Gate-induced insulating state in bilayer graphene devices

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1 Gte-induced insulting stte in ilyer grphene devices JEROEN B. OOSTINGA, HUBERT B. HEERSCHE, XINGLAN LIU, ALBERTO F. MORPURGO* AND LIEVEN M. K. VANDERSYPEN* Kvli Institute of Nnoscience, Delft University of Technology, PO Box 5, GA, Delft, The Netherlnds ARTICLES Pulished online: Decemer 7; doi:1.1/nmt The potentil of grphene-sed mterils consisting of one or few lyers of grphite for integrted electronics origintes from the lrge room-temperture crrier moility in these systems ( 1, cm V 1 s 1 ). However, the reliztion of electronic devices such s field-effect trnsistors will require controlling nd even switching off the electricl conductivity y mens of gte electrodes, which is mde difficult y the sence of ndgp in the intrinsic mteril. Here, we demonstrte the controlled induction of n insulting stte with lrge suppression of the conductivity in ilyer grphene, y using doule-gte device configurtion tht enles n electric field to e pplied perpendiculr to the plne. The dependence of the resistnce on temperture nd electric field, nd the sence of ny effect in single-lyer device, strongly suggest tht the gte-induced insulting stte origintes from the recently predicted opening of ndgp etween vlence nd conduction nds. Grphene systems, consisting of one or few crystlline monolyers of cron toms, stnd out ecuse of their unusul electronic properties nd their potentil for pplictions in nnoelectronics 1 5. Crrier moility vlues s high s 1, cm V 1 s 1 t room temperture ten times higher thn in silicon re routinely otined in these mterils, without the need for sophisticted preprtion techniques 1. Both the high moility nd the possiility of low-cost mss production provide strong drive to explore the use of grphene for future high-speed integrted electronic circuits. To develop such grphene-sed electronics, however, severl prolems need to e overcome. Perhps the most importnt ostcle is the sence of n energy gp seprting the vlence nd conduction nds of grphene grphene is zero-gp semiconductor. As consequence, electricl conduction cnnot e switched off using control voltges 7, which is essentil for the opertion of conventionl trnsistors. It ws recently shown tht conduction cn e switched off y ptterning single-lyer grphene into nrrow rions. Here, we demonstrte tht we cn produce n insulting stte nd switch off electricl conduction in ilyer grphene device, simply y pplying control voltges to two onchip gte electrodes. Our strtegy is motivted y recent theoreticl work tht discusses how ndgp cn e opened in single- nd i-lyer grphene 9,1. To understnd the physicl mechnisms underlying these predictions, we consider the sic electronic properties of grphene-sed mterils in some detil. Monolyer grphene hs honeycom lttice structure with unit cell consisting of two toms normlly referred to s A nd B toms (Fig. 1). The hmiltonin tht descries the electronic properties of grphene ner the Fermi level cn e pproximted s,11 ( H = hv F (k x ik y ) hv F (k x + ik y ) ), (1) where k is the momentum nd v F is the Fermi velocity. This opertor cts on spinors ψ = ( φa φ B ), where φ A nd φ B re the mplitudes of the wvefunction on sulttices A nd B, nd is the onsite energy difference etween the two sulttices. Normlly = nd this hmiltonin results in the Dirc-like liner dispersion reltion E = ± hv F k (Fig. 1). The positive nd negtive solutions, which correspond to conduction nd vlence nds respectively, meet t k =, implying the sence of ndgp. To open gp, the inversion symmetry in the grphene plne must e roken y mking. In this cse, the low-energy hmiltonin (1) leds to gpped dispersion reltion E(k) = ± + ( hv F k). This inversion symmetry reking cn in principle e implemented experimentlly. For instnce, we cn imgine plcing grphene onto oron nitride (BN) sustrte tht hs the sme honeycom lttice structure nd comprle lttice spcing, so tht the A nd B toms experience different onsite energies 9. In prctice, however, the technologicl chllenges tht need to e met to implement such strtegy re highly non-trivil. In ilyer grphene, in contrst, conceptully similr strtegy is within technologicl rech. Bilyer grphene consists of two monolyers stcked s in nturl grphite (Fig. 1). This so-clled Bernl stcking yields unit cell of four toms (one tom of ech of the sulttices A1, B1, A nd B) resulting in four electronic nds. Only two of these nds re relevnt t low energy; they cn e descried y the effective hmiltonin 1 ( H = h (k m x + ik y ) h (k m x ik y ) ). () This opertor hs structure similr to tht of eqution (1) nd, s for the monolyer, it lso leds to spectrum with zero gp etween vlence nd conduction nds when =, ut now with qudrtic dispersion reltion (E = ± h k /m; Fig. 1). Furthermore, nd essentil for our purposes, the opertor () cts on spinors ψ = ( φa1 φ B ), which contin the mplitude of the wvefunction on toms A1 nd B tht re locted in the two different lyers. This mkes it possile to control the difference nture mterils VOL 7 FEBRUARY Nture Pulishing Group

2 c B A B A A1 B1 E... E (ev) E (ev) E (ev) Δ..1 k (Å 1 )..1.1 k (Å 1 )..1.1 k (Å 1 ).1 d V tg V nm Au.5 nm Ti 5 nm Au 5 nm Au 1 nm Ti 1 nm Ti 15 nm SiO Grphene I is 5 nm SiO p-doped Si V g Figure 1 Bndgp in grphene devices.,, Schemtic digrms of the lttice structure of monolyer () nd ilyer () grphene. The green nd red coloured lttice sites indicte the A (A1/A) nd B (B1/B) toms of monolyer (ilyer) grphene, respectively. The digrms represent the clculted energy dispersion reltions in the low-energy regime, nd show tht monolyer nd ilyer grphene re zero-gp semiconductors (for ilyer grphene, pir of higher-energy nds is lso present, not shown in the digrm). c, When n electric field (E ) is pplied perpendiculr to the ilyer, ndgp is opened in ilyer grphene, whose size ( ) is tunle y the electric field. d, Schemtic digrm of doule-gted grphene device s used in our investigtions. Both the Fermi level in the grphene (i)lyer nd the perpendiculr electric field re controllle y mens of the voltges pplied to the ck gte, V g, nd to the top gte, V tg. We study the resistivity of the grphene (i)lyer s function of oth gte voltges y pplying current is (I ) nd mesuring the resulting voltge cross the device, V. Note the different SiO thicknesses of the dielectric lyers for the top nd ck gtes. etween the onsite energy of A1 nd B electrostticlly, simply y pplying sufficiently strong electric field E perpendiculr to the cron tom plnes. In the presence of such n electric field, gp of size opens etween conduction nd vlence nds 1,1,1 (Fig. 1c). Indeed, ndgp originting from this mechnism hs recently een oserved in ngle-resolved photoemission spectroscopy experiments on chemiclly doped grphene ilyer, in which the electric field is ssocited with the chrge trnsfer from the dopnts to the cron toms 1 (see lso ref. 15). Here, we use doule-gte device configurtion to impose perpendiculr electric field onto grphene ilyer, which enles us to demonstrte the controlled trnsition from zero-gp semiconductor to n insultor, y simply djusting the voltges pplied to the two gte electrodes. Figure 1d shows the device configurtion tht we investigte. It consists of single or doule grphene lyers sndwiched etween two gte electrodes, nd connected to metllic leds. These doulegted structures enle simultneous nd independent control of the chrge density in the system (tht is, the position of the Fermi level) nd of the electric field perpendiculr to the grphene lyer. In single lyer, the presence of perpendiculr field is not expected to ffect the trnsport properties: the conductivity of the device should never ecome smller thn minimum vlue of the order of e /h, irrespective of the pplied gte voltges. In ilyer, on the contrry, lrge pplied field results in different electrosttic potentil in the two lyers, which, ccording to theory, should cuse ndgp to open. If the Fermi level is mintined in the gp (tht is, the device is operted ner the chrge-neutrlity point), this should result in n insulting temperture dependence of the conductivity, dropping to well elow e /h t low temperture. A unique signture of this effect is tht the decrese in conductivity with lowering temperture ecomes more pronounced for lrger pplied electric field vlues. This possiility to controllly induce n insulting stte, which is crucil for switching devices, ws missing in erlier experiments on grphene ilyers 1,15 where the gp nd the crrier density could not e gte-controlled independently. The friction of doule-gted grphene devices is similr to wht hs een descried elsewhere 1, nd relies on micromechnicl cleving of nturl grphite. The flkes used in the experiments were selected under n opticl microscope nd identified s singlend doule-lyer grphene, respectively, on the sis of their opticl contrst (see Supplementry Informtion; similr method is used s previously demonstrted in refs 1,17). Contct to the flkes ws mde y mens of electron-em lithogrphy, electron-em evportion of Ti/Au ilyer (1/5 nm) nd lift-off. The topgte insulting lyer nd electrodes were defined susequently, y electron-em deposition of SiO lyer (15 nm) followed y deposition of Ti/Au ilyer (.5/ nm), without reking the vcuum. The comprison etween single- nd doule-lyer 15 nture mterils VOL 7 FEBRUARY Nture Pulishing Group

3 1 μm V tg = V 1.5 V V T =.7 K 1.5 V 1. μm Top gte 1 μm 1.1 μm I = 1 na V 5 1 V g (V) 1 5 c T =.7 K V g = V 5 V 1 V 5 V V 5 V d V g = 5 V V g = V T =.7 K T = 1. K T = 5 K 1 1 V tg ( V) 1 1 Figure Gte voltge nd temperture dependence of trnsport through monolyer grphene., Opticl microscope imges of single-lyer flke (left) nd of the doule-gted device fricted on this flke (right). The yellow lines indicte metl contcts to the flke, nd the lue line corresponds to the top gte. The schemtic digrm of the four-proe device configurtion is lso shown., Resistnce versus ck-gte voltge mesured for different fixed vlues of the top-gte voltge showing n pproximtely gte-voltge-independent height of the chrge-neutrlity pek (the right xis gives n estimtion of the squre resistnce, neglecting the contriutions from the region without the top gte nd ny p n junctions to the mesured resistnce). The periodic fluctutions present ner the chrge-neutrlity pek re reproducile nd re due to quntum interference. The smller extr pek (indicted y the rrow) is the chrge-neutrlity pek originting from the prt of the flke tht is not covered y the top gte. c, Resistnce versus top-gte voltge mesured for different fixed vlues of ck-gte voltge. Agin, the height of the chrge-neutrlity pek is nerly gte-voltge independent. The difference in the mgnitude of the voltge pplied to top nd ck gtes (,c) origintes from the different SiO thicknesses seprting the two gtes from the grphene flke. d, Temperture dependence of the resistnce versus top-gte voltge, mesured for two different ck-gte voltges. Irrespective of the gte-voltge configurtion, the height of the chrge-neutrlity pek is independent of temperture in the rnge.7 5 K. grphene devices is useful not only to illustrte the profound difference etween them nd to identify the mechnism responsile for the gte-induced insulting stte, ut lso to rule out possile spurious effects originting from the device friction (for exmple, dmge to the grphene lyers or disorder introduced y the deposition of the SiO gte dielectric). We now proceed to discuss the systemtic trnsport mesurements tht we hve crried out, strting with the singlelyer device shown in Fig.. Figure,c shows the resistnce mesured s function of the voltge pplied to one of the gtes, with the other gte t constnt potentil s indicted (we extrct crrier moility of, cm V 1 s 1, similr to the moility of n ungted device on the sme flke). Irrespective of which gte voltge is kept constnt, we lwys oserve pek in resistnce chrcteristic of the ehviour of few-lyer grphene nd herefter referred to s the chrge-neutrlity pek (to e precise, we re mesuring device comprising regions of different crrier density, n1 n n1; t the resistnce mximum, n = only). The position of the chrge-neutrlity pek when sweeping one gte shifts linerly with the voltge pplied to the other gte. Irrespective of the gte configurtion, the height of the resistnce pek remins pproximtely constnt. From the topgte dimensions, we cn estimte minimum conductivity vlue close to e /h (the prt of the flke tht is not covered y the top gte lso contriutes to the resistnce, ut given the dimensions, this increses the conductivity estimte y t most fctor of 1.). This is typicl of grphene t the chrge-neutrlity point, which indictes tht the device friction nd the deposition of the top-gte dielectric hve not resulted in sustntil dmge to the mteril. Note lso tht depending on the vlues of the voltges pplied to oth gtes, p n junctions re formed ner the interfces etween the region covered y the top gte nd oth uncovered regions 1. Such p n junctions my e the origin of the wek symmetry seen in mny of the gte sweeps in Fig.,c. However, nture mterils VOL 7 FEBRUARY 15 Nture Pulishing Group

4 1 μm T =. K V μm Top gte V I = 1 na V tg =.5 V V 1.5 V V 1.5 V V.5 V μm μm V g (V) 1 5 c V g = 5 V 5 V T =. K 5 V d T =. K T = 1.5 K T = 55 K V g = 5 V V 5 V V 5 V V 5 V V g = V Figure Gte voltge nd temperture-dependent trnsport through ilyer grphene., Opticl microscope imges of doule-lyer flke (left) nd of the doule-gted device fricted on this flke (right). The yellow lines represent metl contcts nd the lue line represents the top-gte electrode. The two-proe mesurement configurtion is shown in the schemtic digrm (the mesured resistnce thus includes the contct resistnce, which is smller thn 5 )., Resistnce versus ck-gte voltge mesured for different fixed vlues of the top-gte voltge (the right xis gives the squre resistnce, gin ssuming tht the region under the top gte domintes the mesured resistnce; this ssumption is vlid ner the chrge-neutrlity pek where the resistnce of the region with top gte is reltively lrge). The height of the chrge-neutrlity pek systemticlly increses when oth gtes re ised with incresingly lrge opposite voltges. c, Resistnce versus top-gte voltge mesured for different fixed ck-gte voltges showing similr gte-voltge dependence of the height of the chrge-neutrlity pek. d, Temperture dependence of the resistnce versus top-gte voltge mesured for two different vlues of ck-gte voltge. When the voltge difference etween oth gtes is smll, the height of the chrge-neutrlity pek is not ffected y temperture in the rnge. 55 K. However, cler temperture dependence is oserved in this sme rnge when oth gtes re ised with lrge opposite voltges. ner the chrge-neutrlity point, we expect p n junctions to give only smll contriution to the mesured resistnce. Finlly, Fig. d shows tht the gte voltge dependence of the resistnce is not ffected y vrying the temperture etween nd 5 K, prt from reproducile conductnce fluctutions tht increse in mgnitude s the temperture is lowered. These oservtions re consistent with the expected ehviour of electricl trnsport through grphene monolyers,1. The ehviour of the doule-gted grphene ilyer device (Fig. ) is strikingly different. Figure,c shows the (squre) resistnce of ilyer grphene s function of the ck-gte nd top-gte voltges (the crrier moility is 1, cm V 1 s 1, gin similr to n ungted device on the sme flke). Similrly to the monolyer, the position of the chrge-neutrlity pek shifts linerly with the respective gte voltges. Contrry to the monolyer, the chrge-neutrlity peks re nerly perfectly symmetric, ruling out the possiility tht the formtion of p n junctions gives dominnt contriution to the mesured resistnce. More importntly, the mximum resistnce vlue now depends on the configurtion of gte voltges. Specificlly, when the voltge pplied to oth gtes is close to V, the height of the chrge-neutrlity pek corresponds to conductivity of the order of e /h, which is typicl for zero-gp ilyers 5 (gin we rely on the fct tht ner the chrge-neutrlity pek the region under the top gte gives the lrgest contriution to the resistnce). However, s the top nd ck gtes re ised with opposite voltges of incresing mgnitude, the height of the chrge-neutrlity pek exhiits pronounced rise. In ddition, the temperture dependence oserved in the ilyer device is mrkedly different from tht mesured in the single-lyer device (Fig. d). For smll gte voltges, the resistnce ner the chrge-neutrlity pek is essentilly temperture independent, chrcteristic of zero-gp semiconductor. When the difference in top-gte nd ckgte voltge is incresed, however, the mximum resistnce vlue lso increses s the temperture is lowered. The oservtion of 15 nture mterils VOL 7 FEBRUARY Nture Pulishing Group

5 1 1 T = 5 mk A BC 1/R (μs) 1 R (MΩ) V g = V R (MΩ) D E F V g (V).1 V g = +5 V V g (V) c 5 5 T = 5 mk I (na) A B 5 C D E F V is (μv) Figure Gte-induced insulting stte in the ilyer grphene device., Squre resistnce s function of top-gte voltge mesured t different tempertures: T = 55 mk (lue line), T = 7 mk (red line), T = mk (green line) nd T = 1, mk (lck line) (the ck-gte voltge is kept fixed t V g = +5 V). Here, the squre resistnce is plotted, ecuse ner the chrge-neutrlity pek the resistnce is lmost completely dominted y the region under the top gte. A pronounced temperture dependence is oserved when the top nd ck gtes re ised symmetriclly; when oth gtes re symmetriclly ised no temperture dependence is oserved (see inset)., Three-dimensionl plot of the squre resistnce s function of oth top- nd ck-gte voltge t T = 5 mk, showing shrp rise of the height of the chrge-neutrlity pek with electric field. The inset is colour plot of the sme dt, showing tht the position of the chrge-neutrlity pek shifts linerly with oth gte voltges. The drk-coloured region corresponds to voltge configurtions where n insulting stte is oserved. c, I V chrcteristics mesured t different gte-voltge configurtions (the letters correspond to the letters in the inset of, which indicte oth gte voltges). The dt in nd were tken with lock-in detection, using zero-voltge is with 5 µv excittion voltge modulted t 17 Hz. The dt in c were mesured with d.c. voltge is. Note tht the plotted voltge is is corrected for the internl resistnce (1.1 k ) of the current mesurement unit used in the experiment. conductivity much smller thn e /h exhiiting n insulting temperture dependence for oppositely ised gte electrodes is wht we would expect qulittively in ilyer grphene device. To confirm tht in the doule-gted ilyer device lrge differences in voltge etween the top nd ck gte do led to n insulting stte, we hve crried out mesurements in dilution refrigertor, in the temperture rnge etween 5 mk nd 1. K, where the increse in resistnce with lowering temperture should e more pronounced. Indeed, Fig. (note the logrithmic scle) shows tht when the top nd ck gtes re ised symmetriclly, very strong temperture dependence of the squre resistnce is oserved ner the chrge-neutrlity pek, reching vlues etween 1 nd 1 M t 55 mk. This is in strk contrst to the cse of smll gte voltges (Fig., inset), for which temperture-independent resistnce ner the chrge-neutrlity pek corresponding to conductivity of pproximtely e /h persists down to the lowest temperture. The full dependence of the squre resistnce mesured t 5 mk s function of the voltge pplied to oth gte electrodes is shown in Fig., from which the very fst increse in resistnce ner the chrge-neutrlity pek with incresing the electric field pplied perpendiculr to the lyer is pprent. According to the expecttions, the region of high resistnce scles linerly with oth top- nd ck-gte voltge (see the white dotted line in the inset of Fig. ) s it is required to mintin chrge neutrlity in the grphene ilyer. In ddition, we hve lso mesured the I V chrcteristics of the device for different top- nd ck-gte voltge configurtions (Fig. c) nd oserved tht they evolve from exhiiting liner ohmic ehviour fr from the chrge-neutrlity pek, to pronounced nonliner ehviour ner the chrge-neutrlity pek. Finlly, we discuss more quntittively the insulting temperture dependence of the resistnce tht we oserve for lrge oppositely ised gtes. In n idel defect-free insultor, thermlly ctivted trnsport is expected, wherey the mximum resistnce, R, vries with temperture s R(T) exp(e /kt), nture mterils VOL 7 FEBRUARY Nture Pulishing Group

6 .5 ln(r ) () 5 E z = +.15 V nm 1.5 E z = +.15 V nm ln(r ) () n E z (V nm 1 ) E z = +.11 V nm 1 E z = +.11 V nm 1 E z = +.1 V nm 1 E z = +.1 V nm 1 E z = +. V nm 1 E z = +. V nm 1 5 T 1 (K 1 ) T 1/ (K 1/ ) Figure 5 Thermlly ctivted hopping trnsport in ised ilyer grphene., Logrithm of the squre resistnce t the chrge-neutrlity pek versus inverse temperture, for different perpendiculr electric fields (E = (V g V tg )/(d g + d tg ), where d g nd d tg re the thicknesses of the ck- nd top-gte oxides). These plots clerly show suliner ehviour in the temperture rnge from 55 mk to 55 K (the dotted lines re guide to the eye), implying tht the dt cnnot e descried y R(T ) exp(e /kt)., Logrithm of the squre resistnce of the chrge-neutrlity pek s function of T 1/ for different perpendiculr electric fields in the temperture rnge from 55 mk to 55 K. The liner fits to the dt (solid lines) show tht, t the highest fields, the dt re well descried y R(T ) exp(t /T) 1/. At lower fields, the fitted exponent, n, is smller thn 1/ (see inset; the error rs reflect the stndrd devition of the fitted vlues). where k is Boltzmnn s constnt nd E is the ctivtion energy, corresponding to hlf the ndgp. Our dt, however, do not exhiit such simple therml ctivtion ehviour (Fig. 5). Below pproximtely T = 5 K, nd t the highest pplied electric fields, they re much etter descried y R(T) exp(t /T) 1/, s seen in Fig. 5, with fitted vlues of T of.5. K (note tht etween 5 nd 55 K the resistnce drops more rpidly with incresing temperture, ut the rnge is too smll to deduce n ccurte vlue for the ctivtion energy). Qulittively, n n = 1/ exponent is expected for trnsport in two dimensions of non-intercting crriers vi vrile-rnge hopping in insulting mterils where trnsport is medited y loclized impurity sites tht re present inside gp 1,. Such loclized sttes hve een predicted theoreticlly in the cse of disordered ilyer grphene, ut drwing quntittive conclusions s to the properties of these sttes, for exmple, their density of sttes, sptil extension, nd so on, is not strightforwrd from our mesurements nd goes eyond the scope of this rticle. For smller pplied perpendiculr electric fields, the fitted exponent ecomes smller thn 1/ nd decreses towrds zero (see inset of Fig. 5), nd the fitted vlue of T lso decreses. This indictes clerly tht the insulting temperture dependence of the resistnce tht we mesure ecomes stronger when the pplied perpendiculr electric field is higher. We conclude tht the dt unmiguously show the occurrence of n insulting stte in ilyer grphene in the presence of perpendiculr electric field, which hs not een reported erlier. Our oservtion tht the insulting stte occurs only in ilyers nd not in monolyers, nd tht the increse in resistnce with lowering temperture is more pronounced for lrger vlues of the electric field pplied perpendiculr to the mteril, is in greement with the predicted controlled opening of ndgp. In contrst, these two very specific oservtions cnnot e ccounted for simply y n increse in the mount of disorder, for instnce cused y the presence of the top gte. Furthermore, s pointed out erlier, crrier moilities were comprle in devices with nd without top gtes, ctully suggesting equl mounts of disorder. Although we cnnot rule out tht mechnisms other thn the formtion of ndgp could led to the sme striking oservtions, we elieve this explntion is the most plusile. It is cler from the experiments tht possile gp induced in the ilyer device is rther smll. This is consistent with recent theoreticl clcultions 1,1, which, for zero crrier density nd for electric field vlues of the order of those chieved in our experiments, predict gp size elow pproximtely 1 mev depending on, for instnce, the wy in which screening effects in the ilyer re modelled (note tht in refs 1,15, mesurements were done t very high chrge density, where much lrger gp sizes were expected nd oserved). In comprison, the energy scle of disorder cn e estimted to e of the order of few milli-electron volts from mesurements of the spin splitting in the quntum Hll regime, nd lrger from scnning single-electron trnsistor experiments 5. Altogether, it seems tht gp of elow 1 mev in conjunction with the presence of sugp sttes originting from disorder cn ccount for the oserved exp(t 1/ ) dependence of the resistnce in the temperture rnge etween 5 mk nd. K. However, this does not well explin the steep dependence on electric field t 55 K nd on temperture ove. K. It is possile tht the gp is in fct lrger thn predicted, or lterntively there my e other mechnisms lso contriuting to the oserved resistnce increse in this n1 n n1 device. The possiility to use doule-gted structures to suppress the conductivity of ilyer grphene to vlues much lower thn e /h represents n importnt proof-of-principle for the fesiility of future grphene-sed electronic devices. Oviously the development of prcticl devices will require further innovtions, which re needed to switch off electricl conduction t room temperture. Nevertheless, the opertion of devices t cryogenic tempertures tht we hve demonstrted here will lredy enle new fundmentl studies of quntum trnsport in ilyer grphene, through the friction of structures such s quntum point contcts sed on split gtes nd electrostticlly tunle quntum dots. Received 17 July 7; ccepted 1 Novemer 7; pulished Decemer 7. References 1. Novoselov, K. S. et l. Electric field effect in tomiclly thin cron films. Science, 9 ().. Novoselov, K. S. et l. Two-dimensionl gs of mssless Dirc fermions in grphene. Nture, 197 (5). 15 nture mterils VOL 7 FEBRUARY Nture Pulishing Group

7 . Zhng, Y. B., Tn, Y. W., Stormer, H. L. & Kim, P. Experimentl oservtion of the quntum Hll effect nd Berry s phse in grphene. Nture, 1 (5).. Novoselov, K. S. et l. Unconventionl quntum Hll effect nd Berry s phse of π in ilyer grphene. Nture Phys., (). 5. Geim, A. K. & Novoselov, K. S. The rise of grphene. Nture Mter., (7).. Wllce, P. R. The nd theory of grphite. Phys. Rev. 71, (197). 7. Ktsnelson, M. I., Novoselov, K. S. & Geim, A. K. Chirl tunnelling nd the Klein prdox in grphene. Nture Phys., 5 ().. Hn, M. Y., Özyilmz, B., Zhng, Y. & Kim, P. Energy nd-gp engineering of grphene nnorions. Phys. Rev. Lett. 9, 5 (7). 9. Giovnnetti, G., Khomykov, P. A., Brocks, G., Kelly, P. J. & Vn den Brink, J. Sustrte-induced ndgp in grphene on hexgonl oron nitride: A initio density functionl clcultions. Phys. Rev. B 7, 71 (7). 1. McCnn, E. Asymmetry gp in the electronic nd structure of ilyer grphene. Phys. Rev. B 7, 11 (). 11. Semenoff, G. W. Condensed mtter simultion of three-dimensionl nomly. Phys. Rev. Lett. 5, 9 5 (19). 1. McCnn, E. & Fl ko, V. I. Lndu-level degenercy nd quntum Hll effect in grphite ilyer. Phys. Rev. Lett. 9, 5 (). 1. Min, H., Shu, B. R., Bnerjee, S. K. & McDonld, A. H. A initio theory of gte induced gps in grphene ilyers. Phys. Rev. B 75, (7). 1. Oht, T., Bostwick, A., Seyller, T., Horn, K. & Rotenerg, E. Controlling the electronic structure of ilyer grphene. Science 1, (). 15. Cstro, E. V. et l. Bised ilyer grphene: Semiconductor with gp tunle y electric field effect. Phys. Rev. Lett. 99, 1 (7). 1. Blke, P. et l. Mking grphene visile. Appl. Phys. Lett. 91, 1 (7). 17. Aergel, D. S. L., Russell, A. & Fl ko, V. I. Visiility of grphene flkes on dielectric sustrte. Appl. Phys. Lett. 91, 15 (7). 1. Hurd, B. et l. Trnsport mesurements cross tunle potentil rrier in grphene. Phys. Rev. Lett. 9, (7). 19. Willims, J. R., DiCrlo, L. & Mrcus, C. M. Quntum Hll effect in gte-controlled p n junction of grphene. Science 17, 1 (7).. Özyilmz, B. et l. Electronic trnsport nd quntum Hll effect in ipolr grphene p-n-p junctions. Phys. Rev. Lett. 99, 1 (7). 1. Mdelung, O. Introduction to Solid-Stte Theory (Springer, Berlin, Heidelerg, 197).. Shklovskii, B. I. & Efros, A. L. Electronic Properties of Doped Semiconductors (Springer, Berlin, Heidelerg, 19).. Nilsson, J. & Cstro Neto, A. H. Impurities in ised grphene ilyer. Phys. Rev. Lett. 9, 11 (7).. Zhng, Y. et l. Lndu-level splitting in grphene in high mgnetic fields. Phys. Rev. Lett. 9, 1 (7). 5. Mrtin, J. et l. Oservtion of electron-hole puddles in grphene using scnning single electron trnsistor. Nture Phys. dvnce online puliction 5 Novemer 7 (doi:1.1/nphys71). Acknowledgements We grtefully cknowledge P. Jrillo-Herrero for experimentl help in the erly stges of this work, L. P. Kouwenhoven for providing ccess to dilution refrigertor, E. McCnn, A. H. McDonld nd H. Min for useful discussions, nd NWO, FOM nd NnoNed for finncil support. Correspondence nd requests for mterils should e ddressed to A.F.M. or L.M.K.V. Supplementry Informtion ccompnies this pper on Reprints nd permission informtion is ville online t nture mterils VOL 7 FEBRUARY Nture Pulishing Group