Transport through Graphene on SrTiO3

Nuno J. G. Couto, Benjamin Sacepe, and Alberto F. Morpurgo

Department de Physique de la Matiere Condensee (DPMC) and Group of Applied Physics (GAP),University of Geneva, 24 Quai Ernest-Ansermet 1211 Geneve 4, Switzerland

(Received 7 July 2011; published 21 November 2011)

We report transport measurements through graphene on SrTiO3 substrates as a function of magnetic

field B, carrier density n, and temperature T. The large dielectric constant of SrTiO3 very effectively

screens long-range electron-electron interactions and potential fluctuations, making Dirac electrons in

graphene virtually noninteracting. The absence of interactions results in an unexpected behavior of the

longitudinal resistance in the N ¼ 0 Landau level and in a large suppression of the transport gap in

nanoribbons. The ‘‘bulk’’ transport properties of graphene at B ¼ 0 T, on the contrary, are completely

unaffected by the substrate dielectric constant.

DOI: 10.1103/PhysRevLett.107.225501 PACS numbers: 81.05.ue, 73.43.Lp

Experiments on devices with SiO2 [1] and boron nitride[2] gate dielectrics, as well as on suspended layers [3],indicate that the substrate material has a strong influenceon the transport properties of graphene. Whereas investi-gations have mainly aimed at minimizing the amount ofdisorder present, it should be possible to choose the sub-strate material to effectively control different aspects of theelectronic properties of graphene. Here we discuss trans-port experiments through graphene on SrTiO3, a verywell-known insulator where the presence of a low-energyphonon mode [4] brings the material close to a ferroelectricinstability. The softening of this low-energy mode causesthe relative dielectric constant (�) of the material to in-crease from 200–300 at room temperature, to ’ 5000 atliquid helium temperature [4], with most of the increasetaking place when T is lowered from 50 to 10 K. SrTiO3

substrates, therefore, allow the investigation of the effect ofthe dielectric environment on the charge carriers in gra-phene in a broad temperature range.

The effect of dielectric screening in graphene has beeninvestigated previously. In one set of experiments, gra-phene devices were immersed in solvents with � up to50–100 [5]. Although revealing, these studies have beenconfined to temperatures above the solvent freezing point(T > 160 K), which prevented the investigation of physi-cal phenomena taking place at low temperature. In otherwork, the effect of the dielectric environment was inves-tigated by comparing the transport properties of grapheneon SiO2 with and without an adsorbed thin ice layer whichslightly changed the dielectric environment seen by thecharge carriers [6]. SrTiO3 offers the advantage of a verylarge tunable dielectric constant together with the possi-bility of measuring in a broad range of temperatures.

Our studies rely on transport measurements on grapheneHall bars and etched nanoribbons on SrTiO3. At zeromagnetic field, transport through Hall-bar devices showsno temperature dependence between 250 mK and 50 K,and graphene exhibits a behavior identical to that observed

on SiO2 substrates [7]. The importance of the substrate,however, becomes clear in measurements at finite B and innanoribbons. In the quantum Hall regime, we observe thatthe longitudinal resistance peak measured in the N ¼ 0Landau level decreases significantly with lowering T, atrend different from what has been reported in previousexperiments on SiO2 substrates [8,9]. In nanoribbons, themagnitude of the transport gap is 1 order of magnitudesmaller than in identical devices on SiO2 [10–12]. Botheffects are manifestations of the suppression of electron-electron interactions due to substrate screening, whichturns carriers in graphene into virtually noninteractingDirac fermions. The observation of such an effectivescreening also allows us to conclude that at B ¼ 0 TCoulomb interactions and long-range potentials do notsignificantly influence transport through ‘‘bulk’’ grapheneon SiO2.The devices investigated [Fig. 1(a), inset] were prepared

by exfoliating graphene from natural graphite using anadhesive tape, and by its subsequent transfer onto a500 �m thick SrTiO3 single crystalline substrate.Graphene layers were found by inspection under an opticalmicroscope, with mono-, bi-, and trilayer graphene giving acontrast of 1.25%, 2.5%, and 3.75%, respectively [seeFig. 1(b); this contrast is measured on substrates withonly one face polished]. Ti=Au contacts (10=50 nm)were defined by means of electron beam lithography,evaporation, and lift-off. The gate electrode consisted ofa Au film evaporated on the substrate back side.We first discuss measurements performed as a function

of gate voltage Vg and atB ¼ 0 T, at temperatures between

50 K and 250 mK. The increase in the substrate dielectricconstant � upon lowering T is visible in Fig. 1(a), where thegraphene resistance is plotted as a function of Vg, since,

with lowering T, a smaller Vg range is needed to scan

across the resistance peak around the charge neutralitypoint (’’Dirac peak’’). At each gate voltage, the densityof charge carriers n was extracted from the Hall resistance

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(see Supplemental Material [13]). Figure 1(c) shows that ata fixed value of Vg, n increases by approximately 1 order of

magnitude as T is lowered from 50 K down to 250 mK, inagreement with the expected behavior of SrTiO3 that wehave characterized separately through T-dependent capaci-tance measurements (see Supplemental Material [13]).Figure 2(a) shows that, when plotted as a function of n,the Dirac peaks measured at all different temperaturesoverlap nearly perfectly despite the large change in � ofthe substrate.

Finding a complete insensitivity to temperature despitethe large change in the SrTiO3 dielectric constant maycause doubts that water or other adsorbed molecules arepresent in between the graphene layer and the substrate,effectively decoupling the two materials [14]. To rule outthis possibility, it is important to identify measurable ef-fects sensitive to the substrate dielectric constant. Obviouscandidates are phenomena that originate from long-rangeelectron-electron interactions, which should be completelyscreened on SrTiO3. Two such phenomena are the tem-perature dependence of the longitudinal resistance in theN ¼ 0 Landau level in the quantum Hall regime[8] andlow-temperature bias-dependent transport in nanoribbons[10–12,15].

Figure 3 shows data measured in the presence of a 15 Tperpendicular magnetic field. At high magnetic field, well-defined Hall plateaus in the Hall conductivity �xy are

observed up to the maximum temperature investigated[50 K; see Fig. 3(b)]. The plateaus at �xy ¼ �2 and

�xy ¼ �6e2=h confirm that the device is of good quality

and that it indeed consists of a single graphene layer [16].Note the temperature dependence of the peak in the longi-tudinal resistance observed at the charge neutrality, whenthe Fermi level is located inside the N ¼ 0 Landau level:the height of this peak decreases monotonically with low-ering the temperature from 50 K to 250 mK. The effect islarge, as the peak amplitude at 250 mK is more than 3 timessmaller than at 50 K.This behavior is different from what was observed for

graphene on SiO2 in all previously reported experiments.Early measurements on SiO2 found that the height of theresistance peak associated to the N ¼ 0 Landau leveldecreases from room temperature upon cooling, but thetemperature dependence nearly saturates for T < 150 K.Cooling down from 150 to 4.2 K produces at most a 10%change in the peak resistance [9]; i.e., contrary to what weobserve on SrTiO3, between 50 K and 250 mK essentiallyno temperature dependence is observed. More recently, aninsulating temperature dependence was observed by differ-ent groups [8], accompanied by a very rapid (thermallyactivated below T � 20 K) increase in the resistance peakheight with lowering T, which is the opposite of what wefind on SrTiO3. Importantly, the carrier mobility values inthe devices used in these last experiments on SiO2 were

FIG. 2 (color online). (a) Square resistance of graphene onSrTiO3 measured at different temperatures between 250 mK and50 K, as a function of carrier density (extracted from Hall effectmeasurements). (b) Conductivity � of graphene on SrTiO3 as afunction of n (in log scale) at different temperatures, showing thelow density region where � is independent of n [by extrapolatingthe �ðnÞ curve measure at large density—dotted line—weestimate the width of this region to be approximately �n ¼ð6:0� 0:5Þ � 1011 cm�2, independent of temperature]. (c)(blue line) Fitting the experimental data to the dependence of�ðnÞ by taking into account resonant scattering [Eq. (1) of maintext] gives a very good agreement with values for the parameters(ni ¼ 2:9� 1011 cm�2 R ¼ 0:22 nm) very close to thoseobtained for graphene on SiO2.

FIG. 1 (color online). (a) Square resistance of graphene onSrTiO3 as a function of gate voltage, measured for differenttemperatures between 50 K and 250 mK; the arrow points in thedirection of lowering temperature. Inset: Optical microscopeimage with software enhanced contrast (left); the final devicewith contacts attached (right; scale bar is 3 �m long).(b) Optical contrast of mono-, bi-, and trilayer graphene onSrTiO3. (c) Ratio of the carrier density measured by Hall effectat Vg ¼ 2 V at temperature T over the carrier density at T ¼250 mK: this ratio is proportional to the dielectric constant of thesubstrate �ðTÞ and decreases by almost 1 order of magnitudewhen T is increased from 250 mK to 50 K, as expected.

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between 5000 and 10 000 cm2=V s, comparable to thosethat we found in our devices on SrTiO3 (see below), whichimplies that the different behavior of the resistance mea-sured in the N ¼ 0 Landau level on SiO2 and SrTiO3

cannot be simply attributed to a difference in the amountof disorder present. Since it is known that electron-electroninteractions play an important role in determining theproperties of N ¼ 0 Landau level in graphene [17], findinga different behavior for graphene devices on SrTiO3 andSiO2 should be expected and provides a first indication ofthe effectiveness of screening due to the substrate.

The effect of substrate screening is also visible in bias-dependent transport measurements on etched nanoribbons.When these nanoribbons are gate biased near the chargeneutrality point, a transport gap opens, due to the jointeffect of disorder and Coulomb interactions [10–12].Disorder causes electrons to localize in small regions ofthe ribbons, making charging effects important. In simpleterms, a graphene nanoribbon behaves as an array ofCoulomb-blockaded quantum dots, and the transport gaporiginates from the charging energy of the individual is-lands [15]. When the bias applied across the ribbon issufficient to overcome the Coulomb gap, the differentialconductance increases, providing the means to measure thegap magnitude.

Nanoribbons on SiO2 substrates have been investigatedextensively [10–12], and it has been found that the source-drain gap increases with increasing length L and decreas-ing width W. For very short nanoribbons (’ 200 nm orsmaller), source-drain gaps as small as 2 meV have been

reported [12]. However, for nanoribbons having a lengthand width comparable to those that we have studied onSrTiO3 (W ¼ 70 nm and L ¼ 1 �m), the source-draingap was found to range between 10 and 25 meV, and, forthe majority of devices (approximately 80%), in between15 and 20 meV (see Ref. [12] and our own works onnanoribbons on SiO2 [11]).Figure 4(a) shows the conductance of a 70 nm wide and

1 �m long ribbon on SrTiO3 (one of the three devices thatwe measured, all showing similar behavior) as a functionof gate and bias voltage (Vsd). It is apparent that theconductance is suppressed at low bias; i.e., a transportgap is present. The largest size of this gap is only 2 meV,i.e., 1 order of magnitude less than for devices SiO2 withidentical dimensions. The gap magnitude is more clearlyseen in Fig. 4(b), which shows the bias dependence of theconductance measured for three different values of gatevoltages. A large reduction of the transport gap in SrTiO3

devices is expected due to the substrate dielectric constant,which strongly increases the self-capacitance of the islandsin the ribbon, suppressing their charging energy (note thatthe remaining gap of 2 meV also includes a contributiondue to single particle level spacing, which is present even ifthe charging energy is completely suppressed). The obser-vation of a strongly suppressed gap in nanoribbons onSrTiO3, therefore, provides another clear indication ofthe effectiveness of substrate screening.We now go back to discuss the behavior of graphene on

SrTiO3 observed at B ¼ 0 T. We have measured approxi-mately 10 different devices on SrTiO3 (including severalbilayers) and found mobility values in the range between3000 and 10 000 cm2=Vs, which coincides with what wenormally find for similar devices on SiO2. Also, the tem-perature independence of the conductivity, illustrated bythe measurements in Fig. 2, is identical to what is normallyfound for graphene on SiO2. From these results—carriermobility values on SrTiO3 in the same range as on SiO2,showing no temperature dependence below 50 K—we

FIG. 3 (color online). (a) Longitudinal square resistance R as afunction of Vg at B ¼ 15 T, measured at different temperatures

between 250 mK and 50 K. The height of the resistance peak atthe charge neutrality (N ¼ 0 Landau level) decreases signifi-cantly with lowering T, whereas the height of the peaks centeredaround the subsequent N ¼ �1 Landau shows a slight increasein resistance with lowering T [see (c); N ¼ 0 (circles), N ¼ þ1(squares), and N ¼ �1 (triangles)]. (b) The Hall conductivitymeasured at 50 K (B ¼ 15 T) shows very well-developed pla-teaus at �2;�6e2=h, as is characteristic for Dirac fermions ingraphene.

FIG. 4 (color online). (a) Differential conductance G (in unitsof e2=h), of a graphene nanoribbon, as a function of the source-drain and gate voltage, Vsd and Vg. (b) Differential conductance

as a function of Vsd for three specific Vg values, corresponding to

the dotted lines in (a). The interval enclosed by the dashed linesgives the size of the transport gap, which is approximately2 meV for each polarity of Vsd (1 order of magnitude smallerthan for an identical ribbon on SiO2).

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directly conclude that the large dielectric constant ofSrTiO3 does not affect bulk transport through grapheneat B ¼ 0 T. These findings directly rule out long-rangeCoulomb potentials generated by charge impurities nextto the graphene layers as the main, mobility-limiting scat-tering mechanism in graphene [18] (in agreement with theconclusions in Ref. [5], which only explored the hightemperature regime). Our experimental results are betterexplained by resonant scattering due to impurities generat-ing very strong and short-range potentials [19], which leadto the following expression for the carrier density depen-dence of the conductivity �:

� ¼ 2e2

�h

n

niln2ð ffiffiffiffiffiffiffi

n�p

RÞ (1)

(ni is the impurity concentration and R the potential range,respectively). This expression provides an appropriate de-scription of the conductivity away from the charge neutral-ity region, i.e., not in the charge density region where theconductivity is constant [see Fig. 2(b)]. This is shown inFig. 2(c) through a satisfactory fit to our data, where theobtained values for the parameters ni ¼ 2:9� 1011 cm�2

and R ¼ 0:22 nm are very close to those found for gra-phene on SiO2 [20]. Indeed, the potentials responsible forresonant scattering have very short range and cannot bescreened by the substrate, which explains why the B ¼ 0 Tconductivity and mobility of carriers in graphene onSrTiO3 and on SiO2 are the same [21].

Note that the width �n of the low density regionwhere the conductivity � is independent of n [for thedevice whose data are shown in Fig. 2(b), �n ’6:0� 0:5� 1011 cm�2] also shows values essentiallyidentical to those measured on devices on SiO2 [7], wherethe dielectric constant is roughly 1000 times smaller. Themagnitude of �n is usually taken as a measure of potentialfluctuations that give origin to the so-called ‘‘puddles,’’ i.e.,spatial fluctuation in carrier density whose presence hasbeen observed in different kinds of experiments [23–25].Our findings indicate that the density fluctuations thataffect the conductivity cannot be long-ranged: on SrTiO3

all long-ranged potential and charge density fluctuationsare very strongly suppressed as compared to SiO2, and stillthe value of �n on SrTiO3 and on SiO2 coincide.Consistently with this conclusion, �n remains temperatureindependent despite the large increase in �with lowering Tthat occurs in the investigated temperature range. In con-trast to long-range fluctuations, fluctuations of carrier den-sity that vary on a length scale of at most a few nanometers(not much larger than the graphene-substrate distance)cannot be screened effectively by the substrate and canaccount for our observations. Indeed, density fluctuationson such a length scale are present in graphene on SiO2, as ithas been revealed experimentally by scanning tunnelingexperiments [24].

In summary, we have performed a study of low-temperature transport through graphene on SrTiO3 which,through a comparison with results obtained on lower di-electric constant substrates, enables a direct identificationof effects that originate from long-range electron-electroninteractions and Coulomb potentials. Whereas these phe-nomena crucially determine the properties of the N ¼ 0Landau level and the size of the transport gap in nano-ribbons, they do not play a significant role on the transportproperties of bulk graphene at B ¼ 0 T.We acknowledge A. Ferreira for technical assistance, A.

Caviglia, M. Fogler, S. Gariglio, I. Martin, J. B. Oostinga,and N.M.R. Peres for discussions, SNF and the NCCRsMANEP and QSIT for financial support.

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