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SUPPLEMENTARY INFORMATION doi:1.138/nture261 1. Opticl chrcteriztions of 2D ilyer heterojunctions nd monolyer TMDs As shown in Figure S1, Rmn fingerprints of linking ilyer MoS2/WS2 heterostructure (leled in red, the 5 th from the ottom) show the chrcteristic virtionl modes of oth monolyer MoS2 nd monolyer WS2. We did not oserve ny ovious pek vritions for the heterojunction region s compred to its monolyer components, which indictes the wek interlyer interction in linking heterostructures. Similr results were oserved for linking ilyer heterostructure smples with other comintions, such s MoS2/MoSe2, WS2/MoSe2, WS2/WSe2 nd MoSe2/WSe2. Noticely, there is quenching effect of oth the E2g 1 nd A1g modes of MoS2 in MoS2/MoSe2 heterostructure, possily relted to the electron doping from MoSe2. We lso checked the Rmn spectrum of MoS2/WS2 heterostructure in constnt drk emission stte. A cler pek (~28 cm -1 ) shows up, which is ssigned to e the interlyer rething mode. Y offseted intensity vlues E 2g1 /A 1g 2LA A 1g E 2g 1 E 2g A 1g *Si / (drk) /WSe 2 /WSe 2 / / / WSe 2 E 1 2g A 1g 45 9 16 24 32 4 48 56 64 Rmn shift (cm -1 ) Figure S1 Rmn spectr of monolyers nd their heterostructures. From ottom to up: Rmn spectr of monolyers (leled in lck:,,, nd WSe 2), heterostructures which show linking effect (leled in red: /, /, /, /WSe 2, nd WSe 2/), nd / heterostructure with stle drk stte (leled in lue). An interlyer rething mode centered t 28 cm -1 (fitted with single Lorentzin function) ppers in the drk stte heterostructure. All the Rmn spectr were mesured with Hori T64 triple grting spectrometer, excited y 488-nm lser (42 µw, 12 s cquisition time for ech spectrum). * mrks the signl from the SiO 2 (8 nm)/si sustrte. WWW.NATURE.COM/NATURE 1

RESEARCH SUPPLEMENTARY INFORMATION 45 6 75 1 13.9 % 45 6 75 8.6% 45 6 75 9.1% 45 6 75 11.3% 1 5, Trnsmission (%) 98 96 94 92 9 88 86 84 82 A B C 45 6 75 B A C 98 A B 96 C 86 B WSe 2 84 82 45 6 75 45 6 75 45 6 75 Wvelength (nm) B A A 94 92 9 88 Trnsmission (%) Intensity (Counts) 4, 3, 2, 1, WSe 2 (x5) * 6 65 7 75 8 85 Wvelength (nm) Figure S2 Micro-sorption spectr nd photoluminescence spectr of TMD monolyers., Micro-sorption spectr of,, nd WSe 2 monolyers on spphire sustrtes. We use squre spot with side length of 7.6 μm. Monolyer smples with lrger sizes were chosen to mke sure tht it fully covers the light spot. A, B, C (A nd B in WSe 2) exciton peks 1 re leled for ech mteril. Purple line indictes the position of our excittion lser wvelength (4 nm) in the photoluminescence mesurement., Photoluminescence spectr of A excitons of,, nd WSe 2, excited y 4-nm lser with lser power of 1.5 μw. Ech spectrum hs n exposure time of 3 s. * mrks emission of the spphire sustrte. Typicl sorption nd photoluminescence spectr of monolyer TMDs re shown in Figure S2. Exciton peks cn e well resolved in oth sorption nd photoluminescence spectr. As we cn see from the trnsmission spectr provided in Figure S2, the sorption t 4 nm of monolyer TMDs is mesured to e 13.9% for MoS2, 8.6% for WS2, 9.1% for MoSe2 nd 11.3% for WSe2. The corresponding photoluminescence spectr (with corrected response curve) re plotted in Figure S2. Tke MoS2 s reference, the quntum yield (QY) rtio for other monolyers cn e clculted, i.e., 74 for WS2, 81 for MoSe2, nd 55 for WSe2. Considering the fct tht smple vrition of fluorescence intensity cn rech s lrge s one order of mgnitude, our results indicte comprle QY vlue for WS2, WSe2 nd MoSe2 monolyer used in our experiments. We lso implemented sorption mesurements on WSe2/MoSe2 heterostructure smple including regions with different chrge trnsfer sttes (Figure S3). We used the sme smple for trnsient sorption mesurements. There is ner liner reltionship of intensity versus pump power, up to 5 mw (Figure S3). Besides the dt shown in Figure 2g, the chrge trnsfer feture t time-scle of ~12 fs cn e well resolved when the power of pump em is either.5 mw or 1.5 mw. 2 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH Trnsmission (%) 1 98 96 94 92 WSe 2 / -(stte-) WSe 2 / -(stte-d) (B) WSe 2 (A) (A) T/T (x1-3 ) 5 4 3 2 1 T/T t 8 nm T/T t 75 nm c 9 6 65 7 75 8 85 Wvelength (nm) 84 d 1 2 3 4 5 Pump power (mw) 84 81 81 Wvelength (nm) 78 75 72 ~ 12 fs Wvelength (nm) 78 75 72 ~ 12 fs 69 69 2.8 3. 3.2 3.4 2.8 3. 3.2 3.4 Time (ps) Time (ps) Figure S3 Stedy stte sorption spectr nd trnsient sorption of /WSe 2 heterostructure in different chrge trnsfer sttes., Stedy stte sorption spectr, red line: ner neutrl stte region (chrge trnsfer stte ); lck line: drk stte region (chrge trnsfer stte )., Pump power dependent trnsient sorption, indicting ner liner reltionship up to 5 mw. c,d, 2D colormp of trnsient sorption t different pump powers (c:.5 mw; d: 1.5 mw) for the drk region of /WSe 2 smple. Both indicte n interlyer chrge trnsfer time of ~12 fs. Grey re in shows the wvelength rnge of pump em (81-845 nm). WWW.NATURE.COM/NATURE 3

RESEARCH SUPPLEMENTARY INFORMATION 2. Blinking sed on n IICT mechnism in heterostructures with different comintions 2.1 Bidirectionl linking with right nd drk sttes No. of events 7 6 5 4 3 2 1 9.264 s 17.768 s 18.272 s 27.168 s 4.944 s.25.5.75 1. 1.25 1.5 1.75.25.5.75 1. 1.25 1.5 1.75 7 6 5 4 3 2 1.25.5.75 1. 1.25 1.5 1.75 Normlized intensity (.u.) c d (D) (D) (B) in / in / (B).25.5.75 1. 1.25 1.5 1.75 Normlized intensity (.u.) 18 16 14 12 1 8 6 4 2 8 7 6 5 4 3 2 1 No. of events Figure S4 Sttisticl nlyses of the intensity distriution. -d, Monolyer emission of (), monolyer emission of (), emission of from heterostructure (c) nd emission of from heterostructure (d). Single (,, c) nd multiple (d) Gussin peks were used in dt fitting. Figure S4 shows plot of detiled sttisticl nlysis of intensity stte distriution for the dynmic imging result in Figure 1f-i. Sttisticl nlyses show nrrow single Gussin distriution for monolyer regions. The occurrence of right/drk sttes leds to rodened Gussin distriution for WS2 emission t the heterostructure region; while distriution for MoSe2 emission in WS2/MoSe2 is more complicted, exhiiting multiple-pek profile. A type II heterostructure with stggered gp is essentil in the IICT model for idirectionl crrier trnsfer. If type I heterostructure (with strddling gp) is formed, oth electrons nd holes excited in the donor will trnsfer nd ccumulte t the vlence nd (for holes) nd conduction nd (for electrons) of the cceptor, leding to quenching (enhncement) effect for emission in donor (cceptor). As shown in Figure S5, for the four kinds of 2D TMDs (i.e., MoS2, MoSe2, WS2 nd WSe2), ech pir of ilyers (there re six comintions in totl) with two monolyer components will form type II 4 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH heterostructure. Bsiclly, linking effect with right, neutrl nd drk sttes my occur for ll of the possile comintions. -3.5 c d e f -4. -4.5 CBM -5. -5.5-6. VBM WSe 2 WSe 2 WSe 2 Figure S5 Six types of comintions of 1+1 ilyer heterostructure consisting of two species from,, nd WSe 2., /;, /; c, /; d, /WSe 2; e, /WSe 2; f, /WSe 2. Blue text indictes n electron donor while red text indictes n electron cceptor. Bnd lignment is dpted from reference 2. Solid nd dsh lines re -initio clcultion results otined with the Perdew-Burke-Ernzerhof (PBE) nd Heyd-Scuseri- Ernzerhof (HSE6) hyrid functionl, respectively. 2.2 Blinking heterostructures with only right (or drk) sttes Aforementioned discussions re sed on the nd lignment clculted in vcuum while no sustrte/tmosphere induced doping is considered. However, for the vrious kinds of TMDs, i.e., supported y SiO2/Si sustrte nd exposed in ir, doping effect is inevitle which will ffect the interlyer chrge trnsfer in ilyer heterostructures. For our mechniclly exfolited smples, MoS2 nd WS2 re n-type semiconductors, MoSe2 is close to neutrl stte while WSe2 is reported to e p-type semiconductor. The possile initil nd filling of monolyer components nd interlyer interction will led to new lnced doping stte nd ffect the interlyer crrier trnsfer process. For MoS2/MoSe2 ilyer heterojunction in ir s shown in Figure S6, MoSe2 in the heterostructure region shows linking effect, switching etween neutrl nd right sttes. This might e due to the inefficient electron trnsfer process s compred to tht of holes. MoS2 is n n-type semiconductor due to sulfurvcncy 3 ; while for MoSe2, it is nerly neutrl. Considering the fct tht the gp etween conduction nds of MoS2 nd MoSe2 is reltively smll (~.5 ev), the electron trnsfer process finlly ecomes minor. Thus, in the MoS2/MoSe2 heterostructure shown in Figure S6, only intermittent hole chnnel (from MoS2 to MoSe2) is dominnt, thus resulting in right stte switching in the emission of MoSe2. Since the emission of MoS2 is wek, currently the dynmic vrition of MoS2 emission hs not een investigted. WWW.NATURE.COM/NATURE 5

RESEARCH SUPPLEMENTARY INFORMATION 4 / / Intensity (.u.) 3 2 1 μm 1 3 6 9 12 15 18 21 24 27 3 33 36 39 42 Figure S6 A linking / ilyer heterostructure., Opticl imge;, time trce extrcted from 43.6-s video recorded with high speed cmer, 794-nm nd pss filter ws used to extrct the emission signl of. The heterostructure region links with most sttes righter thn re, suggesting tht the electron trnsfer process might e minor. Similrly, for WS2/WSe2 heterostructure, in which WSe2 is n electron donor nd WS2 is supposed to e n electron cceptor. WS2 is n-type nd WSe2 is p-type in our experimentl condition. The lck of electrons in WSe2 possily leds to less occurrence of electron trnsfer process, resulting drk switching sttes in WS2 emission in WS2/WSe2 heterojunction (Figure S7, S8). /WSe 2 c 22 2 18 Bre (position C) B Insensity (.u.) 16 14 12 in /WSe 2 (position B) A C 1 in /WSe 2 (position A) 8 3 6 9 12 15 18 21 24 27 3 33 36 39 42 Figure S7 A /WSe 2 ilyer heterostructure tht ws divided into severl isolted ilyer heterostructure regions., Opticl imge., Fluorescence imge tken with 645-nm nd pss filter. c, Blinking profiles (emission t ~645 nm) of two heterostructure region (position A nd B) nd re region (position C). Scle r in nd is 1 μm. 6 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH Intensity (counts/ms) 1.85 1.9 1.95 2. 2.5 2.1 2.15 14 12 1 8 6 4 2 8 6 4 2 8 6 Primry dt Sum Exciton fitting Trion fitting 4 Drk 2 t = 47.8 s 1.85 1.9 1.95 2. 2.5 2.1 2.15 Emission evergy (ev) WSe 2 Neutrl Weker t = 64.7 s c Integrted PL totl intensity (counts) Exciton (x ) emission energy (ev) 7, 6, 5, 4, 1.5 1.4 1.3 1.2 1.1 1. 2 4 6 8 1 12 1.988 2.68 2.66 2.64 2.62 2.6 2.58 1.978 2.56 2 4 6 8 1 12 Figure S8 Time vrition of chrged nd neutrl excitons of in linking /WSe 2 ilyer heterostructure., Typicl emission spectr with Gussin fitting of re (top), righter stte (ut weker thn re ; t = 64.7 s, middle), nd drker stte (t = 47.8 s, ottom) of the linking /WSe 2 heterojunction. Right insets re illustrtions of different crrier trnsfer sttes, i.e., slight hole trnsfer (weker) nd strong hole trnsfer (drk)., Time trce of integrted totl emission intensity of in /WSe 2 [I(X +X - ), red curve] nd time trce of intensity rtio of trion/exciton [I(X - )/I(X ) of in /WSe 2, lue curve]. c, Time trce of emission energy vrition of neutrl exciton [E(X ), red curve] nd trion [E(X - ), lue curve]. Sttisticl nlyses of stte distriution sed on time trces shown in nd c re shown in Figure 3e-f. Integrted Trion/Exciton rtio 1.986 1.984 1.982 1.98 Trion (X - ) emission energy (ev) Bndgp renormliztion nd phse filling re relted with the initil doping, free crrier genertion due to excittion lser sorption nd more importntly, intermittent interlyer chrge trnsfer (fter certin degree of chrge ccumultion). Among which, the lst is the origin of the correlted linking phenomenon, while free crrier shll e relted to excittion power density. Actully, some electric gte-tuned emission experiments hve demonstrted tht, the controlled injection of holes or electrons will led to pek shift of trions nd neutrl excitons due to ndgp renormliztion nd phse filling 4,5. We lso conducted power-dependent photoluminescence experiments on monolyer WS2. In our experiments, excittion power is quite low (on the level of μw) thus the lser induced nd shift might not e WWW.NATURE.COM/NATURE 7

RESEARCH SUPPLEMENTARY INFORMATION experiments on monolyer WS2. In our experiments, excittion power is quite low (on the level of μw) thus the lser induced nd shift might not e prominent. However, we cn still oserve cler shift of trion pek even t n excittion power s low s 5 μw (~4 mev, s compred to tht of.5 μw excittion) (Figure S9). Thus we cn find tht the nd gp renormliztion nd phse-filling phenomenon is common in monolyer TMDs even with continuous wve (CW) excittion, which llows us to crefully study the chrge-trnsfer induced exciton fine-structures during linking. 125 W Normlized emission intensity (.u.) 5 W 25 W 12.5 W 5 W.5 W.5 W 1.85 1.9 1.95 2. 2.5 2.1 Emission energy (nm) Emission energy (ev) 2.5 2. 1.995 1.99 1.985 1.98 1.975 1.97 1.965 1.96 Neutrl exciton Trion.1 1 1 1 Power ( W) Figure S9 Power dependent emission of monolyer., Power dependent emission spectr (lck trces) together with Gussin fitting results (lue trces for neutrl excitons, pink trces for trions nd red trces for oth excitons), excited y 532-nm lser with excittion power from.5 μw to 125 μw., Plot of emission energy versus excittion power, which indictes cler red shift for trion emission (lue) nd slight lue shift for neutrl exciton emission (red) when excittion power increses. 2.3 Non-linking 2D ilyer heterostructures Among the 38 smples investigted, there re 12 heterojunction regions, which emit light with constnt intensity (non-linking). Among which 9 of 8 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH them exhiit stle neutrl or right stte; while 3 of them shows stle drk stte. For exmple, right region nd drk region re shown in Figure S1. Severl resons cn cuse such non-linking effect: (1) interlyer distnce is too lrge or too smll, s hs een discussed in the text; (2) inefficient periodic crrier ccumultion nd trnsfer, which might e relted with the edge structure of heterostructure. For heterojunctions formed with monolyers with rough edges, hot crriers excited in ech monolyer component might hve more prominent loss t the edge. In fct, we do oserve tht roughly edged smples re hrdly found to e linking; (3) in certin cses, oth the hole-chnnel nd the electron-chnnel ecome inhiited (might fter n initil chrge-trnsfer process). Non-linking heterostructures re stle single-stte systems which llow us to investigte specified stte esier. 1+1-H2 c 25, / -H1 (drk) / -H2 (right) 1+1-H1 Intensity (counts/s) 2, 15, 1, 5, 2 μm 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2. 2.1 2.2 1+1-H2 d 1 95 Emission enery (ev) / -H1 (drk) / -H2 (right) 1+1-H1 Intensity (counts/s) 9 85 8 75 7 65 2 μm 6 1.4 1.45 1.5 1.55 1.6 1.65 1.7 Emission enery (ev) Figure S1 Non-linking / Heterostructures with constnt emission., Opticl imge., Fluorescence imge recorded with colored cmer (MP5.- RTV-R-CLR-1), showing drk (H1) region nd right region (H2). c, Emission spectr of re (lue curve), H1 (lck curve) nd H2 (red curve). d, Zoom-in region corresponding to the mrked re s shown in (c), it shows n interlyer exciton emission t round 1.55 ev for lck curve (the drk region, H1). WWW.NATURE.COM/NATURE 9

RESEARCH SUPPLEMENTARY INFORMATION 3. Fluorescence cross-correltion spectroscopy in linking 2D heterostructures SPAD detectors provide time-correlted single photon counting informtion without energy resolution, while stedy stte mesurements with spectrl fetures without dynmic detils. Comined study will e helpful in demonstrting solid proof of linking phenomenon, s well s providing deeper insights of its origin. Intensity (counts/s) Intensity (counts/ms) 15 1 5 c 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2. Emission energy (ev) 3.2 2.8 2.4 2. 1.6 1.2.8.4. WSe 2 Dt Sum WSe 2 /WSe 2 + t=3.3s 1.55 1.6 1.65 1.7 1.75 Emission energy (ev) Integrted intensity (counts/ms) d Intensity (counts/ms) 7 6 5 3.2 2.8 2.4 2. 1.6 1.2.8.4. WSe 2 in WSe 2 + in WSe 2 + 1 2 3 4 5 6 Dt Sum WSe 2 t=25.6s 1.55 1.6 1.65 1.7 1.75 Emission energy (ev) Figure S11 FCCS nlyses of ilyer /WSe 2 heterostructure mesured with micro-rmn spectrometer., Typicl emission spectr of isolted monolyer (lue curve) nd WSe 2 monolyer (red curve) nd ilyer /WSe 2 heterostructure (lck curve). Excited with 532-nm CW lser, 3 lines mm -1 grting is used to enle the simultneous cquisition of emission from nd WSe 2. Inset shows the corresponding opticl imge of the smple., Time trces of 6-s period showing the intensity vrition of emission from WSe 2 nd in the /WSe 2 heterostructure. c,d, Selected spectr for t = 3.3 s nd t = 25.6 s. Ech spectrum hs 5 ms exposure time nd time intervl for next cquisition is 5 ms. Scle r in is 1 µm. 1 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH 3.1 Stedy stte study of correlted dynmic fluorescence fluctutions with spectrl feture informtion Besides the results shown in Figure 4-c, we lso conducted experiments on correlted linking dynmics with spectrl informtion of MoSe2/WSe2 heterostructure, using HR evolution spectrometer with 3 lines mm -1 grting, the emission of A excitons of WSe2 (t round 745 nm) nd MoSe2 (t round 79 nm) cn e recorded simultneously in single cquisition. As shown in Figure S11, intensity vritions of emission from WSe2 nd MoSe2 in the heterostructure region show mirror symmetry, which indictes negtively correlted fluorescence fluctutions. 3.2 Fluorescence cross-correltion pumped with fs-pulsed lser 6, IRF Gussin fit Intensity (Counts) 4, 2, 53 ps.95 1. 1.5 1.1 Dely time (ns) Figure S12 Instrument response function of the TCSPC system. Fitted y Gussin function yielding n FWHM of 53 ps. Figure S12 shows the instrument response function (IRF) of our FLIM system, with n FWHM (full-width hlf mximum) of 53 ps. Lifetime informtion ws extrcted y deconvolution of the IRF, thus we cn mesure time decy down to ~3 ps (~1/2 of IRF). For typicl linking quntum dot, chrge trnsfer hppens etween the quntum dot nd the environment (which is usully non-rditive). Blinking experiments re thus minly focused on the quntum dots itself, nd we cn hrdly monitor the dynmicl emission of chrge donor nd chrge cceptor t the sme time. Fluorescence cross-correltion spectroscopy (FCCS) re previously used for description of diffusion in fluorescent molecules or prticles. In linking 2D heterojunction, emission of the two monolyer components re found to e cross-correlted, since interlyer crrier exchnge cuses fluorescence WWW.NATURE.COM/NATURE 11

RESEARCH SUPPLEMENTARY INFORMATION fluctutions in oth monolyers. Thus, FCCS is n effective wy to monitor the dynmic process of interlyer crrier trnsfer. Figure S13 shows the intensity nd lifetime vrition of full 12-s frme of the FCCS experiment discussed in Figure S13, with inning time of 1 ms. To view in more detil, s shown in Figure S14, the intensity trces with inning time of 1 ms, 1 ms nd.2 ms re lso plotted. All trces exhiit noticele mirror symmetry for the MoSe2 emission nd WS2 emission, indicting negtive correltion effect during linking process. Notly, when inning time goes smller, decresed signl-to-noise rtio mkes it hrd for us to study correltion on shorter timescles. ( ) (Counts/ms) Averged lifetime ( ) (ns) 8 6 4 2 4.8 3.6 2.4 1.2.. 1 2 3 4 5 6 7 8 9 1 11 12 8 6 4 2.4.3.2.1 ( ) (Counts/ms) Averged lifetime ( ) (ns) Figure S13 Time trces of full 12-s period for the FCCS experiment. Top pnel, intensity trces of emission from in / (red trce) nd in / (lue trce); Bottom pnel, lifetime trces of emission from in / (red trce) nd in / (lue trce). Red rectngulr pttern mrks the selected region which hs een discussed in the text. Binning time is 1 ms. 12 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH 6 8 4 6 4 2 2 c 12 2 4 1 ms 6 8 1 (MoSe2) (counts/ms) 4 4 2 2 4 d 12 4 6 8 1 64 68 72 76 8 8 6 6 4 4 2 2 12 64 f 1 8 68 72 76 8 4 5 3 4 2 4 2 3 1 3 1 2 2 1-1 1-1 -2-2 -1-3 -1-4 12-2 2 4 6 8 1 (MoSe2) (counts/ms) (WS2) (counts/ms) -2 (WS2) (counts/ms) 6 3 4.2 ms 5 (MoSe2) (counts/ms) 6 2 2 1-2 4 6 (WS2) (counts/ms) 6 e (WS2) (counts/ms) 8 6 6 8 1 8 1 2 12 1 8 12 (WS2) (counts/ms) (WS2) (counts/ms) 1 1 14 8 12 16 (MoSe2) (counts/ms) 14 (MoSe2) (counts/ms) 1 1 ms (MoSe2) (counts/ms) 16-3 64 68 72 76 8-4 Figure S14 Time trces for the sme FCCS experiment clculted with different inning time.,, 1 ms; c,d, 1 ms; e,f,.2 ms. -c, intensity trces of the whole 12-s period of emission from WS2 in WS2/MoSe2 (red trce) nd MoSe2 in WS2/MoSe2 (lue trce). -d, Zoom-in region showing the 62-82 s period s mrked in dshed squres shown in -c. As control experiment, we conducted correltion mesurements on non-linking WS2/MoSe2 heterostructure, dt were plotted in Figure S15. No cler reltion etween the two intensity trces cn e found, nd the G( ) function exhiits fluctutions close to zero. 32 MoSe2.3 WS2 28. 26 G( ) (%) Intensity (kcnts) 3 24 22 2 -.6 x3 18 16 -.3 -.9 2 4 6 8 1 12-2 1-1 1 1 1 1 Correltion time (ms) 2 1 3 1 Figure S15 Control experiments of correltion on non-linking WS2/MoSe2 heterostructure. Mesured with single photon counters on FLIM system., timedependent fluorescence emission intensity of (lck trce) nd WS2 (red trce)., G( ) function clculted from the intensity dt point in. W W W. N A T U R E. C O M 14/ N A T U R E 1 3

RESEARCH SUPPLEMENTARY INFORMATION 3.3 Fluorescence cross-correltion spectroscopy monitored with SPADs excited with CW lser There hs een reports on distinct linking ehvior of QDs under CW lser excittion versus pulsed lser 6, which might e due to different chrge ccumultion dynmics. Here we lso conducted correlted linking experiments with SPADs excited with 532-nm CW lser, to verify linking ehvior of 2D ilyer heterostructures under different excittion conditions (Figure S16). As shown in Figure S16-, the time trces of intensity vrition exhiit mirror symmetry for WS2 emission (red) nd MoSe2 emission (lue), negtive correltion cn e found in Figure S16c. ( ) (kcounts) c 15 12 9 6 3-3 Binning time 1 ms 2 4 6 8 1 12 7. 6.3 5.6 4.9 4.2 3.5 2.8 ( ) (kcounts) ( ) (Counts) d 1.6 1.4 1.2 1..8.6.4.8.7.6.5.4.2.3 Binning time 1 ms. 2 4 6 8 1 12 Smple SPAD1 ( ) (Counts) G( ) (%) -.4 -.8 ojective BS1 BS2 645 BP 794 BP SPAD2 1-2 1-1 1 1 1 1 2 1 3 Correltion time (ms) 532 nm CW lser TCSPC electronics Figure S16 Fluorescence cross-correltion spectroscopy excited with 532-nm CW lser. -, Time trces of emission intensity of nd from / heterostructure region under excittion of 532 nm CW lser, with inning time of 1 ms () nd 1 ms (), respectively. Smple is the sme s tht shown in Figure 4. c, G(τ) function clculted with the intensity trces, which shows negtive correltion. d, Schemtic of the opticl setup, in which the 4-nm femtosecond lser used in FCCS experiments in Figure 4 is replced with 532-nm CW lser for excittion. 14 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH References 1 Kozw, D. et l. Photocrrier relxtion pthwy in two-dimensionl semiconducting trnsition metl dichlcogenides. Nt. Commun. 5, 4543 (214). 2 Kng, J., Tongy, S., Zhou, J., Li, J. & Wu, J. Bnd offsets nd heterostructures of two-dimensionl semiconductors. Appl. Phys. Lett. 12, 12111 (213). 3 Qiu, H. et l. Hopping trnsport through defect-induced loclized sttes in molydenum disulphide. Nt. Commun. 4, 2642 (213). 4 Liu, B. et l. Engineering ndgps of monolyer nd on fluoropolymer sustrtes y electrostticlly tuned mny-ody effects. Adv. Mter. 28, 6457-6464 (216). 5 Mk, K. F. et l. Tightly ound trions in monolyer. Nt. Mter. 12, 27-211 (213). 6 Smyder, J. A. et l. The influence of continuous vs. pulsed lser excittion on single quntum dot photophysics. Phys. Chem. Chem. Phys. 16, 25723-25728 (214). WWW.NATURE.COM/NATURE 15