Gate-defined quantum confinement in suspended bilayer graphene

Transcription

1 Reeived 26 Jn 212 Aepted 31 My 212 Pulished 3 Jul 212 DOI: 1.138/nomms1945 Gte-defined quntum onfinement in suspended ilyer grphene M. T. Allen 1, J. Mrtin 1, & A. Yoy 1 Quntum-onfined devies tht mnipulte single eletrons in grphene re emerging s ttrtive ndidtes for nnoeletronis pplitions. Previous experiments hve employed ethed grphene nnostrutures, ut edge nd sustrte disorder severely limit devie funtionlity. Here we present tehnique tht uilds quntum-onfined strutures in suspended ilyer grphene with tunnel rriers defined y externl eletri fields tht open ndgp, therey eliminting oth edge nd sustrte disorder. We report len quntum dot formtion in two regimes: t zero mgneti field B using the energy gp indued y perpendiulr eletri field nd t B> using the quntum Hll ν = gp for onfinement. Coulom lokde osilltions exhiit periodiity onsistent with eletrostti simultions sed on lol top-gte geometry, diret demonstrtion of lol ontrol over the nd struture of grphene. This tehnology integrtes single eletron trnsport with high devie qulity nd ess to virtionl modes, enling rod pplitions from eletromehnil sensors to quntum its. 1 Deprtment of Physis, Hrvrd University, Cmridge, Msshusetts 2138, USA. Present ddress: College of Engineering, Mthemtis nd Physil Sienes, University of Exeter, Exeter EX4 4QL, UK. Correspondene nd requests for mterils should e ddressed to A.Y. (emil: yoy@physis.hrvrd.edu). nture ommunitions 3:934 DOI: 1.138/nomms Mmilln Pulishers Limited. All rights reserved.

2 nture ommunitions DOI: 1.138/nomms1945 Nnoptterned grphene devies, from field-effet trnsistors to quntum dots 1 3, hve een the sujet of intensive reserh euse of their novel eletroni properties nd two-dimensionl (2D) struture 4,5. For exmple, nnostrutured ron is promising ndidte for spin-sed quntum omputtion 6 euse of the ility to suppress hyperfine oupling to nuler spins, dominnt soure of spin deoherene 7 9, y using isotopilly pure 12 C. Grphene is prtiulrly ttrtive host for lterl quntum dots s oth vlley nd spin indies re ville to enode informtion, feture sent in GAs Yet grphene lks n intrinsi ndgp 5, whih poses serious hllenge for the retion of suh devies. Trnsport properties of on-sustrte grphene nnostrutures defined y ething 2,3 re severely limited y oth edge disorder nd hrge inhomogeneities rising from ionized impurities in gte dieletris 13,14. The sene of spin lokde in ethed doule dots is perhps symptomti of these ostles 15,16. Unzipping ron nnotues yields len nnorion dots, ut this pproh nnot produe ritrrily shped nnostrutures with tunle onstritions 17. However, lol ndgp engineering in ilyer grphene enles prodution of tunle tunnel rriers defined y lol eletrostti gtes 18, thus providing len eletron onfinement isolted from edge disorder. Bernl stked ilyer grphene is nturlly suited for ndgp ontrol euse of its rih system of degeneries tht ouple to externlly pplied fields. At B =, reking lyer inversion symmetry opens n energy gp tunle up to 25 mev with n externl perpendiulr eletri field E (refs 19 25) tht n e used for onfinement. In devies with low disorder nd t high mgneti fields, gpped sttes emerge from Coulom-driven effets tht rek its eightfold degenery (spin, vlley nd oritl), resulting in quntum Hll plteus t ll integer multiples of e 2 /h for eletron hrge e nd Plnk s onstnt h (ref. 26). Beuse of the Puli exlusion priniple, Coulom repulsions etween eletrons fvour spontneous spin nd/or vlley polriztion (or omintions of those), known s quntum Hll ferromgnetism, resulting in gp t zero rrier density tht fr exeeds the Zeemn splitting energy gµ B B (refs 27,28). The lrge exhnge-enhned energy gp of = 1.7 mev/t mesured for the ν = stte is idelly suited for quntum onfinement 29. Beuse vlley nd lyer indies re identil in the lowest Lndu level, one my dditionlly indue tunle vlley gp in the density of sttes y pplying perpendiulr E field tht reks lyer inversion symmetry 3. This oupling of vlley index to E-field is the key property tht enles diret experimentl ontrol of the reltive spin nd vlley gp sizes in mgneti field. Here we demonstrte tehnology tht enles mirosopi ndgp ontrol in grphene for the first time. We report fully suspended quntum dots in ilyer grphene with smooth, tunle tunnel rriers defined y lol eletrostti gting. Lol gp ontrol in grphene opens n venue to explore vriety of intriguing systems, inluding spin quits 6, topologil onfinement nd vlleytronis 31, quntum Hll edge modes in n environment well-isolted from edge disorder, gte-ontrolled superondutivity, nd mny more. Although not the sole use for this tehnology, quntum dots provide good experimentl pltform to rigorously demonstrte lol ndgp engineering due to the preise quntittive reltionship etween dot re nd quntized hrge tunnelling periodiity. Our tehnique, whih rtifiilly modifies the ndgp of ilyer grphene over nnometer sles, hieves len eletron onfinement isolted from oth edge nd sustrte disorder. Results Devie frition. We frite fully suspended quntum dots with 15 to 45 nm lithogrphi dimeters s illustrted shemtilly in Fig. 1 following the proedure desried in the Methods. Grphene is suspended etween two Cr/Au eletrodes nd sits elow suspended lol top gtes (Fig. 1 nd Supplementry Fig. S1). Energy V V t Gte 1 Gte 2 y SiO 2 E F V sd Si sustrte Bilyer grphene E C Cr/Au ontt Cr/Au top gte Cr/Au ontt Cr/Au ontt E V2 gte 2 dot Gte 3 Gte 4 Figure 1 Suspended gte-defined ilyer grphene quntum dot. () Shemti ross-setion of suspended gte-defined ilyer grphene quntum dot. The eletri field nd rrier density profiles re ontrolled with k nd top-gte voltges V nd V t, while pplition of is V sd ross the eletrodes enles trnsport mesurements. () Snning eletron mirogrph of quntum dot devie similr to D4 (see Methods for smple lelling key). Bilyer grphene (not visile) is suspended etween two eletrodes elow lol top gtes. Green nd lue lines indite ross-setionl uts in () nd (), respetively. Red lines mrk the estimted grphene oundries. Sle r, 1 µm. () Quntum dot formtion t B =, illustrted in ross-setionl ut of energy versus position. E C nd E V mrk the edges of the ondutne nd vlene nds. Tunnel rriers re formed y induing ndgp with n externl E field while fixing V t nd V t rtio tht ples the Fermi energy E F within the gp. Unompensted k-gte voltge in the nontop-gted regions enles hrge umultion in the dot nd leds. Before mesurement, the devies re urrent nneled in vuum to enhne qulity. The high qulity of our suspended flkes is evident from the full lifting of the eightfold degenery in the quntum Hll regime (Supplementry Fig. S2) 3 nd lrge resistnes ttined y opening the E-field-indued gp t B = nd E = 9 V/nm, hundred times greter thn the resistne reported for on-sustrte ilyers t similr eletri fields 22,3. Mesurements re onduted in dilution refrigertor t n eletron temperture of 11 mk, s determined from fits to Coulom lokde osilltions. Quntum onfinement t zero mgneti field. At B =, the eletri field effet in ilyer grphene enles the prodution of x nture ommunitions 3:934 DOI: 1.138/nomms Mmilln Pulishers Limited. All rights reserved.

3 nture ommunitions DOI: 1.138/nomms1945 ARTICLE V t12 (V) V DC (mv) V (V) V t12 (V) V ( 1 2, V 1 ) d V t34 (V) V t12 ( 1 2, V 1 ) V t12 (V) 1, dt is E C ~.4 mev. Fig. 2d indites tht the periodi Coulom lokde osilltions hve omprle pitive oupling to eh pir of top gtes. Furthermore, n even odd effet is visile in Coulom lokde plot s funtion of V t12 t fixed V t34 = 9.27 V nd V = 1.7 V (Supplementry Fig. S5), onsistent with the presene of twofold degenery. The ondutne modultions tht ouple exlusively to the k gte in Fig. 2 likely result from wek prllel ondutne hnnels under gtes 3 nd 4 (s lelled in Fig. 1) nd re unrelted to the entrl gte-defined quntum dot formtion, euse pitive oupling to V t12 is sent. The horizontl modultions in Fig. 2d ouple only to V t34 ut not V t12 nd re thus expeted to hve similr origins. Beuse these fetures re sprse nd periodi in nture, we expet tht they re not generted y rndom dot formtion in the onstritions or under the lol gtes. We note tht the highly resistive v = gp in the quntum Hll regime enles more roust onfinement thn the eletri fieldindued gp, nd we demonstrte tht ll kground ondutne flututions re ompletely eliminted in Fig. 3. Figure 2 Coulom lokde t B =. () Condutne mp (units of e 2 /h) of Coulom lokde osilltions s funtion of k-gte voltge (V ) nd the voltge on top gtes 1 nd 2 (V t12 ) t T = 11 mk in four-gte dot (devie D4). The voltge on top gtes 3 nd 4 is fixed t V t34 = 9.27 V. () 2D fst Fourier trnsform (units of e 2 /h V) of () revels the periodi struture. A pek orresponding to n osilltion sping of ~11 mv in V reflets strong periodiity, wheres the pperne of higher hrmonis revels the non-sinusoidl nture of the Coulom lokde peks when kbt EC. () Coulom dimonds re shown in plot of G/ V t12 s funtion of V t12 nd V DC, where G is ondutne in units of e 2 /h nd V DC is the DC is ross the eletrodes. The voltges V = 1.7 V nd V t34 = 9.27 V re held onstnt. Symmetri Coulom dimonds suggests equl tunnel oupling to soure nd drin leds. The dot-hrging energy is E C.4 mev. (d) Condutne mp (units of e 2 /h) of Coulom lokde osilltions s funtion of V t12 nd V t34 t fixed k-gte voltge V = 1.7 V. quntum-onfined strutures with smooth, tunle tunnel rriers defined y lol gting 1, thus voiding the disorder rising from the physil edge of the flke. Broken lyer inversion symmetry opens ndgp E = ( Vt V )/2ee, where V t nd V re top nd k-gte voltges with oupling ftors α nd β, respetively, nd ε is vuum permittivity. Coupling to the k gte β is extrted from Lndu fns in the quntum Hll regime nd the reltive gte oupling α/β n e determined from the Dir pek slope in V t versus V plot of ondutne t B =. Properties of individul quntum point ontts re desried in greter detil in Supplementry Figs S3 nd S4, where pinh-off nd ehviour onsistent with ondutne quntiztion re oserved. Quntum dot formtion t B = is illustrted shemtilly in Fig. 1. To rete tunnel rriers eneth the top gtes, we indue ndgp y pplying field E while fixing V t nd V t rtio tht mintins zero rrier density n, where n = αv t + βv. In the non-top-gted regions, there is finite hrge umultion due to n unompensted k-gte voltge. For gtes in quntum dot geometry, this restrits eletron trnsport to resonnt tunnelling events through the onstritions. Periodi Coulom lokde osilltions re oserved t B = tht ouple to oth top nd k gtes (Fig. 2). A pek in the 2D Fourier trnsform orresponding to n osilltion sping of ~11 mv in V reflets this strong periodiity (Fig. 2), nd the pperne of higher hrmonis revels the non-sinusoidl nture of the Coulom lokde peks when kbt EC, where k B is Boltzmnn s onstnt, T is temperture, nd E C is the dot-hrging energy. Coulom dimonds shown in Fig. 2 hve symmetri struture tht suggests equl tunnel oupling to oth the soure nd drin leds. The dot-hrging energy extrted from the DC is Coulom lokde in the quntum Hll regime. Coulom lokde osilltions n lso e generted t finite B field using the exhnge-enhned ν = gp. Here the ilyer is nturlly in gpped quntum Hll stte t zero density, where high resistnes due to quntum Hll ferromgnetism mke this system idel for onfinement. An isolted puddle of hrge is reted y fixing the Fermi energy in the top-gted regions t the middle of the ν = gp while llowing ouption of higher Lndu levels elsewhere, shown shemtilly in Fig. 3. It should e noted tht mesurements in the quntum Hll regime re onduted in the vlley-polrized ν = stte, fr from the trnsition to the spin-polrized phse 3. Figure 3 shows over 4 onseutive Coulom lokde osilltions generted t 5.2 T in 2-gte dot with 4-nm lithogrphi dimeter. The slopes of the resonnes indite symmetri oupling to the two top gtes, s expeted for entrlly loted dot. As top-gte voltges re swept to more positive vlues, pek mplitude is suppressed, reveling moderte tunnel rrier tunility. Also seen in Fig. 3 re interruptions in the ondutne resonnes (vertil nd horizontl fetures) tht ouple exlusively to single top gte; owing to their sprse nd periodi nture, we elieve tht they represent hrging events elow the gtes. Coulom lokde osilltions re roust over wide voltge rnge: Fig. 3 shows n dditionl 4 peks generted under new gte onditions. The Coulom dimonds exhiit symmetri tunnel oupling to soure nd drin leds nd dot-hrging energy of E C.4 mev. The strongly periodi nture of the osilltions is evident in the Fourier trnsform of the dt (Fig. 3d) (See Supplementry Fig. S6 for dditionl Coulom lokde dt). Geometri ontrol over Coulom lokde period. To demonstrte geometri ontrol over dot size, we exmine the orrespondene etween top-gte dimensions nd Coulom lokde pek sping. Mesurements were performed on 5 dots with lithogrphi dimeters rnging from 15 to 45 nm t mgneti fields of to 7 T. The ility to derese pek sping y inresing lithogrphi dot size is illustrted in Fig. 4. Figure 4, shows Coulom lokde pek ondutne s funtion of k-gte voltge V, oserved in devie D1 t B = 5.2 T, nd D2 t B = 7 T, respetively (see Methods for smple lelling key). Blk points represent dt nd the red lines re fits used to extrt pek positions. Figure 4 shows reltive pek position, V(p) V, plotted s funtion of pek numer p for the first 1 peks of Fig. 4,, where V(p) is the position of pek p in k-gte voltge, nd V is the position of the first pek. Eh dt set is ompnied y orresponding plot 8 q= of y( p) =[ ( 1/ 9 )Σ V( q + 1) V( q)] p, where p nd q re pek index numers, representing the verge pek sping (lk lines in Fig. 4). The dot re extrted from quntized hrge tunnelling is nture ommunitions 3:934 DOI: 1.138/nomms Mmilln Pulishers Limited. All rights reserved.

4 nture ommunitions DOI: 1.138/nomms1945 y 12.4 Energy 2 = E f =6 =4 =2 V t2 (V) Density of sttes Gte 1 Gte 2 = x V t1 (V) d V DC (mv) V t1 (V) V t2 ( 1 2, V 1 ) V t1 ( 1 2, V 1 ) Figure 3 Coulom lokde t B = 5.2 T. () Quntum dot formtion t B>, illustrted in ross-setionl ut of energy versus position. Tunnel rriers re formed using the exhnge-enhned ν = gp, where high resistnes due to quntum Hll ferromgnetism re idel for onfinement. An isolted puddle of hrge is reted y fixing the Fermi energy in the top-gted regions t the middle of the ν = gp while llowing ouption of higher Lndu levels elsewhere. Inset: shemti illustrtion of the top-gte geometry for devie D1. () Condutne mp (units of e 2 /h) of Coulom lokde osilltions s funtion of V t1 nd V t2 in two top-gte dot (devie D1), t fixed k-gte voltge V = 15.4 V nd T = 11 mk. The slopes of the resonnes indite symmetri oupling to the two top gtes, s expeted for entrlly loted dot. As top-gte voltges re swept to more positive vlues, pek mplitude is suppressed, reveling moderte tunnel rrier tunility. Inset: snning eletron mirogrph of devie similr to D1. Sle r, 2 nm. () Coulom dimonds re shown in plot of ondutne (units of e 2 /h) s funtion of V t1 nd DC is V DC, where V t2 = 11 V nd V = 14.4 V re fixed. Symmetri Coulom dimonds suggests equl tunnel oupling to soure nd drin leds. The dot-hrging energy is E C.4 mev. (d) 2D fst Fourier trnsform (units of e 2 /h V) of the oxed region in (), reveling the strongly periodi nture of the osilltions nd higher hrmonis. given y A = 1/(β V ), where V is the k-gte voltge needed to inrese dot ouption y one eletron (Supplementry Tle S1). A omprison of mesured dot dimeter, d = 2 A/p, with effetive lithogrphi dimeter, dlith = 2 Alith/p, indites tht d generlly exeeds d lith. This is ontrry to the redued dimensions oserved in GAs dots, where smller dimensions re oserved euse of depletion 32. To otin etter quntittive understnding of the disrepny etween lithogrphi nd mesured dot sizes, we use ommeril finite element nlysis simultion tool (COMSOL) to lulte the expeted dot re for eh top-gte geometry. The sptil rrier density profile is modelled for fixed top-gte potentil y solving the Poisson eqution ssuming metlli flke in free spe (Fig. 4d nd Supplementry Fig. S7). This ssumption is justified y lol ompressiility mesurements of the v = stte yielding dm/ dn = evm 2 t 2 T, whih trnsltes to sreening of 99% of the pplied V voltge y the ilyer 29. Remrkly, one my lulte dot size purely from gte geometry without relying on mesured gp prmeters. Assuming tht hrge umultion in the quntum dot ours when the rrier density exeeds fixed utoff d, the dot size is defined s the re ounded y the intersetion with the density distriution f(x,y) with the utoff. Here the utoff d is pled t the sddle points of the simulted density profile within the onstritions. This ondition enles mximl tunnelling without loss of onfinement, ssuming tht the tunnelling proility into the dot deys exponentilly with rrier width. Moving the utoff to densities fr greter thn d would pinh off the onstritions nd suppress tunnelling, while plement fr elow d would led to high rrier trnspreny nd eventul loss of onfinement. The simulted dot re from this method, plotted in Fig. 4 (inset), is simply the re ounded y the losed ontour of f(x,y) t fixed density d (Supplementry Fig. S7). Alterntively, one my lulte dot size y imposing utoff equlling the mesured gp width (Supplementry Tle S2 nd ounting for density offsets due to displement of the mesurement voltge from the hrge neutrlity point (see Supplementry Disussion). The utoffs extrted y these two models re equivlent to within dn 1 1 m 2, the rrier density flututions due to disorder in our suspended ilyers (Supplementry Fig. S7) 27. Disussion Our model estlishes quntittive link etween mesured dot size nd lithogrphi geometry nd, therefore, my serve s design tool for future ilyer nnodevies requiring sumiron sptil ontrol. These inlude doule dot systems tht form the sis of spin-sed quntum omputer 6. The prodution of suspended grphene quntum dots lso enles study of oupling etween quntized eletroni nd virtionl degrees of freedom 33,34, with potentil pplitions to nnoeletromehnil devies nd the detetion of quntized mehnil motion in memrne Furthermore, the omintion of high smple qulity with lol gting enles study of edge modes tht emerge t the interfe of nture ommunitions 3:934 DOI: 1.138/nomms Mmilln Pulishers Limited. All rights reserved.

5 nture ommunitions DOI: 1.138/nomms1945 ARTICLE G (e 2 /h) G (e 2 /h) d Soure V (V) V (V) Brrier Dot Brrier Drin Reltive pek position V(p) V (Volts) Mesured dot dimeter (nm) Dot dimeter from model (nm) Pek numer p 1 Figure 4 Geometri ontrol over Coulom lokde period. () Coulom lokde pek ondutne s funtion of k-gte voltge V oserved in devie D1 t B = 5.2 T. Blk points represent dt nd the red line indites funtionl fit used to extrt pek positions. The top-gte voltges re fixed t V t1 = V nd V t2 = 12 V.() Coulom lokde in devie D2 t B = 7 T. The top-gte voltges re fixed t V t1 = V t3 = 13 V nd V t2 = V t4 = 12 V. () Reltive pek position, V(p) V, plotted s funtion of pek numer p for the first 1 peks of () nd (). V(p) is the position of pek p in kgte voltge V, nd V is the position of the first pek (V = V nd V for plots () nd (), respetively). Eh lk line is plot 8 of y( p)=[ ( 1/ 9 )Σ q=v( q + 1) V( q)] p, where p nd q re pek index numers, representing the verge pek sping for the prtiulr dt set. Inset: simulted-dot size versus mesured size. Error rs represent the rnge of dimeters expeted for mesured Coulom lokde pek spings within 1 s.d. of the men. (d) COMSOL simultion of density profile (in.u.) for the lithogrphi gte pttern of devie D4 for top-gte voltge V t1 = V t2 = 12 V. Eletron trnsport is restrited to resonnt tunnelling events through the onstritions, indited y the rrows. roken symmetry quntum Hll sttes in n environment wellisolted from edge disorder (Supplementry Fig. S2). Methods Devie frition. Following mehnil exfolition of highly oriented pyrolyti grphite rystls, grphene is deposited on 3-nm thermlly grown SiO 2 lyer, whih overs doped silion sustrte funtioning s glol k gte. Bilyer flkes re identified sed on ontrst to the sustrte with n optil mirosope nd lter verified through quntum Hll dt. Cr/Au (3/1 nm) eletrodes re defined on seleted ilyers using eletron em (E-em) lithogrphy, therml evportion, nd lift-off in etone. A SiO 2 -sper lyer, ~15-nm thik is deposited with E-em evportion fter seond lithogrphy step. Lol top gtes re pled over the SiO 2 spers in two-step E-em lithogrphy proess. First, smll fetures tht define the tunnel rriers nd onstritions re ptterned using Cr/Au of thikness 3/75 nm, nd thiker support strutures onstruted of 3/3 nm of Cr/Au tht trverse the evported SiO 2 step re deposited immeditely fterwrds. The devies re immersed in 5:1 uffered oxide eth for 9 s nd dried in ritil point dryer, whih leves oth the grphene nd the top gtes suspended. Dot geometries nd mesurement onditions. We nlyse five fully suspended quntum dots with lithogrphi dimeters, dlith = 2 Alith/p, of 15 to 45 nm. Listed here re detils on individul smple geometries nd mesurement onditions. Devie D1 is irulr two-gte dot with d lith = 4 nm mesured t B = 5.2 T with the vlley polrized v = gp used for onfinement. Devie D2 is irulr dot with d lith = 15 nm, onsisting of three min gtes with plunger gte suspended ove (Supplementry Fig. S1). Mesurements were onduted t B = nd 7 T with the E-field indued nd v = gps used for onfinement, respetively. Devie D3 is irulr four-gte dot with d lith = 3 nm, mesured t B = 7 T. Devie D4 is irulr four-gte dot with d lith = 4 nm mesured t B = nd 3 T. Devie D5 is two-gte elliptil dot with ross-setionl lengths of 2 nd 25 nm mesured t B = 5 T. Additionl snning eletron mirosope imges of lolly gted quntum dot devies re provided in Supplementry Fig. S1. Top-gte lelling for devies D2 nd D4 is provided in Supplementry Fig. S1 nd Fig. 1, respetively. All mesurements re onduted using stndrd Lokin tehniques in Leiden Cryogenis Model Minikelvin 126-TOF dilution refrigertor. A voltge is set-up is used, where AC exittions rnging from 4 8 µv re pplied t frequeny of Hz with 1 ms time onstnt. An eletron temperture of T = 11 mk is extrted from Coulom lokde fits. Despite the omplex frition proess required to mke lol gted devies, the grphene exhiits high qulity s evidened y symmetry reking in the quntum Hll regime. Supplementry Fig. S2 ontins Lndu fns (mesured in devie D4 nd in two-gte split-gte devie) plotted s ondutne s funtion of k-gte voltge V nd mgneti field B, with zero voltge on the top gtes. In the split-gte devie, mp of quntized ondutne s funtion of the voltges on eh split top gte is provided in Supplementry Fig. S2, where the voltge V = 3 V nd field B = 4 T re held onstnt. This provides evidene of lol ontrol over roken symmetry quntum Hll sttes in suspended ilyer grphene. Mesured dot size extrted from oulom lokde fits. The dot re extrted from quntized hrge tunnelling is given y A =1/( V ), where V is the k-gte voltge needed to inrese dot ouption y 1 eletron nd β is the rrier density indued y 1 V on the k gte. The glol density to voltge onversion is otined y fitting Lndu level filling ftors v = nh/eb from ulk i+1 i quntum Hll dt. The pek sping V V,res V,res of given dt set is extrted y fitting eh Coulom lokde osilltion to the ondutne expression: 2 e V V,res G( V ) = A osh 2.5kBT where e is the eletron hrge, k B is Boltzmnn s onstnt, T is temperture, A is pek mplitude, V,res, is the k-gte voltge t resonne, nd = Cg/(C 1 + C r + C g ) is determined from the slopes of the Coulom dimonds (C g is pitne to the k gte nd C 1 nd C r re pitnes ross the left nd right tunnel rriers, respetively). This expression is vlid in the regime 2 E kbt e / C, where E is the single prtile level sping. This funtionl fit to the dt is shown expliitly in Fig. 4,. Coulom lokde dt from n dditionl devie is provided in Supplementry Fig. S4. Referenes 1. Meri, I. et l. Current sturtion in zero-ndgp, top-gted grphene fieldeffet trnsistors. Nt. Nnoteh. 3, (28). 2. Stmpfer, C. et l. Tunle Coulom lokde in nnostrutured grphene. Appl. Phys. Lett. 92, 1212 (28). (1) nture ommunitions 3:934 DOI: 1.138/nomms Mmilln Pulishers Limited. All rights reserved.

6 nture ommunitions DOI: 1.138/nomms Ponomrenko, L. A. et l. Choti Dir illird in grphene quntum dots. Siene 32, (28). 4. Novoselov, K. S. et l. Two-dimensionl gs of mssless Dir fermions in grphene. Nture 438, (25). 5. CstroNeto, A. H., Guine, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The eletroni properties of grphene. Rev. Mod. Phys. 81, (29). 6. Truzettel, B., Bulev, D. V., Loss, D. & Burkrd, G. Spin quits in grphene quntum dots. Nt. Phys. 3, (27). 7. Khetskii, A. V., Loss, D. & Glzmn, L. Eletron spin deoherene in quntum dots due to intertion with nulei. Phys. Rev. Lett. 88, (22). 8. Pett, J. R. et l. Coherent mnipultion of oupled eletron spins in semiondutor quntum dots. Siene 39, (25). 9. Koppens, F. H. L. et l. Driven oherent osilltions of single eletron spin in quntum dot. Nture 442, (26). 1. Reher, P., Nilsson, J., Burkrd, G. & Truzettel, B. Bound sttes nd mgneti field indued vlley splitting in gte-tunle grphene quntum dots. Phys. Rev. B 79, 8547 (29). 11. Wu, G. Y., Lue, N. Y. & Chng, L. Grphene quntum dots for vlley-sed quntum omputing: A fesiility study, Preprint t s/ (211). 12. Culer, D., Cywinski, L., Li, Q., Hu, X. & DsSrm, S. Quntum dot spin quits in silion: Multivlley physis. Phys. Rev. B 82, (21). 13. Todd, K., Chou, H., Amsh, S. & Goldher-Gordon, D. Quntum dot ehvior in grphene nnoonstritions. Nno Lett. 9, (28). 14. Mrtin, J. et l. Oservtion of eletron-hole puddles in grphene using snning single-eletron trnsistor. Nt. Phys. 4, (28). 15. Molitor, F. et l. Trnsport through grphene doule dots. Appl. Phys. Lett. 94, (29). 16. Liu, X. L., Hug, D. & Vndersypen, L. M. K. Gte-defined grphene doule quntum dot nd exited stte spetrosopy. Nno. Lett. 1, (21). 17. Wng, X. et l. Grphene nnorions with smooth edges ehve s quntum wires. Nt. Nnoteh. 6, (211). 18. Pereir, J. M., Vsilopoulos, P. & Peeters, F. M. Tunle quntum dots in ilyer grphene. Nno Lett. 7, (27). 19. MCnn, E. & Fl ko, V. I. Lndu-level degenery nd quntum Hll effet in grphite ilyer. Phys. Rev. Lett. 96, 8685 (26). 2. MCnn, E. Asymmetry gp in the eletroni nd struture of ilyer grphene. Phys. Rev. B 74, (26). 21. Cstro, E. V. et l. Bised ilyer grphene: Semiondutor with gp tunle y the eletri field effet. Phys. Rev. Lett. 99, (27). 22. Oosting, J. B., Heerhe, H. B., Liu, X., Morpurgo, A. F. & Vndersypen, L. M. K. Gte-indued insulting stte in ilyer grphene devies. Nt. Mter. 7, (27). 23. Zhng, Y. et l. Diret oservtion of widely tunle ndgp in ilyer grphene. Nture 459, (29). 24. Xi, F., Frmer, D. B., Lin, Y. & Avouris, P. Grphene field-effet trnsistors with high on/off urrent rtio nd lrge trnsport nd gp t room temperture. Nno. Lett. 1, (21). 25. Tyhtnpt, T. & Jrillo-Herrero, P. Eletroni trnsport in dul-gted ilyer grphene t lrge displement fields. Phys. Rev. Lett. 16, (21). 26. Nomur, K. & MDonld, A. H. Quntum Hll ferromgnetism in grphene. Phys. Rev. Lett. 96, (26). 27. Feldmn, B. E., Mrtin, J. & Yoy, A. Broken symmetry sttes nd divergent resistne in suspended ilyer grphene. Nt. Phys. 5, (29). 28. Zho, Y., Cdden-Zimnsky, P., Jing, Z. & Kim, P. Symmetry reking in the zero-energy Lndu level in ilyer grphene. Phys. Rev. Lett. 14, 6681 (21). 29. Mrtin, J., Feldmn, B. E., Weitz, R. T., Allen, M. T. & Yoy, A. Lol ompressiility mesurements of orrelted sttes in suspended ilyer grphene. Phys. Rev. Lett. 15, (21). 3. Weitz, R. T., Allen, M. T., Feldmn, B. E., Mrtin, J. & Yoy, A. Brokensymmetry sttes in douly gted suspended ilyer grphene. Siene 33, (21). 31. Mrtin, I., Morpurgo, Y. M. & Morpurgo, A. F. Topologil onfinement in ilyer grphene. Phys. Rev. Lett. 1, 3684 (28). 32. Chklovskii, D. B., Shklovskii, B. I. & Glzmn, L. I. Eletrosttis of edge hnnels. Phys. Rev. B 46, (1992). 33. Leturq, R. et l. Frnk Condon lokde in suspended ron nnotue quntum dots. Nt. Phys. 5, (29). 34. Steele, G. A. et l. Strong oupling etween single-eletron tunneling nd nnomehnil motion. Siene 325, (29). 35. Shytov, A. V., Levitov, L. S. & Beenkker, C. W. J. Eletromehnil noise in diffusive ondutor. Phys. Rev. Lett. 88, (22). 36. LHye, M. D., Buu, O., Cmrot, B. & Shw, K. C. Approhing the quntum limit of nnomehnil resontor. Siene 34, (24). 37. Bunh, J. S. et l. Eletromehnil resontors from grphene sheets. Siene 315, (27). 38. Chen, C. et l. Performne of monolyer grphene nnomehnil resontors with eletril redout. Nt. Nnoteh. 4, (29). Aknowledgements We thnk B. Feldmn, O. Dil, H. Bluhm, nd G. Ben-Shh for helpful disussions. This work is supported y the U.S. DOE Offie of Bsi Energy Sienes, Division of Mterils Sienes nd Engineering under wrd DE-SC1819, nd y the 29 U.S. ONR Multi University Reserh Inititive (MURI) on Grphene Advned Terhertz Engineering (Gte) t MIT, Hrvrd, nd Boston University. Nnofrition ws performed t the Hrvrd Center for Nnosle Systems (CNS), memer of the Ntionl Nnotehnology Infrstruture Network (NNIN) supported y NSF wrd ECS M.T.A. knowledges finnil support from the DOE SCGF fellowship, dministered y ORISE-ORAU under ontrt no. DE-AC5-6OR231. Author ontriutions M.T.A. ontriuted to smple design, frited the devies, rried out the experiments nd dt nlysis, performed the simultions, disussed the results, nd ommented on the mnusript. J. M. ontriuted to smple design, disussed the results, nd ommented on the mnusript. A.Y. ontriuted to smple design, rried out the experiments nd dt nlysis, performed the simultions, disussed the results, nd ommented on the mnusript. Additionl informtion Supplementry Informtion ompnies this pper t ntureommunitions Competing finnil interests: The uthors delre no ompeting finnil interests. Reprints nd permission informtion is ville online t reprintsndpermissions/ How to ite this rtile: Allen, M.T. et l. Gte-defined quntum onfinement in suspended ilyer grphene. Nt. Commun. 3:934 doi: 1.138/nomms1945 (212). nture ommunitions 3:934 DOI: 1.138/nomms Mmilln Pulishers Limited. All rights reserved.