Electron Nuclear Interaction in \(^{13}C \) Nanotube Double Quantum Dots

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1 Eletron Nuler Intertion in \(^{3}C \) Nnotue Doule Quntum Dots The Hrvrd ommunity hs mde this rtile openly ville. Plese shre how this ess enefits you. Your story mtters Cittion Churhill, Hugh Olen Hill, Andrew J. Bestwik, Jennifer W. Hrlow, Ferdinnd Kuemmeth, Dvid Mros, Crolyn H. Stwertk, Susn K. Wtson, nd Chrles Msmed Mrus. 9. Eletron-nuler intertion in 3C nnotue doule quntum dots. Nture Physis 5(5): Pulished Version doi:.38/nphys47 Citle link Terms of Use This rtile ws downloded from Hrvrd University s DASH repository, nd is mde ville under the terms nd onditions pplile to Open Aess Poliy Artiles, s set forth t nrs.hrvrd.edu/urn-3:hul.instrepos:dsh.urrent.terms-ofuse#oap

2 Eletron-nuler intertion in 3 C nnotue doule quntum dots H. O. H. Churhill, A. J. Bestwik, J. W. Hrlow, F. Kuemmeth, D. Mros, C. H. Stwertk, S. K. Wtson, nd C. M. Mrus Tehniques to prepre, mnipulte, nd mesure feweletron spin sttes in quntum dots hs dvned onsiderly in reent yers, with the leding progress in III-V semiondutor systems,3,,. All stle isotopes of III-V semiondutors, suh s GAs, hve nonzero nuler spin, nd the hyperfine oupling of eletron spins to host nulei is dominnt soure of spin deoherene in these mterils,,,3. To eliminte this soure of deoherene, group IV semiondutors vrious forms of ron, silion, nd silion-germnium whih hve predominntly zero nuler spin, re eing vigorously pursued s the sis of oherent spin eletroni devies. Dou- Present ddresses: Deprtmento de Teorı de l Mteri Condensd, Instituto de Cieni de Mteriles de Mdrid, CSIC, Cntolno 849, Mdrid, Spin (D.M.); Deprtment of Physis, Middleury College, Middleury, Vermont 5753, USA (S.K.W.). d 3 S R VR (V) 6 4 M L I dd (na) μm VL (V). I dd (na).5.7 VR (V) For oherent eletron spins, hyperfine oupling to nulei in the host mteril n either e dominnt soure of unwnted spin deoherene,,3 or, if ontrolled effetively, resoure llowing storge nd retrievl of quntum informtion4,5,6,7. To investigte the effet of ontrollle nuler environment on the evolution of onfined eletron spins, we hve frited nd mesured gte-defined doule quntum dots with integrted hrge sensors mde from single-wlled ron nnotues with vrile onentrtion of 3 C (nuler spin I = /) mong the mjority zero-nuler-spin C toms. Spin-sensitive trnsport in doule-dot devies grown using methne with the nturl undne ( %) of 3 C is ompred with similr devies grown using n enhned ( 99%) onentrtion of 3 C. We oserve strong isotope effets in spinlokded trnsport nd from the dependene on externl mgneti field, estimte the hyperfine oupling in 3 C nnotues to e on the order of µev, two orders of mgnitude lrger thn ntiipted theoretilly8,9. 3 C-enhned nnotues re n interesting new system for spinsed quntum informtion proessing nd memory, with nulei tht re strongly oupled to gteontrolled eletrons, differ from nulei in the sustrte, re nturlly onfined to one dimension, lk qudrupolr oupling, nd hve redily ontrollle onentrtion from less thn one to 5 per eletron. VR (V) rxiv:8.336v [ond-mt.mes-hll] De 8 Deprtment of Physis, Hrvrd University, Cmridge, Msshusetts 38, USA VM =.5 V.8 VM =.7 V VL (V) VL (V).65 Figure : Nnotue doule dot with integrted hrge sensor., SEM mirogrph (with flse olor) of devie similr to the mesured C nd 3 C devies. The ron nnotue (not visile) runs horizontlly under the four Pd ontts (red). Top-gtes (lue) rete voltge-tunle tunnel rriers llowing the formtion of single or doule quntum dot etween ontts nd. Plunger gtes L nd R (green) ontrol the oupny of the doule dot. A seprte single dot ontted y Pd ontts 3 nd 4 is ontrolled with gte plunger gte S (gry) nd is pitively oupled to the doule dot vi oupling wire (ornge)., Current through the doule dot, Idd, (olor sle) with the top-gtes onfigured to form lrge single dot., When rriers eneth the middle gte, M, re depleted, Idd shows typil doule-dot trnsport ehvior, demrting the honeyom hrge stility pttern. d, Within ertin gte voltge rnges, honeyom ells with lrger ddition energy nd fourfold periodiity (outlined with dshed lines) indite the filling of spin nd oritl sttes in shells. Soure-drin is is. mv for,, nd d. le quntum dots hve reently een demonstrted in ron nnotues4,5,6, inluding reent investigtion of spin effets7,8. The devies reported re sed on single-wlled ron nnotues grown y hemil vpor deposition using methne feedstok ontining either 99% 3 C (denoted 3 C devies) or 99% C (denoted C devies; see Methods)9. The devie design (Fig. ) uses two pirs of Pd ontts on the sme nnotue; depletion y topgtes (lue, green, nd gry in Fig. ) forms doule dot etween one pir of ontts nd single dot etween

3 the other. Devies re highly tunle, s demonstrted in Fig., whih shows tht tuning the voltge on gte M (Fig. ) djusts the tunnel rte etween dots, llowing ross-over from lrge single-dot ehvior (Fig. ) to doule-dot ehvior (Fig. ). Left nd right tunnel rriers n e similrly tuned using the other gtes shown in lue in Fig.. A notle feture of nnotue quntum dots tht is not shred y GAs dots is tht the energy required to dd eh susequent eletron, the ddition energy, often shows shell-filling struture even in the mny-eletron regime 8. An exmple of shell-filling pttern, with lrger ddition energy every fourth eletron in the right dot, is seen in Fig. d. We find, however, tht evident shell filling is not neessry to oserve spin lokde t finite is. Figures nd show urrent through the doule dot, I dd, s funtion of gte voltges V R nd V L for wekly oupled, mny-eletron 3 C doule dot t + nd mv soure-drin is, respetively, in rnge of dot oupny tht does not show shell struture in the ddition spetrum of either dot. With mgneti field B = mt pplied long the tue xis, urrent flow is oserved throughout the finite-is tringles t positive is, ut is suppressed t negtive is for detuning elow.8 mev, whih presumly indites where n exited stte of the right dot enters the trnsport window. Current retifition of this type is hllmrk of spin lokde (Fig. e): t positive is, urrent flows freely s eletrons of pproprite spin re drwn from the right led to form the singlet ground stte; t negtive is, urrent is loked whenever triplet stte is formed etween seprted eletrons, s the exess eletron on the left n neither reenter the left led nor oupy the lowest oritl stte on the right without flipping its spin. Spin lokde ws identified in ll four devies mesured, two eh of C nd 3 C. Spin lokde ws osionlly found to follow regulr even-odd filling pttern, s seen in few-eletron GAs dots, though no pttern ws seen djent to the re in Fig.. Eletrostti sensing of the doule-dot hrge stte is provided y gte-defined quntum dot formed on seprtely ontted portion of the sme nnotue. The sensing dot is pitively oupled to the doule dot y µm oupling wire (ornge gte in Fig. ) ut eletrilly isolted y depletion gte etween the Pd ontts. Chrge sensor ondutne g s s funtion of V R nd V L, quired simultneously with trnsport dt in Fig.,, is shown in Fig.,d. The lotion of the oupling wire mkes g s espeilly sensitive to oupny of the right dot. Inside the positive-is tringles (Fig. ), g s is intermedite in vlue etween their ordering regions, inditing tht the exess eletron is rpidly shuttling etween the dots s urrent flows through the doule dot. In ontrst, inside the negtiveis tringles (Fig. d), g s shows no exess eletron on the right dot s result of spin lokde. These sensor vlues re onsistent with models of finite-is hrge V R (mv) V R (mv) e -4 V L (mv) is _ is + mv is B = mt T S T S -3 g ( e /h) s (mv) V R (mv) V R d f. - mv is B = mt -4 V L (mv) mv is - mv is Figure : Spin lokde in 3 C nnotue doule dot., Current I dd (olor sle) t +. mv soure-drin is, the nonspin-lokded is diretion. Trnsport is dominted y resonnt tunneling through the ground stte t the se of the finite is tringles nd through n exited stte t detuning of.7 mev., I dd (olor sle) t. mv soure-drin is, the spin-lokded is diretion. I dd is suppressed exept ner the tips of the trnsport tringles, where n exited stte of the right dot eomes essile. Suppressed trnsport for one is diretion is the signture of spin lokde., Chrge sensing signl, g s, (ondutne of the sensing dot etween ontts 3 nd 4 in Fig. ), quired simultneously with detets the the time-verged ouption of the right dot. d, Chrge sensing signl g s for. mv is (lokde diretion). The trnsfer of hrge from the left dot to the right is delyed until the exited stte is rehed t high detuning. In d dshed lines indite llowed regions for urrent flow in the sene of lokde. e, Shemti of spin-lokded trnsport. Any spin my oupy the left dot, ut only spin singlet is llowed in the right dot, suppressing negtive is urrent one n eletron enters the left dot nd forms triplet stte. f, Current I dd t zero detuning s funtion of mgneti field for positive is (non-lokde, red tre) nd negtive is (lokde, purple tre). sensing in the spin-lokde regime. The mgneti field dependene of spin lokde provides importnt informtion out eletron spin relxtion mehnisms,3. A first look t field dependene (Fig. f) for 3 C devie shows tht for negtive is (purple), spin-lokde lekge urrent is strongly peked t B =, while for positive is, the unlokded urrent does not depend on field. As disussed elow, this field dependene n e understood in terms of hyperfinemedited spin relxtion. The striking differene in field dependene of spinlokde lekge urrent etween C nd 3 C devies is illustrted in Fig. 3,. These dt show tht for neg- -3 g ( e /h) s

4 3 Detuning (mev) d V R (V) B = B = 5 mt V L (V) V L (V) 3.96 e 5 5 C -5 5 Detuning (mev) V R (V) f C -5 5 Figure 3: Contrsting mgneti field dependene of lekge urrent for C nd 3 C devies. Lekge urrent through spin lokde (olor sle) s funtion of detuning nd mgneti field, B, for () C nd () 3 C devies. The vertil xes in nd re interdot detuning s indited y the ornge lines in nd d, respetively. In B ws swept nd detuning stepped, while in detuning ws swept nd B stepped. Bis is.5 mv in nd 4 mv in d. e nd f show uts long B t the detunings indited y the red lines in nd, respetively. The fit in e is Lorentzin with width of 3 mt, nd the fit in f is to the theory of Jourvlev nd Nzrov, providing mesure of B nu = 6. mt. tive (spin-lokded) is, lekge urrent is minimum t B = for the C devie nd mximum t B = for the 3 C devie. In fourteen instnes of spin lokde mesured in four devies (two 3 C nd two C), we find tht lekge urrent minim n our t B = in oth C nd 3 C devies, prtiulrly for stronger interdot tunneling. For weker interdot tunneling, however, only the 3 C devies show mxim of spin-lokde lekge t B =. In ll ses, the positive is (non-spinlokde) urrent shows no ppreile field dependene. Figure 3e shows spin-lokde lekge urrent s funtion of B t fixed detuning (the detuning vlue is shown s lk line in Fig. 3), long with est-fit lorentzin, for the C devie. The lorentzin form ws not motivted y theory, ut ppers to fit rther well. The width of the dip round B = inreses with interdot tunneling (onfigurtion Fig. 3e hs t 5 µev, sed on hrge-stte trnsition width ). We note tht omprle zero-field dip in spin-lokde lekge urrent ws reently reported in doule dot formed in n InAs nnowire 4, mteril system with strong spinorit oupling. In the present system, the zero-field dip my lso e ttriutle to spin-orit oupling 5, resulting in phonon-medited relxtion tht vnishes t B =. Hyperfine oupling ppers to the onfined eletrons s n effetive lol Zeemn field (the Overhuser field) tht flututes in time independently in the two dots, driven y therml exittion of nuler spins. The differene in lol Overhuser fields in the two dots will indue rpid mixing of ll two-eletron spin sttes whenever the pplied field is less thn the typil differene in flututing Overhuser fields. (At higher fields, only the m = triplet n rpidly mix with the singlet). How hyperfinemedited spin mixing trnsltes to field dependene of spin-lokde lekge urrent ws investigted experimentlly in GAs devies 3, with theory developed y Jourvlev nd Nzrov. Field dependene of spin-lokde lekge urrent for the 3 C devie is shown Fig. 3f, long with theoretil fit (Eq. () of Ref., with onstnt kground urrent dded), from whih we extrt root men squre mplitude of flututions of the lol Overhuser fields, B nu = 6. mt. Assuming gussin distriuted Overhuser fields nd uniform oupling, B nu is relted to the hyperfine oupling onstnt A y gµ B B nu = A/ N, where g is the eletron g-ftor nd N is the numer of 3 C nulei in eh dot. Tking N 3 4 nd g = (see Supplement), yields A 4 ev, vlue tht is two orders of mgnitude lrger thn predited for ron nnotues 8 or mesured in fullerenes. 9 Signtures of dynmi nuler polriztion provide further evidene of strong hyperfine intertion in 3 C doule dots. Hysteresis in the spin-lokde lekge urrent ner zero detuning is oserved when the mgneti field is swept over tesl-sle rnge, s shown in Fig. 4. The dt in Fig. 4, re from the sme 3 C devie s in Fig. 3, ut with the rriers tuned suh tht otunneling proesses provide signifint ontriution to the lekge urrent. We interpret the hysteresis in Fig. 4 s resulting from net nuler polriztion indued y the eletron spin flips required to irumvent spin lokde 6. This nuler polriztion genertes n Overhuser field felt y the eletron spins tht opposes B one B psses through zero. The vlue of the oerive field, B.6 T, the externl field t whih the two urves rejoin, ples lower ound for the hyperfine oeffiient, A gµ B B.7 4 ev (equlity orresponding to full polriztion), independent of the vlue inferred from the width of the lekge urrent pek round zero field (Fig. 3). If we insted use the vlue of A inferred from the urrent pek width (Fig. 3), the size of B implies 5% polriztion for the dt in Fig. 4. Hysteresis is not oserved for non-spin-lokded trnsport in the 3 C devies nd is not oserved in the C devies, suggesting tht this effet nnot e ttriuted to soures suh s the Fe tlyst prtiles or intertion with nulei in the

5 B (T) Time (s).4. ().4. 4 Time (s) B =.5 T 3 4 Time (min) Figure 4: Hysteresis nd flututions in lekge urrent., The spin-lokde lekge urrent for 3 C devie mesured for deresing (inresing) mgneti field (sweep rte.4 mt/s), shown in lue (red), fter witing t + T ( T) for minutes. Hysteresis is seen on field sle >.5 T for oth sweep diretions., Dey of lekge urrent over time mesured y stopping downwrd sweep t.5 T. The fit is to n exponentil dey with time onstnt of 9 min., Dependene of lekge urrent on B ner zero detuning in seond 3 C devie. The lekge urrent flututes over time t some vlues of B, while remining stedy t others (insets). sustrte or gte oxide. Figure 4 shows tht the indued nuler polriztion persists for minutes, two orders of mgnitude longer thn similr proesses in GAs doule dots 7. The long relxtion time indites tht nuler spin diffusion is extremely slow, due oth to the one-dimensionl geometry of the nnotue nd mteril mismth etween the nnotue nd its surroundings. Field nd oupny dependene of relxtion were not mesured. Lrge flututions in I dd re seen t some vlues of mgneti field, ut not t others (Fig. 4), similr to ehvior oserved in GAs devies 3. This presumly reflets n instility in nuler polriztion tht n rise when polriztion or depolriztion rtes themselves re polriztion dependent 6,8. An importnt onlusion of this work is tht the hyperfine oupling onstnt, A 4 ev, in the 3 C devies (for oth eletron nd holes, see Methods) is muh lrger thn ntiipted 8,9. It is possile tht the sustrte or gte oxide my enhne the degree of s-oritl ontent of ondution eletrons, thus strengthening the ontt hyperfine oupling. We lso note tht reent theoretil study of eletron-nuler spin intertions in 3 C nnotues found tht the one-dimensionl hrter of hrge rriers gretly enhnes the effetive eletron-nuler intertion 9. Finlly, we note tht lrge vlue of A motivtes the frition of isotopilly enrihed C nnotues to redue deoherene nd the use of 3 C tues s potentil sis of eletrilly ddressle quntum memory. Methods Cron nnotues re grown y hemil vpor deposition using methne feedstok nd 5 nm thik Fe tlyst islnds on degenertely doped Si sustrtes with µm therml oxide. C devies re grown with methne ontining nturl undne (.%) 3 C; 3 C devies re grown with 99% 3 CH 4 (Sigm-Aldrih). Nnotues re loted fter growth using snning eletron mirosope, nd tlyst islnds, soure nd drin eletrodes (5 nm Pd), nd top-gtes (3 nm Al) re ptterned using eletron-em lithogrphy. After ontting with Pd, smples re oted with nonovlent funtionliztion lyer omining NO nd trimethylluminum, followed y tomi lyer deposition (ALD) of 3 nm Al O 3 top-gte insultor (Cmridge Nnoteh Svnnh ALD system) 3. Mesurements were performed in dilution refrigertor with se temperture of 3 mk nd eletron temperture of mk, determined from the hrge sensing trnsition width. Nnotues presented in Figs. nd hve smll ndgps (E g 5 mev); the 3 C nnotue in Fig. 3,d,f nd the other C nnotue (dt not shown) re lrge-gp semionduting nnotues. Chrges oupying the dots nd leds re eletrons, exept the dt in Fig. 3,d,f nd Fig. 4,, where the hrge rriers re holes. No signifint differenes re seen etween devies with eletron nd hole rriers. A. V. Khetskii, D. Loss, nd L. Glzmn. Eletron spin deoherene in quntum dots due to intertion with nulei. Phys. Rev. Lett. 88, 868 ().

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