=2K
T=4K 2 VB G = -2.2V T=400mK
3
Ω)
M
200 r (NP1 S)
μ
r (kΩ) 00 100 200 300 g (NP2
T (K)
100
1
0
-6 -4 -2 0 2 0
(b) V (V) -0.2 -0.1 0 0.1 0.2
BG
B (T)
50 V = -2.2V
BG FIG. 3: Conductance at the charge neutrality point gNP as a
functionofthemagneticfieldattwodifferenttemperatures,T=2K
20
(dashedgreyline)andT=400mK(blackline)
10
S) 5
μ
g (NP2 tmueraesudreepdenindeRnecfe.[i1s7a]l(saonsdloewxeprecttheadnfrtohme Tth2edBeopletnzmdeanncne
1 equationwithelectron-electronscattering). Anevolution
.5 similar to ours was reported in suspended graphene [15],
although the overall conductance was several orders of
magnitude higher.
.01 .05 .1 .5 1 5 10 50100
g (B) for T=2K and 400mK in the range
T (K) NP
|B|(cid:54)250mT exhibits 2 strong peaks located symmetri-
FIG. 2: (a) Resistance as a function of VBG at T=300K (dashed cally at B=±70mT (Fig. 3). The peak conductance
grey line) and T=2K (black line). Insert: Resistance at the at ±70mT has less T dependence than g (B=0). A
NP
charge neutrality point(VBG =−2.2V)as afunction oftempera- strongmagneto-conductancewasseeninRef.[17]aswell
ture.(b) Conductance as a function of temperature on a log scale,
and was fit to the weak localization theory for graphene.
at VBG = −2.2V. Open circles and filled squares correspond to
data points taken in the dilution fridge and variable temperature However, our observed magneto-conductance is distinct
cryostatrespectively. Errorbarscorrespondtoonestandarddevi- from that seen previously in Ref. [17] or in typical two-
ation: for T>5K, these are smaller than the dots. The grey line dimensional conductors in two ways. First the magneto-
corresponds to a fit σNP ∝ Tα, with α ≈ 0.48 for T<80K. At conductance around B=0 has positive curvature, differ-
highertemperatureσNP riseswithafasterexponent.
entfromthecusp-like,negativecurvaturetypicalofWL.
Second,afterthepeakat±70mT,theconductancedrops
to what is commonly seen in good-quality, single-layer abruptlytowardszero,indicatingthatthedevicereturns
graphene devices. r was measured at lower temper- to an insulating state. It appears that the magneto-
NP
ature in a separate cool-down using a dilution fridge: conductance peak is not due to Anderson localization,
further lowering T to 400mK increases r , at which but rather marks a transition between the zero-field in-
NP
point it measures 2.3MΩ, then remains constant down sulating state and the ν =0 insulator.
to 20mK within experimental error. The full-width at To investigate this transition, a low field fan diagram
half-maximum in r (V ) at 20mK corresponds to a [g(V ,B)]ismeasuredatT=2KandshowninFig.4(a).
NP BG BG
residualimpuritydensityonorder1010cm−2. Forcarrier Away from the CNP, we observe plateaus for ν =2,6,10
densities higher than ∼5×1010cm−2, r decreases when (dashedlines)thatarewell-developedontheholesidefor
T is lowered, similarly to what has been observed else- B>0.5T.Thecutg(V ,B=1T)showstheseplateausin
BG
where on high-quality samples without a top gate [15] additiontotheν=0plateauaroundtheCNP[Fig. 4(c)].
and in our control device [20]. Fig. 2(b) shows g (T), Quantum Hall plateaus are better resolved on the hole
NP
which follows a power law g ∝ Tα as a function of sidethanontheelectronside,whichwefoundtobecom-
NP
the temperature, with α=0.48±0.05, as extracted from mon for two-terminal quantum Hall conductance mea-
a linear fit to the curve. This insulating behavior is not surements on other graphene on boron nitride devices.
due to the opening of a band gap, which would lead to Interestingly, the broken-symmetry ν=0 state seems to
an exponentially-activated conductivity. The tempera- persist all the way down to very low fields (solid blue
4
(a) 0 g(e2 /h) 14 vice, where the conductance around the charge neutral-
0 ity point is never quantized and always very small com-
pared to 2e2/h [Fig. 4(b)]. The conductance is heav-
ily suppressed on the high field side of the conductance
0.5 peak discussed earlier, corresponding to an opening of
the ν = 0 gap at ∼100mT. In a magnetic field, the en-
ergy of Coulomb interactions is on the order E = e2 ,
B (T)1 ν=10 wherel isthemagneticlengthl =(cid:113) (cid:126) . WhilCetofi(cid:15)lrBst
B B eB
order these interactions preserve valley symmetry, it has
1.5 ν=6 beenshownthathigher-ordertermsbreakthissymmetry
and are on order δE = a E , where a is the spacing
C lB C
ν=2 between neighboring carbon atoms [31–33]. A naive es-
2 timate of this contribution gives δE ∼1meV/T. Inter-
C
-4 -2 V (V) 0 2 4
BG estingly, the field dependence of the ν=0 gap has been
4 V =-1.1V (b) B=1T (c) studied in Ref [33], where it was found that the effec-
BG 10 tive g factor g ≡ d∆ /dB for the ν = 0 state had
∆0 o
3 h) this same order of magnitude. We can use this result to
μS)2 e /2 6 estimate the Landau level broadening due to the Fermi
g ( g ( level fluctuations from the onset of the ν = 0 gap at
1 2 100mT. We find δEF∼100µeV, in good agreement with
our previous estimate based on the low-temperature sat-
0 0
0 0.5 1 1.5 2 -4 -2 0 2 4 uration of gNP(T). This confirms that the Fermi energy
B (T) V (V) fluctuations are at least one order of magnitude lower
BG
in our double-gated device than they are in suspended
FIG.4: (a)Conductancegasafunctionofthetransversemagnetic graphene [15, 34].
fieldBandVBG,atT=2K,measuredinatwoprobesconfiguration. Using E = (cid:126)v √πn, our inferred fluctuations in E
Thetransitionsbetweenplateausareunderlinedforν=0,2,6,10. F F F
(b) Cut of g(B) at the charge neutrality point VBG =−1.1V. (c) correspond to density fluctuations on the order of 106
Cutofg(VBG)atB=1T. cm−2, two orders of magnitude lower than in most re-
ported suspended devices [34]! The density of impuri-
ties is unlikely to be this small, but probably on order
region that runs between VBG ∼0 and -1V). 109 to 1010cm−2 [6, 19] and similar to our control de-
Discussion. Typically the disorder in the sample may vice. This is internally consistent: while Coulomb in-
beextractedfromthetemperaturebelowwhichg(T)sat- teractions are usually barely screened at the CNP [35],
urates [5]. The temperature dependence in our device is the nearby grounded metallic plane provides additional
very strong down to T≈ 400mK, at which point it may screeningandtheFermienergyfluctuationsaretherefore
remainflatdownto20mK,thedilutionfridge’sbasetem- expected to be weakened.
perature, although the temperature dependence in this The improved screening is likely to be responsible for
rangeishardertotrackduetocurrentnoiseinoursetup. the diverging resistivity we observe. As charge puddles
Thetemperaturedependenceisexpectedtobeflatwhen getshallowerandfurtherapart,theminimumconductiv-
k T isbelowtheFermienergy’sfluctuationsδE ,allow- ityisexpectedtodropasitbecomesharderforelectrons
B F
ingustocoarselyestimateδE andfindanunexpectedly to percolate [16, 36]. We note that σ was calculated
F NP
low value δE ≈40µeV. in the percolating regime [36] and predicted to depend
F
Another way to estimate δEF is to look at the mag- on density fluctuations as σNP ∝ δn0.41, a result that
netic field at which the ν=0 plateau develops. For our may be relevant here as the resistance at p-n boundaries
control device [20] the two-terminal conductance devel- between charge puddles grows to dominate sample resis-
ops plateaus at a moderate magnetic field (∼1-2T) with tivity [37]. However, the top gate is tens of nanometers
value 2e2/h around the CNP (corresponding to ν=±2). awayfromtheflake,significantlyfurtherthanreportedin
In typical graphene-on-BN devices, we and others [33] Ref.[17], anditisthereforesurprisingthatthescreening
find that the two-probe conductance at the CNP only should have such dramatic consequences, as interactions
starts decreasing from 2e2/h to zero for B∼2-3T [20], should naively be screened only on distances larger than
as the valley degeneracy of the n=0 Landau level is the spacing to the top gate. Further work is therefore
lifted [30]. The ν = 0 gap is usually fully developed neededtobetterunderstandtheroleofscreeninginsuch
at around 5T, at which point the current becomes un- systems.
measurable with our setup. This is qualitatively dif- We thank A. Bestwick, P. Gallagher, M. Lee, J.
ferent from what we observe with our top-gated de- Sanchez-Yamagishi, C. Dean and P. Jarillo-Herrero for
5
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Cullen, ACS Nano, 6(9), 8335-8341(2012).
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[20] Supplementary information
6
SUPPLEMENTARY INFORMATION
Device fabrication
Polyvinyl alcohol (2% in water) is spun at 6000 rpm
onbaresiliconandbakedat160◦Cfor5minutes,result-
ing in a 40nm thick layer. Then, a layer of PMMA (5%
in anisole) is spun at 2400 rpm and baked 5 minutes at
160◦C. The total polymer thickness is on the order of
450nm. Graphene is then exfoliated on this stack using
Nitto tape, located using optical microscopy, and char-
acterized with Raman spectroscopy. Boron nitride flakes
areexfoliatedonasiliconwaferpiecewitha300nmthick
thermal oxide, then baked in flowing Ar/O2 at 500◦C to FIG. 5: Scanning electron micrograph of a graphene on boron
removetaperesidue. Thecleanlinessandthicknessofthe nitridedevicewithasuspendedtopgate. Scalebar=1µm.
flakesarecharacterizedwithatomicforcemicroscopyand
Raman spectroscopy.
ThePVAlayerisdissolvedindeionizedwaterat90◦C,
which lifts-off the PMMA membrane with the graphene
ahtotlaecihneadgtloasist.sliTdehe[Sm1]eamnbdrbaankeeidsatth1e1n0a◦dChe.rWedetahcernosussae b. units)780 Si GBN
a home-made probe-station to align the graphene flake ar
on top of the boron nitride substrate. Once both flakes nts (760
u
are in contact, the stack is baked at 120◦C to promote co
n
adhesion. The PMMA layer is dissolved in hot acetone, o
ot740
then rinsed in IPA, which leaves the graphene flake on Ph
top of the boron nitride flake. This stack is annealed
in flowing Ar/O2 at 500◦C for 4 hours, which removes 720
process residue and leaves the graphene flake pristine, as 0 500 1000 1500 2000 2500 3000
Wave number k (cm- 1 )
checked by Raman spectroscopy.
900
We use regular electron beam lithography combined
wbaitrh. IonxyorgdeenrptolafsambariceattcehiangsutsopepnadtetedrtnopaggartaephabenoeveHtahlel b. units)850
device, the samples are spin-coated at 6krpm with a so- ar
lution of polymethyl-methacrylate (950k), 3% in anisole, nts (
u
then baked at 160◦C for 5 minutes. An additional layer o800
c
n
of methyl-methacrylate (8.5% in ethyl lactate) is spin- o
ot Si G G 2D
coated at 6krpm and baked 5 minutes at 160◦C. The Ph BN
750
MMA layer is 50% more sensitive to electron irradiation
than the PMMA layer and it is therefore possible to de-
0 500 1000 1500 2000 2500 3000
velop the top resist layer without exposing the bottom
Wave number k (cm- 1 )
layer. The e-beam writing system we used is a JEOL
6300, with an acceleration voltage of 100keV. The con- FIG. 6: a) Raman spectrum of the boron nitride flake used for
tacts and the feet of the suspended bridge are exposed the device described in the main paper, prior to transferring the
with 1000µC/cm2, which is enough to dissolve both re- graphene flake. The boron nitride Raman peak is labelled GBN.
b)Ramanspectrumofthewholegrapheneonboronnitridedevice
sistlayersupondevelopmentinMIBK/IPA(1:3)for45s.
afteroxygenannealingandbeforecontactsweremadetotheflake.
The span of the suspended bridge is only exposed with ThepeakslabelledGand2Dareattributedtographene.
a base dose of 650µC/cm2, which only develops the top
resist layer. After development, the device is cleaned for
2 minutes with UV ozone, then metallized with 1nm of
chromium and 200nm of gold.
Figure 5 is a scanning electron micrograph of a usingthisrecipe. Theseusuallyresistfurtherheattreat-
graphene on boron-nitride device with a suspended top- ment as well as cryogenic temperatures. We found that
gatethathasbeenfabricatedusingthesamerecipe. Sus- gate voltages as high as 40V can be applied to the top-
pended gates as long as 7 microns have been fabricated gate without damaging it.
7
0 10 20 30
10 g(e 2 /h)
8 8
6
Ω) 6
k
R(
4
)
T
B( 4
2
0 2
-10 0 10
V (V)
BG
FIG. 7: Resistivity as a function of the back-gate voltage for the 0
-10 0 10 20
controldevice V (V)
BG
B=2T
22
Raman spectra B=4T
18
We check the cleanliness of every boron nitride flake
we use with atomic force microscopy and Raman spec- h)14
troscopy. Figure 6.a shows the Raman spectrum of the 2e /
boron nitride flake used in the device studied in the pa- g(
10
per,priortotransferringthegrapheneflake. Theabsence
of a broad background signal [S2] is a very clear indica- 6
tion that the flake is free of any kind of organic contam-
ination. The Raman spectrum of the transferred device 2
before the last lithographic step -when the suspended 0
-10 0 10 20
gate is patterned, is shown on Figure 6.b. The ratio of V (V)
BG
theamplitudesofthe2DandGpeakisI /I =5.5,and
2D G
the full half width of the 2D peak is 19 cm−1, indicating
FIG.8: a)Twoterminalinductanceasafunctionofthetransverse
with no ambiguity that the flake studied here is single- magnetic field and the back-gate voltage. b) Cuts of the conduc-
layer graphene [S3]. The absence of a broad background tance as a function of the back gate voltage at B=2T (black line)
andB=4T(redline).
signal attests for the cleanliness of the device.
Resistance of a non top-gated sample
sulating, around the charge neutrality point.
The resistivity of a non top-gated part of the sample As the magnetic field increases, the degeneracy of
described in the main paper is shown on figure 7, mea- each Landau level splits and we observe new quantized
sured at T=4K. The peak resistivity is ∼10kΩ and does plateaux. In particular, the ν=0 phase slowly appears
not diverge as the temperature is lowered. around B=3T: this is in sharp contrast with the abrupt
transition seen in figure 4b of the main paper, which oc-
curs at a much lower field. Figure 8b shows two sections
Quantum Hall conductance of a non top-gated of the Fan diagram at B=2T and B=4T. The conduc-
device tance at 2T shows the standard sequence of plateaux, as
seeninothertwoterminaldeviceswithnosplittingofthe
The two-terminal quantum Hall conductance of a Landau levels [S4]. We stress that the small dip in con-
graphene on boron nitride device with no top-gate is ductanceattheneutralitypointat2Tisonlyanartifact
shown on Figure 8. The conductance is measured at from the two terminal geometry, as shown in Ref. [S4],
T=2K in a two-probe configuration. Most of the mea- and is not related to the opening of the ν=0 gap. At
surements in this paper use this geometry, as voltage- 4T, the device starts being insulating around the charge
biased measurements of the conductance are more con- neutralitypoint,astheν=0gapopensup,andtheother
venient than current-biased ones when the device is in- plateaus become further resolved.
8
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Sorgenfrei,K.Watanabe,T.Taniguchi,P.Kim,K. Rev. Lett. 97, 187401 (2006)
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