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1 doi:1.138/nture11297 A Newtonin pproh to extrordinrily strong negtive refrtion Hosng Yoon 1, Kitty Y. M. Yeung 1, Vldimir Umnsky 2 & Donhee Hm 1 Metmterils with negtive refrtive indies n mnipulte eletromgneti wves in unusul wys, nd n e used to hieve, for exmple, su-diffrtion-limit fousing 1, the ending of light in the wrong diretion 2, nd reversed Doppler nd erenkov effets 2. These ounterintuitive nd tehnologilly useful ehviours hve spurred onsiderle efforts to synthesize rod rry of negtiveindex metmterils with engineered eletri, mgneti or optil properties 1 1. Here we demonstrte nother route to negtive refrtion y exploiting the inerti of eletrons in semiondutor two-dimensionl eletron gses, olletively elerted y eletromgneti wves ording to Newton s seond lw of motion, where this elertion effet mnifests s kineti indutne 11,12. Using kineti indutne to ttin negtive refrtion ws theoretilly proposed for three-dimensionl metlli nnoprtiles 13 nd seen experimentlly with surfe plsmons on the surfe of threedimensionl metl 14. The two-dimensionl eletron gs tht we use t ryogeni tempertures hs lrger kineti indutne thn three-dimensionl metls, leding to extrordinrily strong negtive refrtion t gighertz frequenies, with n index s lrge s 27. This pronouned negtive refrtive index nd the orresponding redution in the effetive wvelength opens pth to minituriztion in the siene nd tehnology of negtive refrtion. The ide of reting negtive refrtion y exploiting the olletive eletron elertion (inerti) effet, or kineti indutne, ws theoretilly proposed for speifi rrngements of three-dimensionl (3D) metlli nnoprtiles 13. Experimentlly, inerti-sed negtive refrtion ws implied in work where prtiulr guiding of surfe plsmon polritons on the surfe of 3D metl led to negtive refrtion 14 ; this nnot e explined without eletron elertion, euse defining omponent of plsmons is the time-vrying kineti energy of their onstituent eletrons, whih implies their elertion. emiondutor two-dimensionl (2D) eletron gses (2DEs) possess muh lrger kineti indutne thn 3D ulk metls. Here we rete negtive-index metmterils y fully exploiting this lrge kineti indutne, whose impt is mnifested in the extrordinrily lrge negtive index, whih we mesure to e s lrge s n 527. This is two orders of mgnitude lrger thn the index of n < 25to21 in surfe-plsmon-sed negtive refrtion 14, nd indites tht inerti is muh more importnt ftor in our 2DE se. It is lso muh lrger thn the theoretil expettion sed on the kineti indutne of 3D metlli nnoprtiles 13, whih is orders of mgnitude smller thn our 2D kineti indutne (upplementry Informtion, setion 1). We hoose As/AlAs 2DE s demonstrtion pltform. Here eletrons n elerte for,.2 ns t temperture of 4 K without sttering, with the result tht their lrge kineti indutne effet is not msked y the sttering t nd ove gighertz frequenies. peifilly, our metmteril is periodi rry of mes-ethed 2DE strips (Fig. 1, ), eh of whih is onneted to ground lines (lelled in Fig. 1) t oth ends vi ohmi ontts. Eh strip s width nd length re respetively denoted W nd l, nd the entre-to-entre distne etween neighouring strips, or periodiity, is denoted. This metmteril is exited y eletromgneti wves guided y the left signl line (lelled in Fig. 1), whih, flnked y the ground lines, forms n on-hip oplnr wveguide (PW) with 5-V hrteristi impedne. This left signl line is extended to over few 2DE strips on the left-hnd side of the metmteril, with dieletri etween the signl line nd the 2DE strips. The metmteril s response is piked up y the right signl line (lso lelled ) of nother PW on the right-hnd side of the metmteril. The eletri fields of the exittion eletromgneti wve, osillting etween the signl nd ground lines of the left PW, olletively elerte eletrons in the leftmost few 2DE strips, produing urrents long the strips. The resulting ltertions of hrge distriution in these strips will pitively ouple to neighouring strips to the right, elerting eletrons there. This proess repets to deliver n effetive wve from left to right, perpendiulr to the diretion of the strips. From the iruit point of view, eh 2DE strip long whih eletrons olletively elerte, with the resulting urrent lgging the elerting voltge y 9u ording to Newton s seond lw of motion ts s non-mgneti indutne of kineti origin 11,12. This 2D kineti indutne,, results from Newton s lw: 5 m*/(n 2D e 2 ) 3 (l e /W), where m*, e nd n 2D re respetively the eletrons effetive mss, hrge nd density per unit re, nd l e, whih will e identified shortly, is the effetive length of eh strip, within whih eletrons elerte in response to the exittion. Our metmteril is then n rry of pitively oupled kineti indutors (Fig. 1 nd upplementry Informtion, setion 2), nd my e l 2 μm W V m 1 V m AlAs As Effetive wve r/au V m+1 2DE Figure 1 Devie desription., Optil imge of 2DE strip-rry metmteril prototype. round signl ground () on-hip PWs diret eletromgneti wves to nd from the metmteril. The inset shows mgnified portion of the strip rry. In this speifi prototype, W 5 1 mm, l mm nd mm., hemti of the metmteril (not drwn to sle), with the front fe orresponding to ut through the dshed symmetry line in., iruit desription of the hlf of the metmteril elow or ove the symmetry line long the effetive wve propgtion diretion (upplementry Informtion, setion 2). 1 hool of Engineering nd Applied ienes, Hrvrd University, mridge, Msshusetts 2138, UA. 2 Deprtment of ondensed Mtter Physis, Weizmnn Institute of iene, Rehovot 761, Isrel. 2 A U U T V O L N AT U R E Mmilln Pulishers Limited. All rights reserved

2 REEARH LETTER likened to left-hnded trnsmission line 15 17, whih is n rry of pitively oupled mgneti indutors nd is known to e negtively refrting. However, our negtive refrtion origintes in different physil phenomenon: our devie uses extremely lrge 2DE kineti indutne, wheres the left-hnded trnsmission line relies on muh smller mgneti indutne. To exmine the negtive refrtion ehviour of our devie, we represent the effetive wve, in terms of the voltge t the tip of the mth kineti indutor (Fig. 1), s V m (t) / e i(vt2mk),wherev is the ngulr frequeny nd k is the effetive wvenumer. The stndrd iruit nlysis of Fig. 1 yields dispersion reltion v(k) 5 v /jsin(k/2)j, where v ; [2!( )] 21 is the ut-off frequeny t the oundry of the first Brillouin zone (k 56p/)nd is the pitne etween djent strips over the effetive length (upplementry Informtion, setion 2). For v. v, the dispersion reltion (Fig. 2) predits negtive refrtion, euse the tngentil slope dv/dk (the group veloity) nd the slope v/k (the phse veloity) hve opposite signs 1. The ut-off ehviour results from the metmteril s high-pss nture, nd n lso e seen from the urrent distriutions ross the metmteril elow nd ove the ut-off frequeny (Fig. 2), whih we simulted using n eletromgneti field solver (upplementry Informtion, setion 6). Beyond the ut-off frequeny (Fig. 2, right), the urrent is onentrted t the ottom nd top regions of the strips, from whih l e n e estimted. We note tht, wheres single sheet of 2DE exhiits ordinry dispersion 18, the elertion of eletrons long n rry of strips of 2DE, perpendiulr to the diretion of effetive wve propgtion, uses negtive refrtion. The dispersion reltion of our metmteril hs the sme form s tht of the left-hnded trnsmission line 15 17, ut with the mgneti indutne repled with the muh lrger 2DE kineti indutne; the 2DE kineti indutne is 1.25 nh mm 21 for 1-mm wide 2DE strip, whih is,2,8 times lrger thn the sme strip s mgneti indutne,.44 ph mm 21 (upplementry Informtion, setion 1). The effetive refrtive index derived from the dispersion is n 522/(v) 3 sin 21 (v /v), where is the speed of light in vuum, nd hs the mximum ttinle mgnitude of 2/(v ) 5 4/ 3!( ), whih is exeedingly lrge owing to the lrge 2DE kineti indutne, orresponding to the sustntil slowing of the effetive wve. Mirowve sttering experiments with on-hip proing onfirm this extrordinrily strong negtive refrtion. The refletion of n eletromgneti wve inident on the left on-hip PW nd its trnsmission to the right on-hip PW fter propgtion through the metmteril re mesured over rnge of,1 5 Hz using vetor k/(π/) urrent density (.u.) Figure 2 Theory nd simultion., Plot of v(k) 5 [2!( ) sin(k/ 2) ] 21, with 5 39 nh nd ff estimted for the struture mesured for Fig. 3 (W 5 1 mm, mm, l mm). The group nd phse veloities, dv/dk nd v/k, hve opposite signs, showing negtive refrtion; this ours for oth k. nd k,, ut we show only the ltter, whih is relevnt to our mesurements., imulted urrent distriutions elow (left; 5 Hz) nd ove (right; 3 Hz) the ut-off frequeny. Red nd lue olours indite high nd low urrent densities, respetively. Aove the ut-off frequeny, regions of high, onstnt urrent density re oserved, from whih the effetive strip length l e is estimted..u., ritrry units. l e l e network nlyser. Propgtion delys in the two on-hip PWs nd prsiti ouplings etween them ypssing the metmteril were seprtely mesured nd de-emedded; from the resulting trnsmission nd refletion oeffiients, s 21 nd s 11, t eh mesurement frequeny, we extrt, using well-estlished method 19 23, the effetive wve s phsor hnge e 2ikd due purely to propgtion of distne d ross the metmteril (upplementry Informtion, setion 3). Figure 3 shows the frequeny wvenumer (f k) dispersion so otined t tempertures of 4.2, 1 nd 2 K for 13-strip metmteril with W 5 1 mm, l mm, l e 5 31 mm nd mm. Beuse the mesured prmeters s 21 nd s 11 set the left-to-right energy propgtion diretion (tht is, the diretion of the group veloity) s the positive referene diretion, if our metmteril is negtively refrting, the sign of the extrted wvenumer will e negtive with no miguity, whih is indeed seen in Fig. 3. Negtive refrtion is lso onsistently onfirmed in Fig. 3 y the ft tht dv/dk nd v/k hve opposite signs ove the 12-Hz ut-off frequeny. This mesured dispersion, inluding the ut-off frequeny, differs in its detils from the lultion tht uses lumped iruit elements, ignores losses due to eletron sttering in the 2DE strips nd ohmi ontts, nd onsiders only nerest pitive ouplings (Fig. 2). But it hs the sme underlying fetures, demonstrting negtive refrtion. The drk re in Fig. 3, where the distintively spurious ehviour of the dispersion ppers, is inditive of the ut-off region, whih is irrelevnt to the opertion of the devie (upplementry Informtion, setion 3). From this f k dispersion, we otin the effetive refrtive index using n 5 k/v, whose rel prt is s lrge s 25 (Fig. 3). This lrge negtive index, whih is diffiult, if not impossile, to hieve with mgneti indutne 3 5,15 17,24,25, llows drsti devie minituriztion nd n filitte ultr-suwvelength loliztion. The sme mesurements performed on the 2DE strip rry, ut with energy propgtion long the strips, yield positive refrtion, further highlighting our negtive refrtion strtegy (upplementry Informtion, setion 5). We find tht jre(n)j dereses with frequeny (Fig. 3), euse s the frequeny inreses djent strips re oupled more pitively, whih inresingly ypsses the eletron elertion effet within eh seprted strip. Figure 3 shows the figure of merit, jre(n)/im(n)j, whih here reflets losses due to eletron sttering in the 2DE strips nd ohmi ontts. It tkes vlue of,2 over resonly lrge prt of the negtive refrtion region, similrly to negtive refrtion devies using metls t optil frequenies 24,25. Figure 3 shows tht the negtive refrtion ehviour is essentilly the sme regrdless of temperture (4.2, 1 nd 2 K), inditing tht the degree of eletron sttering in the 2DE strips nd ohmi ontts remins lrgely the sme within this temperture rnge, not msking the inerti effet. In Fig. 3, the figure of merit is lrgest t 1 K insted of t, ut these vritions with respet to temperture rise mostly from inonsistent proe lndings during multiple lirtion steps, whih re done for mesurements t eh temperture. Flututions t high frequenies, for exmple, in Fig. 3, re lso due to imperfet lirtion. At 297 K, eletron sttering in eh 2DE strip eomes so severe tht the elertion effet is ompletely msked. Equivlently, the strip s ohmi resistne eomes fr lrger (,1 kv) thn the impedne of its kineti indutne. The strip rry then eomes essentilly n open iruit, using the signl to e mostly refleted. This refletion n e seen from the vlue of the refletion oeffiient, js 11 j < 1, mesured t 297 K, whih differs from js 11 j t ryogeni tempertures, where the strip rry exhiits negtive refrtion (Fig. 3d). The trnsmission oeffiient, js 21 j, eomes smller t 297 K lso euse of the open-iruit ehviour, ut is not unppreile (Fig. 3d). To understnd this, we frited extly the sme struture s the previous devie, ut without the strip rry, thus reting n tul open iruit etween the two on-hip PWs. The ehviour of js 21 j for this open devie t losely resemles tht of js 21 j for the strip rry t 297 K (Fig. 3d). This demonstrtes tht the ehviour in the strip rry t 297 K is due lrgely to the prsiti oupling etween the two PWs ypssing the 66 NATURE VOL AUUT Mmilln Pulishers Limited. All rights reserved

3 REEARH K 2 K Re(k) (m 1 ) 15 ( 1 4 ) Re(n) K 2 K /Im( n) K 2 K Figure 3 Temperture-dependent mesurements., Dispersion of the 13- strip metmteril t 4.2, 1, nd 2 K. The drk region is inditive of the utoff ehviour., Re(n) versus frequeny., Figure of merit Re(n)/Im(n) versus frequeny. d, Prmeters s 11 nd s 21 of the metmteril, seprtely d s 11, s 21 (db) 1 2 s 11 s K 4 2 K 297 K Open, indited y the dshed ovls, t 4.2, 1, 2 nd 297 K. Also shown re s 11 nd s 21 of the open-iruit devie t. Unlike the dt in, nd, these re rw s prmeters without de-emedding, showing the prsiti oupling etween the two PWs. strip rry, onfirming the open-iruit nture of the devie t 297 K (in ft, the phses of the trnsmission nd refletion prmeters re lso muh the sme in the open devie t nd the strip rry t 297 K; see upplementry Informtion, setion 4). These results provide further onfirmtion tht the negtive refrtion we oserve t ryogeni tempertures is due to the kineti indutne. Also, in most of the drk re in Fig. 3d, the js 21 j vlue of the metmteril even t ryogeni tempertures is very similr to tht of the open devie, onfirming the ut-off nture in tht region. To exmine further the impt of kineti indutne on negtive refrtion, we mesure new set of devies of vrious geometri prmeters. omprison of devies with different vlues of l (nd, thus, l e ) for the sme vlues of W nd is espeilly instrutive; hnging l sles, nd v proportionlly to l e, ffeting the index n 52(2/v) 3 sin 21 (v /v) with only one prmeter, v. peifilly, devie with longer strips, with lrger vlues of nd, nd smller v vlue, will hve negtive index with lrger mximum ttinle mgnitude, 2/v, rehing the frequeny region foridden for shorter-strip devie. In the frequeny region essile y oth longer- nd shorter-strip devies, the shorter-strip devie will hve lrger negtive index thn the longer-strip devie if the two re ompred t the sme frequeny (upplementry Fig. 4). This ler-ut property emerges in mesurements of pir of devies oth with mm ut with differing vlues of l (112 versus 52 mm) or l e (31 versus 14 mm) (Fig. 4). This property is onfirmed gin in two dditionl pirs of devies (Fig. 4), where the refrtive index is s lrge s 27. Altering the periodiity, whih in generl my hve to e omined with ltering W, ffets the index n 52(2/v) 3 sin 21 (v /v) in more omplited mnner, owing to simultneous hnges in nd v. For l mm, s we derese (, W) first from (1.5 mm, 1 mm) to (1.25 mm, 1 mm) nd then to (.75 mm,.6 mm), with the first redution inresing y ftor of 1.2 with unhnged, nd the seond redution inresing y ftor of 1.7 with unhnged, v does not vry s muh s, owing to the squre-root dependene of v on nd. Thus, smller periodiity will yield lrger negtive index for the sme frequeny wy from the ut-off regions, s evident in mesurements (Fig. 4). In these nd W vritions, the hrteristi impedne nd, thus, the impedne mismth is vried. This results in imperfet de-emedding of the prsiti ouplings ner ut-offs, osuring the ut-off ehviours. The tendeny of the index to e more negtive for smller periodiities is seen gin for l 5 52 mm with the sme vritions of nd W (Fig. 4d). The rossing of the respetive dt for the devies with nd 1.5 mm is n nomly tht we suspet rises from the impedne mismth vrition. The exeedingly strong inerti-sed negtive refrtion demonstrted here requires solid-stte pltform with very lrge kineti indutne nd low eletron sttering. To meet these requirements, we used As/AlAs 2DE t ryogeni temperture. ling the 2DE metmteril to higher frequenies y simultneous redution of the strip length nd periodiity (Fig. 4 nd upplementry Informtion, setion 2) would relx the ondition on eletron sttering time (nd, thus, temperture); demonstrtion 26 of terhertz plsmoni devies t room temperture with As/AlAs 2DE odes well for high-temperture pplitions. rphene, nother type of 2D ondutor with high moility t room temperture 27, my lso e pltform for terhertz-frequeny negtive refrtion sed on 212 Mmilln Pulishers Limited. All rights reserved 2 AUUT 212 VOL 488 NATURE 67

4 REEARH LETTER = 1.25 μm, I = 112 μm = 1.25 μm, I = 52 μm =.75 μm, I = 112 μm =.75 μm, I = 52 μm 6 = 1.5 μm, I = 112 μm = 1.5 μm, I = 52 μm d =.75 μm, I = 112 μm 6 = 1.25 μm, I = 112 μm = 1.5 μm, I = 112 μm Figure 4 eometry-dependent mesurements t., Re(n) for pir of 13-strip metmterils with mm nd W 5 1 mm, ut with different l vlues., Re(n) for nother two pirs of 13-strip metmterils with different l vlues: (, W) 5 (.75 mm,.6 mm) nd (1.5 mm, 1 mm).,re(n)forl mm similr kineti pproh. Although eletrons in grphene t s mssless prtiles, nd thus re non-newtonin, they still possess kineti energy, exhiiting plsmoni ehviour with impliit kineti indutne. In ft, terhertz light plsmon oupling hs een reently oserved t room temperture 28. Ahieving strong negtive refrtion sed on the kineti pproh with higher isotropy nd t optil frequenies using different mteril systems is lso open to further investigtion. METHOD UMMARY We frite the devies on As/AlAs 2DE sustrtes otined y moleulr em epitxy. The lyer struture ove the 2DE omprises 4-nm Al As, 14-nm i-doped Al As, 1-nm Al As nd 7-nm As p. At 4 K, the moility of the 2DE is m 2 V 21 s 21 nd the rrier density is m 22, oth in the drk. 2DE strips re defined y eletron em lithogrphy, followed y wet ething (.71-nm depth) with 15:1:1 H 2 O:H 2 O 2 :NH 4 OH. Ohmi ontts re defined y photolithogrphy followed y therml evportion of Ni (5 nm)/au (2 nm)/e (25 nm)/au (1 nm)/ni (5 nm)/ Au (4 nm), nd nneling t 42 u for 5 s. PWs re defined y photolithogrphy nd formed y therml evportion of r (8 nm)/au (5 nm). The mirowve sttering nlysis is performed in Lke hore ryotronis ryogeni proe sttion t feedk-ontrolled ryogeni tempertures in the drk. round signl ground mirowve proes, with pith of 1 mm, onneted to proe rms re tthed to on-hip PWs. oxil les led to the proes from n Agilent E8364A network nlyser, whih genertes exittion signls of frequenies up to 5 Hz, delivering 245 dbm power to the devies, nd mesures the sttering prmeters. To see the effet of the metmteril (strip rry) only, we first lirte the system, t eh mesurement temperture, up to the tips of the proes y using the NIT-style multiline TRL tehnique 29, nd then perform dditionl de-emedding to remove the on-hip PW delys nd prsiti ouplings etween the PWs, whih ypss the metmteril (upplementry Informtion, setion 3). The PWs used for this lirtion 3 re frited on 2 =.75 μm, I = 52 μm 25 = 1.25 μm, I = 52 μm = 1.5 μm, I = 52 μm with different nd W vlues. d, Re(n) for l 5 52 mm with different nd W vlues. nd d re rerrngements of the dt in nd to filitte omprison for the sme l. Eh devie result is shown ove its respetive utoff frequeny. undoped As sustrtes nd designed using onnet eletromgneti solver to hve 5-V hrteristi impedne, whih is the hrteristi impedne of the network nlyser, les nd proes. Reeived 2 Deemer 211; epted 31 My 212. Pulished online 1 August Pendry, J. B. Negtive refrtion mkes perfet lens. Phys. Rev. Lett. 85, (2). 2. Veselgo, V.. The eletrodynmis of sustnes with simultneously negtive vlues of e nd m. ov. Phys. Usp. 1, (1968). 3. mith, D. R., Pdill, W. J., Vier, D.., Nemt-Nsser,.. & hultz,. omposite medium with simultneously negtive permeility nd permittivity. Phys. Rev. Lett. 84, (2). 4. hely, R. A., mith, D. R. & hultz,. Experimentl verifition of negtive index of refrtion. iene 292, (21). 5. Linden,. et l. Photoni metmterils: mgnetism t optil frequenies. IEEE J. el. Top. Quntum Eletron. 12, (26). 6. uuku, E., Aydin, K., Ozy, E., Foteinopoulou,. & oukoulis,. M. Eletromgneti wves: negtive refrtion y photoni rystls. Nture 423, (23). 7. Vlentine, J. et l. Three-dimensionl optil metmteril with negtive refrtive index. Nture 455, (28). 8. Podolskiy, V. A. & Nrimnov, E. E. trongly nisotropi wveguide s nonmgneti left-hnded system. Phys. Rev. B 71, 2111 (25). 9. Hoffmn, A. J. et l. Negtive refrtion in semiondutor metmterils. Nture Mter. 6, (27). 1. Pendry, J. B. A hirl route to negtive refrtion. iene 36, (24). 11. Meservey, R. Mesurements of the kineti indutne of superonduting liner strutures. J. Appl. Phys. 4, (1969). 12. Burke, P. J., pielmn, I. B., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. High frequeny ondutivity of the high-moility two-dimensionl eletron gs. Appl. Phys. Lett. 76, (2). 13. Enghet, N. iruits with light t nnosles: optil nnoiruits inspired y metmterils. iene 317, (27). 14. Leze, H. J., Dionne, J. A. & Atwter, H. A. Negtive refrtion t visile frequenies. iene 316, (27). 68 NATURE VOL AUUT Mmilln Pulishers Limited. All rights reserved

5 REEARH 15. Eleftherides,. V., Iyer, A. K. & Kremer, P.. Plnr negtive refrtive indexmedi using periodilly L loded trnsmission lines. IEEE Trns. Mirow. Theory Teh. 5, (22). 16. loz,. & Itoh, T. Trnsmission line pproh of left-hnded (LH) mterils nd mirostrip implementtion of n rtifiil LH trnsmission line. IEEE Trns. Antenn. Propg. 52, (24). 17. ri, A. & Eleftherides,. V. Overoming the diffrtion limit with plnr lefthnded trnsmission-line lens. Phys. Rev. Lett. 92, (24). 18. tern, F. Polrizility of two-dimensionl eletron gs. Phys. Rev. Lett. 18, (1967). 19. hen, X., rzegorzyk, T. M., Wu, B.-I., Pheo, J. & Kong, J. A. Roust method to retrieve the onstitutive effetive prmeters of metmterils. Phys. Rev. E 7, 1668 (24). 2. mith, D. R., Vier, D.., Koshny, T. & oukoulis,. M. Eletromgneti prmeter retrievl from inhomogeneous metmterils. Phys. Rev. E 71, (25). 21. Burgos,. P., de Wele, R., Polmn, A. & Atwter, H. A. A single-lyer wide-ngle negtive-index metmteril t visile frequenies. Nture Mter. 9, (21). 22. hoi, M. et l. A terhertz metmteril with unnturlly high refrtive index. Nture 47, (211). 23. hnd, D. et l. Lrge-re flexile 3D optil negtive index metmteril formed y nnotrnsfer printing. Nture Nnotehnol. 6, (211). 24. hlev,v.m.optilnegtive-indexmetmterils.nturephoton.1, 41 48(27). 25. oukoulis,. M., Linden,. & Wegener, M. Negtive refrtive index t optil wvelengths. iene 315, (27). 26. Mezini, Y. M. et l. Room temperture terhertz emission from grting oupled two-dimensionl plsmons. Appl. Phys. Lett. 92, 2118 (28). 27. Den,. R. et l. Boron nitride sustrtes for high-qulity grphene eletronis. Nture Nnotehnol. 5, (21). 28. Ju, L. et l. rphene plsmonis for tunle terhertz metmterils. Nture Nnotehnol. 6, (211). 29. Mrks, R. B. A multiline method of network nlyzer lirtion. IEEE Trns. Mirow. Theory Teh. 39, (1991). 3. Andress, W. F. et l. Ultr-suwvelength two-dimensionl plsmoni iruits. Nno Lett. 12, (212). upplementry Informtion is linked to the online version of the pper t Aknowledgements The uthors re grteful for support for this reserh y the Air Fore Offie of ientifi Reserh under ontrt numers FA nd FA Devie frition ws performed in prt t the enter for Nnosle ystems t Hrvrd University. The uthors thnk W. F. Andress for ssistne with devie frition nd mirowve mesurements. Author ontriutions H.Y. nd D.H. hd the ide for the projet. V.U. frited the 2DE. H.Y. designed, frited nd mesured the properties of the devies. H.Y., K.Y.M.Y. nd D.H. nlysedthe dt. H.Y. ndd.h. wrote the pper. All uthorsdisussed the results nd reviewed the mnusript. Author Informtion Reprints nd permissions informtion is ville t The uthors delre no ompeting finnil interests. Reders re welome to omment on the online version of this rtile t orrespondene nd requests for mterils should e ddressed to D.H. (donhee@ses.hrvrd.edu). 2 A U U T VO L N AT U R E Mmilln Pulishers Limited. All rights reserved