# Fileset

[s41467-022-33647-5.pdf](https://mdr.nims.go.jp/filesets/fc36f60e-503c-4956-8541-4b8e72142a43/download)

## Creator

Arjun Ashoka, Nicolas Gauriot, Aswathy V. Girija, Nipun Sawhney, Alexander J. Sneyd, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Jooyoung Sung, Christoph Schnedermann, Akshay Rao

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Direct observation of ultrafast singlet exciton fission in three dimensions](https://mdr.nims.go.jp/datasets/c465803d-256f-43c7-b1e2-8fcadb30604d)

## Fulltext

Direct observation of ultrafast singlet exciton fission in three dimensionsArticle https://doi.org/10.1038/s41467-022-33647-5Direct observation of ultrafast singletexciton fission in three dimensionsArjun Ashoka1, Nicolas Gauriot1, Aswathy V. Girija 1, Nipun Sawhney1,Alexander J. Sneyd1, Kenji Watanabe 2, Takashi Taniguchi 3,Jooyoung Sung 4, Christoph Schnedermann 1 & Akshay Rao 1We present quantitative ultrafast interferometric pump-probe microscopycapable of tracking of photoexcitations with sub-10 nm spatial precision inthree dimensions with 15 fs temporal resolution, through retrieval of the fulltransient photoinduced complex refractive index.Weuse thismethodology tostudy the spatiotemporal dynamics of the quantum coherent photophysicalprocess of ultrafast singlet exciton fission. Measurements on microcrystallinepentacene films grown on glass (SiO2) and boron nitride (hBN) reveal a 25 nm,70 fs expansion of the joint-density-of-states along the crystal a,c-axesaccompaniedby a6nm, 115 fs change in the excitondensity along the crystalb-axis. We propose that photogenerated singlet excitons expand along thedirection of maximal orbital π-overlap in the crystal a,c-plane to form corre-lated triplet pairs, which subsequently electronically decouples into free tri-plets along the crystal b-axis due to molecular sliding motion of neighbouringpentacene molecules. Our methodology lays the foundation for the study ofthree dimensional transport on ultrafast timescales.Elucidating the three-dimensional transport of excitations in con-densed matter is key to advancements in our understanding andutilisation of functional materials ranging from novel quantum sys-tems to next-generation optoelectronic materials1–4. Of particularinterest are quantum coherent processes in heterogeneous, dis-ordered systems which require both ultrafast time resolution andlocal measurements to study and understand their transportcharacteristics5–7. Singlet exciton fission is a widely studied exampleof such a process that has gained relevance in the fields of photo-voltaics and quantum computing. Here a photogenerated singletexciton converts to an electronically and spin entangled pair of tri-plets at nearly half the singlet energy on ultrafast timescales. Thecorrelated triplet pair then separates into individual triplet excitonsthrough the loss of electronic and spin coherence8–11. Numerousultrafast studies have probed the coherent dynamics of the singletfission process, however direct observation of the real space three-dimensional spatial dynamics of ultrafast singlet fission remains anoutstanding goal8,10.The field of optical pump-probe microscopy, which extendsstandard pump-probe spectroscopy to amicroscope geometry, is wellsuited to study coherent transport processes in condensed mattersystems, as it provides direct visualisation of the transport ofexcitations12–14. Conventionally, optical pump-probe microscopy hasused point-scanning methodologies which provide a two-dimensionalpicture of the transport process with 10 s of nm resolution and 100 fstime resolution. In contrast, reports of widefield optical pump-probemicroscopy have demonstrated that interferometric contrast couldprovide a way to visualise three-dimensional transport14. However,while the use of phenomenological Gaussian point-spread functions todescribe the measured images can yield sub-10 nm lateral precision, itcannot quantify out-of-plane transport12,14–17. Moreover, the measuredimages naturally arise from changes in the full complex refractiveReceived: 11 May 2022Accepted: 26 September 2022Check for updates1Cavendish Laboratory, University of Cambridge, J. J. ThomsonAvenue, CambridgeCB30HE, UK. 2ResearchCenter for FunctionalMaterials, National InstituteforMaterials Science, 1-1Namiki, Tsukuba 305-0044, Japan. 3International Center forMaterials Nanoarchitectonics, National Institute forMaterials Science, 1-1Namiki, Tsukuba 305-0044, Japan. 4Department of Emerging Materials Science, DGIST, Daegu 42988, Republic of Korea. e-mail: cs2002@cam.ac.uk;ar525@cam.ac.ukNature Communications |         (2022) 13:5963 11234567890():,;1234567890():,;http://orcid.org/0000-0002-5586-2818http://orcid.org/0000-0002-5586-2818http://orcid.org/0000-0002-5586-2818http://orcid.org/0000-0002-5586-2818http://orcid.org/0000-0002-5586-2818http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0003-2573-6412http://orcid.org/0000-0003-2573-6412http://orcid.org/0000-0003-2573-6412http://orcid.org/0000-0003-2573-6412http://orcid.org/0000-0003-2573-6412http://orcid.org/0000-0002-2841-8586http://orcid.org/0000-0002-2841-8586http://orcid.org/0000-0002-2841-8586http://orcid.org/0000-0002-2841-8586http://orcid.org/0000-0002-2841-8586http://orcid.org/0000-0003-4261-0766http://orcid.org/0000-0003-4261-0766http://orcid.org/0000-0003-4261-0766http://orcid.org/0000-0003-4261-0766http://orcid.org/0000-0003-4261-0766http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-33647-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-33647-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-33647-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-33647-5&domain=pdfmailto:cs2002@cam.ac.ukmailto:ar525@cam.ac.ukindex, n + ik, which cannot be retrieved using such phenomenologicalGaussian point-spread-functions, which in turn rules out the quanti-tative measurement of the transient joint-density-of-states ( JDOS).Here we introduce quantitative interferometric ultrafast pump-probe microscopy. Using a first-principles analytic optical model, weshow it is possible to fully describe these interferometric pump-probeimages and quantify changes in the full transient complex refractiveindex n(t) + ik(t) and retrieve both lateral and out-of-plane transportwith sub-10 nm precision, with 15 fs time resolution (see Supplemen-tary Note 6 for localisation precision and Supplementary Note 4for demonstration of time resolution). We report a full three-dimensional picture of ultrafast singlet exciton fission in polycrystal-line pentacene films, suggesting that the photoexcited singlet excitonexpands along the direction of maximal orbital π-overlap (a,c-axes) toform correlated triplet pairs, which subsequently electronicallydecouples into free triplets along the crystal b-axes due to latticemodes that drive the intermolecular sliding motion of neighbouringpentacene molecules.Results and discussionExperimental setup and optical modelOur experimental setup (Fig. 1a) is based on a transmission widefieldpump-probe microscope equipped with an oil-immersion objective(numerical aperture = 1.1). A pump pulse (560 nm, 13 fs) is focusedonto the sample with the objective to produce a near-diffraction-limited local photoexcitation (Supplementary Note 1). After a variabletime delay, a counter-propagating widefield probe pulse (750nm, 7 fs,~20μmat full-width-half-maximum) is transmitted through the sampleand imaged onto an emCCD detector. The effect of the pump pulse isto photoinduce a three-dimensional spatially varying, local complexrefractive index change, Δ~n=Δn + iΔk (Fig. 1a). This index changeweakly perturbs the time-delayed plane-wave probe pulse incident onthe sample, leading to local changes in its phase and amplitude18. Thelarge background unperturbed probe field interferes with this per-turbed probe field to form a spatial interference pattern along thepropagation direction. The objective and imaging lens then image thisspatial interference pattern combined with the attenuation of theprobe on a camera.Our optical model is based on the treatment of the diffraction-limited optical perturbation produced by the pumppulse in a thin filmsemiconductor as a well-defined local complex refractive index per-turbation, similar to a gold nanoparticle or polystyrene bead (Fig. 1a).Before the pump pulse arrives, when the system is in the ground state(pump-off), the polarisation P measured by the probe is given by,P = ϵ0χ(1)E. Using D = ϵE = ϵ0E + P, the ground state dielectric functionϵoff is therefore given by, ϵoff = ϵ0(1 + χ(1)). After the arrival of the pumppulse, the system is in the excited state (pump-on), the polarisationP measured by the probe is given by, P = ϵ0( χ(1)E + χ(3)EpuEpuE), whereEpu is the pump electric field. Similarly, the excited state dielectricfunction ϵon is therefore given by, ϵon = ϵ0(1 + χ(1) + χ(3)EpuEpu). As theprobe pulse is always temporally separated from the pump, time-ordering allows us to treat the pump-on and pump-off probe signals asmeasures of thephotoexcited andground state dielectric functions (orcomplex refractive index) of the material, respectively. The overallperturbation to the dielectric function can therefore be written as,ϵon � ϵoff =Δϵ= ϵ0χð3ÞE2pu, ð1Þwhere χ(3) is the third order non-linear susceptibility, ϵ0 is thepermittivity of free space and Epu is the pump electric field19,20. Inorder to link this to the refractive index, we use the fact that as ~n=ffiffiffiϵp,Δ~n= 12ffiffiϵp Δϵ for small perturbations. As the time-integrated intensity ofthe pump absorbed by the material is given by Ipu =cn0ϵ02 E2pu, thephotoinduced refractive index change can be written as,Δ~nðr,zÞ= 12n0χð3Þ2cn0Ipuðr,zÞ ð2Þwhich importantly shows that upon photoexcitation, Δ~n is propor-tional to the intensity of the pump pulse.Fig. 1 | Experimental setup and optical model. a A schematic of the propagationof a time-delayed weakly interacting probe through a locally perturbed three-dimensional sample imaged on a camera. b Transient transmission and extractedtransient complex refractive index spectra, measured bands indicated in grey.c Radially averaged differential transmission images measured at different planesthrough a film of pentacene 150 fs after photoexcitation. The radial averages aremirrored about the x =0 plane for clarity. Dashed lines indicate the inter-ferometrically enhanced planes chosen for measurement. d Microscope image ofthe microcrystalline domains of the measured pentacene film on hBN and SiO2substrates, with labelled crystal geometries relative to the substrate. (Scalebar = 20μm).Article https://doi.org/10.1038/s41467-022-33647-5Nature Communications |         (2022) 13:5963 2As the intensity at the back-focal-plane of the objective is a TEM00mode, exploiting radial symmetry to average over polarisation effects,the pump is a focused Gaussian beam attenuated through the depth ofthe sample,Ipuðr,zÞ= I0σ0σðzÞ� �2exp�r22σðzÞ2� ωpuαzc� �ð3Þwhere σðzÞ= σ0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 + zzR� �2r, zR being the Rayleigh range, ωpu is thepump frequency and α is dimensionless, thickness-corrected extinc-tion coefficient for the pump. For thin film samples of thickness lessthan zR, and ignoring in-plane anisotropy, σ can be approximated to beconstant (O z=zR� �2) through the thickness of the sample. We cantherefore approximate the photoinduced refractive index change as,Δ~nðrÞ= ðΔn0 + iΔk0Þ exp�r22σ20� ωpuαzc" #ð4Þover the sample length, where we have absorbed the constants and χ(3)into the transient optical constants Δn0 + iΔk0 =12 ~n0χð3Þ 2cn0I0. Wecompute the near-field electric field by multiplying the incident fieldwith the laterally varying Fresnel complex transmission coefficients ofa Gaussian disc situated about the photoexcitation’s principal plane zc,Enf ðr,zcÞ= Ei½ð1� r1ðrÞ�½1� r2ðrÞÞ�tðrÞ, ð5Þwhere t = eiL~nκ captures the attenuation of Ei through the sample,r1 =nair�~nnair + ~n captures the reflection at the air-sample interface andr2 =~n�ns~n+ns, captures the substrate-sample interface. As the microscopesystemwe study is an oil-immersion system, the substrate-oil interfacejust before the objective is near index matched and not taken intoconsideration. Here ns is the substrate refractive index, L is the samplethickness and κ is the probe wavevector. The amplitude and phase ofEnf, therefore, encodes three-dimensional spatial information ofphotoexcited carrier transport through Δ~nðrÞ and zc.The probe electric field at the objective’s input aperture can beapproximated as the Fourier transform of the near-field electric field,Ef f ðkr ,zcÞ=FðEnf ðr,zcÞÞ, wherekr is the spatial frequencyof theprobe inthe radial direction and F is the Fourier transform. To study the spatialinterference of the probe in different planes in the object space wherethe field is interferometrically enhanced, we calculate the far-fieldelectric field of the plane Δz = z0 − zc by propagating the plane-wavedecomposition an extra distance Δz, Ef f ðkr ,ΔzÞ= eiΔzffiffiffiffiffiffiffiffiffiffiκ2�k2rpEf f ðkr ,zcÞ.To calculate the image on the camera by the objective-imaginglens system, we compute an inverse Fourier transform after filteringthe high spatial frequencies as the objective’s NA specifies, yielding,Eimðr0,Δz,n,kÞ=Z κNA�κNAEf f ðkr ,ΔzÞe�ikr r0dkr ð6Þwhich is a simplified version of the Richards–Wolf integral21–23.We calculate the widefield normalised differential transmittedimage of a photoexcited refractive index change (at a given probewavelength), Δ~nðrÞ=ΔnðrÞ+ iΔkðrÞ centred at zc = z0 −Δz on a spatiallyconstant, static background ~n0ðrÞ=n0 + ik0 centred about z0,ΔTTðr0,z0 � Δz,Δ~nÞ= ∣Eimðr0,Δz, ~n0 +Δ~nðrÞÞ∣2∣Eimðr0,z0, ~n0Þ∣2� 1: ð7ÞExperimental control over the image plane z0 is achieved bytranslating the imaging lens in the infinity space of the objective torelay different conjugate planes to the camera24. The effective axialdistance accessible bymoving the imaging lens by a distance z0 is givenby the axial magnification of the imaging system (SupplementaryNote 7). Ensuring that neither the imaging lens nor the objective moveduring a pump-probe measurement fixes z0, allowing us to trackchanges in zc, σ and transient refractive index Δ~n as a function ofpump-probe delay.Our model, therefore, characterises the normalised differentialtransmitted images in terms of the physical parametersΔ~nðr,σ,z0Þ, theprobewavelength and the sample thickness.Webenchmarkourmodelagainst Finite-Difference-Time-Domain (FDTD) calculations and findexcellent agreement, demonstrating that our near-field approxima-tions and the computational challenging aberrations are systematicallycancelled in the differential far-field images (Supplementary Note 2and 3). Critically, this enables us to extract the three-dimensionaltransport and Δn0 + iΔk0 through fitting the measured data set, whichwould be prohibitively computationally challenging using purelyFDTD methods.The process of ultrafast singlet fission is considered to occur inthree steps. First, the photogenerated singlet S1 converts to an elec-tronically and spin entangled triplet pair state TT. Second, through theloss of electronic correlation the TT state converts to a spatiallyseparated triplet pair T...T. Finally, through the loss of spin correlation,the spatially separated spin entangled triplet pair T...T separates intotwo uncorrelated triplets T + T8. As spin coherence is typically lost onlonger timescales than the electronic coherence in polyacenes and aswe probe the electronic states through their optical transitions, wesolely focus on the loss of electronic correlation from TT to T...T andmake no comment on the spin correlation8. We study the dynamics ofsinglet exciton fission in two well-explored spectral bands of thearchetype organic semiconductor pentacene: the photobleachingband at 670 nm and the photoinduced absorption (PIA) band at740nm (Fig. 1b)25. It has been established that the 670nm band pri-marily tracks the ground-state bleach and hence contains the JDOS ofboth the photoexcited singlet S1 and resulting entangled TT anduncorrelated T...T triplet pairs25,26. The 740nm feature, however, is notpresent immediately after photoexcitation and tracks the JDOS of onlythe entangled TT and separated T...T triplet pair through transitions tohigher lying triplet states.We describe the transitions in these systemsthrough their JDOS rather than as single energetic transitions as inextended thin film systems, the molecules are not isolated and thedensity of states cannot be treated as one-dimensional.Analysis of the transient transmission spectra based on aKramers–Kronig differential dielectric function predicts Δn > 0 andΔk <0 at 670 nm and Δn <0 and Δk > 0 at 740nm (Fig. 1b)27. Wedemonstrate our interferometric sensitivity to the photoexcitation bymeasuring the differential transmitted images 150 fs after photo-excitation at both wavelengths through several image planes (Fig. 1c),demonstrating three dimensional point-spread-functions that arereminiscent of those reported in state-of-the-art static interferometricscattering microscopy28. We access different image planes by trans-lating the imaging lens in the infinity space of our microscope to relaydifferent planes from the image space onto the camera, similar to theconcept of remote focusing24. The degree of interferometric contrastdetermines our ability to resolve out-of-plane carrier transport andaccurately retrieve the transient refractive indices. We, therefore,study spectral bandswith a non-zero real refractive index change and asuitable imaging plane within the axial focus (Fig. 1c, dashed lines)(Supplementary Note 7)19,29.In order to unravel the three-dimensional dynamics of singletfission in microcrystalline pentacene films, we study pentacene filmsevaporated on SiO2 and on hexagonal boron nitride (hBN). On SiO2pentacene crystallises with its b-axis near-perpendicular to the sub-strate, whereas on hBN pentacene crystallises with the b-axis in-plane(Fig. 1d and Supplementary Note 8)30. This enables us to validate anyArticle https://doi.org/10.1038/s41467-022-33647-5Nature Communications |         (2022) 13:5963 3measured out-of-plane transport against in-plane transport in theorthogonal orientation as well as confirm the direction of the out-of-plane transport. We begin by studying the uncongested PIA band at740nm to establish the spatial dynamics of the triplet excitons and usethis information to study the more complicated dynamics of theground state bleach band at 670 nm.Loss of triplet pair electronic correlationWe study the TT and T...T exciton dynamics in the 740 nm PIA band(on both SiO2 and hBN) at 250μJ cm−2 where singlet exciton fission isthe dominant photophysical process (Fig. 2)31. At these densities,there is on average one photoexcitation per 100 pentacene mole-cules. As shown in Fig. 2a, there are spatiotemporal changes to thesignal during the first 500 fs. Our model is able to capture the mea-sured differential transmission image in this regime (Fig. 2b) (seeSupplementary Note 5 for details on the fitting procedure). A PIAband is expected to result from an increased JDOS, as the triplets areformed via the fission process and as the JDOS∝ Im(~ϵ), where ~ϵ is thedielectric function and ~ϵ= ~n2, Δk > 0 is expected at 740 nm. Weretrieve the expected signs ofΔn andΔk (Fig. 1b) and find an ultrafastrise due to formation of triplets and a subsequently constant JDOS,identical between both studied crystal orientations as anticipated(Fig. 2c–e). Transport of the photoexcitation in the a,c-crystal planemeasured through σa,c on SiO2 and Δza on hBN (Fig. 2c, f) is absent towithin our noise floor of 4 nm peak-to-peak. However, transportalong the b-crystal direction measured through Δzb on SiO2 displaysclear few nm transport with a timescale of 115 ± 11 fs (Fig. 2g). Whenmeasured in the rotated crystal orientation on hBN, this transportappears as the 6 nm change in the exciton density in the b,c-crystalplane measured through σb,c (Fig. 2g).The 6 nm, 115 fs change in the exciton density along the crystalb-axis at 740 nmmust correspond to a photophysical process relatingexclusively to the triplet population. This process must be distinctfrom the formation of the TT state which would be correlated with therise of this spectral feature. Further, the 115 fs timescale is distinct frompreviously reported TT formation timescales in pentacene25. Hencethis processmust be related to the loss of electronic correlation in thetriplet pair. Recent reports suggest that a 1 THz (1-ps period) latticevibration in pentacene crystals associated with sliding motion ofneighbouring pentacene molecules along the crystal b-axis modulatesthe π-overlap and therefore the J-coupling between adjacent penta-cene molecules, resulting in triplet pair separation from TT→ T...T32.Our measured 6 nm change in the spatial triplet exciton density alongthe same crystal b-axis over 500 fs could be related to a lattice dis-tortion arising from this 1 THzmodewhich changes the local excitonicdensity along this axis. A full 1-ps oscillation period of the 1 THz slidingmode is not needed to decouple the TT state to the T...T state, and aswe show below, free triplets are formed within 200 fs of photo-excitation.We additionally note that the triplet exciton in pentacene isknown to be polarised along the b-axis which further suggests a strongchange in polarisability due to this mode33. Further theoretical inves-tigations of the response of the excitonic wavefunction to phonon(g)(a)(d) (e)(f )(b)(c)cabbcaSiO2hBNFig. 2 | Triplet decoupling dynamics at 740nm and 250μJ cm−2. a Measuredradially averagedΔT/Tmap and spatially averaged signal kinetic.b Fit of the opticalmodel to the radial average at 13, 70, and 1000 fs. c Schematic of the measuredpentacenefilmonhBNandSiO2 substrates,with labelled crystal geometries relativeto the substrate. d, e Transient optical constants display the expected signs basedon Fig. 1b and show an ultrafast rise followed by a constant JDOS. f Transport in thea,c-crystal planemeasured in-plane on SiO2 (blue) and along the a-crystal directionmeasured out-of-plane on hBN (orange) is absent. g Transport in the b,c-crystalplane measured in-plane on hBN (orange) and along the b-crystal direction mea-sured out-of-plane on SiO2 (blue) displays a few nm 115 fs change in the excitondensity (dashed line fits an exponential).Article https://doi.org/10.1038/s41467-022-33647-5Nature Communications |         (2022) 13:5963 4modes along this axis in the vibronic and transient delocalisation fra-mework are called for34–36.Singlet to correlated triplet transitionWestudy the spatiotemporal dynamics of the S1 excitonvia the 670nmphotobleachingband in the samefluence regimeof 250μJ cm−2 (Fig. 3).As shown in Fig. 3a, there are spatiotemporal changes to the signalduring the first 500 fs. Our model captures the measured differentialtransmission image and we are able to retrieve the correct signs of theΔ~n based on Fig. 1b for both crystal orientations (Fig. 3b–e)27. We recallthat the 670nm band is congested due to overlapping spectral fea-turesof the S1,TT,T...T anddifferent oscillator strengthswhichmakes aquantitative interpretation of Δ~nðtÞ at 670 nm challenging. Transportof the photoexcitations in the a,c-crystal plane of pentacene is trackedthrough σa,c on SiO2 and Δza on hBN (Fig. 3c). We observe a 25 nmexpansion in σa,c with a timescale of 72 ± 13 fs, but no measurablecorrelated transport in Δza (Fig. 3f). We note that the high localisationprecision is significantly diminished on this spectral band as therequired interferometric contrast can only be gained through sub-stantially defocussing (∣Δz∣ > 500nm at 670 nm compared to ∣Δz∣ <50 nm at 740nm), where the remote focussing model begins to fail(see Supplementary Note 7).As the triplet (TT, T...T) excitons studied at 740 nm and display notransport in the a,c-crystal plane, any transport of in the a,c-crystalplane measured at the 670nm ground state bleach necessarily arisesfrom the S1 exciton. The 70 fs timescale matches previously reportedtimescales of singlet fission that are sensitive to the S1→ TTtransition10,25. The presence of this feature in the crystal-a,c plane isconsistent with the fact that the J-coupling between pentacene mole-cules required for the S1→ TT transition is maximal in direction ofmaximalπ-overlap, i.e., the crystal-a,cplane37 (Fig. 1). This suggests thatthe S1→ TT transition occurs in the crystal-a,c plane which results in aspatial expansion of the exciton density potentially due to the forma-tion of charge transfer (CT) states yielding a velocity Oð105Þms−1.Theoretical calculations of singlet exciton fission in solid pentaceneusing ab-inito Green’s function methods predict a singlet excitonbandwidth of 100meV over the unit cell, which yield an estimate of agroup velocity of Oð104Þms−1, suggesting that this transport phe-nomena cannot be rationalised as typical coherent transport of the S1state38. The slower timescale of the expansion along the b-crystaldirection measured in the b,c-crystal plane of pentacene is trackedthrough σb,c on hBN is, however, difficult to interpret due to theoverlapping transport of the triplets at 740 nm along the same direc-tion (Fig. 3g).Triplet-triplet annihilationLastly, at high excitation densities, triplet-triplet annihilation (TTA)can dominate the photo-physics of pentacene and influence sub-sequent triplet transport and decay pathways. To study the effects ofTTA in the ultrafast regime, we study the 740 nm band in the high(a) (b)(g)(d) (e)(f )(c)cabbcaSiO2hBNFig. 3 | Singlet fission dynamics at 670nm and 250μJ cm−2. a Measured radiallyaveraged ΔT/Tmap and spatially averaged signal kinetic. b Fit of the optical modelto the radial average at 13, 70 and 1000 fs. c Schematic of the measured pentacenefilm on hBN and SiO2 substrates, with labelled crystal geometries relative to thesubstrate. d, e Transient optical constants display the expected signs based onFig. 1b along with a sub-1-ps feature associated with the singlet exciton fissionprocess and subsequent constant JDOS. f Transport in the a,c-crystal plane mea-sured in-plane on SiO2 (blue) and along the a-crystal direction measured out-of-plane on hBN (orange) displays a 25 nm 70 fs expansion, which can be resolved inσa,c (dashed line is exponential fit). g Transport in the b,c-crystal planemeasured in-plane on hBN (orange) and along the b-crystal direction measured out-of-plane onSiO2 (blue) displays a 30 nm 180 fs expansion (dashed lines are exponential fit).Article https://doi.org/10.1038/s41467-022-33647-5Nature Communications |         (2022) 13:5963 5fluence regime at 750μJ cm−2 (Fig. 4)31. At these densities, there is onaverage one photoexcitation per 30 pentacene molecules and thespatiotemporal dynamics show a decay over the first picosecond(Fig. 4a). Even in the high-density limit, our model satisfactorilycaptures the measured data demonstrating robustness to the mag-nitude of the external ~n perturbation (Fig. 4b). We find that both Δnand Δk decay as a function of time as would be expected for areduction in the JDOS of triplets through a TTA process, again, withnear identical response irrespective of the crystal orientation(Fig. 4c–e).As the exciton-exciton annihilation cross-section scales with theexciton density, the decay rate varies spatially over the photoexcita-tion profile. With time, this leads to a flat-topped exciton densityprofile, which when approximated as a Gaussian in Eqn. (4), results inan apparent expansion39.We resolve the apparent expansion fromTTAin thea,c-crystal plane throughbothmeasured in-plane throughσa,conSiO2 and out-of-plane through Δza on hBN (Fig. 4c, f). We resolve asimilar expected apparent expansion in the b-crystal direction, sug-gesting that the TTA process is isotropic (Fig. 4g). The fast timescalefor the onset of TTA suggests that such free triplets are formed within200 fs in pentacene as TTA typically occurs for spatially separatedtriplets, i.e., T...T. This fast triplet annihilation process must be tohigher lying triplet states and not back to the singlet manifold as thelatter process is endothermic and would be expected to occur onlonger timescales. The fast sub-200 fs transport along the b-crystal axisseen in the low-fluence regime at 250μJ cm−2 also appears to bepresent in the high-density regime, suggesting that this feature isrelated to the singlet fission process.To summarise, we have utilised interferometric pump-probemicroscopy to reveal the three-dimensional picture of singlet excitonfission and triplet annihilation inmicrocrystalline pentacene films withsub-10 nm spatial precision and 15 fs temporal resolution. Our resultssuggest that the photoexcited singlet exciton expands along thedirection of maximal orbital π-overlap in the crystal a,c plane to formcorrelated triplet pairs, which subsequently decouple into free tripletsalong the crystal b-axis due to molecular sliding motion of neigh-bouring pentacene molecules. The fast formation of free triplets inpentacene results in the fast onset of isotropic triplet annihilationdynamics at high excitation densities, critical to applications of singletfission that utilise triplets. Our technique is not limited to studyingexcitons in pentacene through optical pump-probe techniques onfemtosecond timescales, but can be applied for other pump-probeschemes involving electron or X-ray sources over any experimentallyaccessible timescale40. Going forward our approach will enable directinsights into the transport of excitations in a range of condensedmatter systems over a variety of timescales.MethodsPump-probe microscope setupThe design of the pump-probe microscopy setup was detailedpreviously12,17. Here, a pump pulse (560 nm, 13 fs) is focused onto thesample with the objective to produce a near-diffraction-limited local(a) (b)(g)(d) (e)(f )(c)cabbcaSiO2hBNFig. 4 | Fast triplet annihilation dynamics at 740nm and 750μJ cm−2.aMeasured radially averaged ΔT/T map and spatially averaged signal kinetic. b Fitof the optical model to the radial average at 45, 70, and 1000 fs. c Schematic of themeasured pentacene film on hBN and SiO2 substrates, with labelled crystal geo-metries relative to the substrate. d, e Transient optical constants display theexpected signs based on Fig. 1b and the JDOS decays due to triplet-triplet annihi-lation expected at these fluences. f, g Apparent transport due to the density-dependent TTA cross-section is seen on both SiO2 and hBN and appears to beisotropic.Article https://doi.org/10.1038/s41467-022-33647-5Nature Communications |         (2022) 13:5963 6photoexcitation. After a variable time delay, a counter-propagatingwidefield probe pulse (750 nm, 7 fs, ~20μm full-width-half-maximum)is transmitted through the sample and imaged onto an emCCD cam-era (Rolera Thunder, QImaging). Widefield probe images in the pre-sence and absence of the pump excitation are recorded by choppingthe pumppulse at 40Hz. The pumpandprobe pulses are derived froma Yb:KGW amplifier (1030 nm, 5W, 200 kHz, 200 fs, LightConversion)via white-light-continuumgeneration and subsequent spectralfilteringand compression with chirped mirrors (Supplementary Note 1)12,17.Fabrication of the hBN-pentacene samplehBN crystals were synthesized at 4 GPa and 1600 °C for 240 hours withBa-BN solvent by using Belt-type high pressure apparatus. 100 nm thickhBN flakes were exfoliated from bulk crystals on a glass substrate.100 nmonpentacenewas then evaporated on the sample. Thin films ofpentacene were prepared by thermal evaporation in an ultrahighvacuum environment of 10−8 mbar at a constant evaporation rate of0.02 nm/s. The rate was monitored using a calibrated quartz crystalmicrobalance and the deposition was stopped once the desired filmthickness of 100nmwasobtained. Thedepositionwasdoneonto 1mm-thick quartz substrates and 0.2mm-thick glass coverslips that werecleaned by sequential sonication in acetone and isopropyl alcohol.Data availabilityThe data that support the plots within this paper and other findings ofthis study are available at the University of Cambridge Repository(https://doi.org/10.17863/CAM.88392).References1. Anderson, P. W. Absence of diffusion in certain random lattices.Phys. Rev. 109, 1492–1505 (1958).2. Klitzing, K. V., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based onquantized hall resistance. Phys. Rev. Lett. 45, 494–497 (1980).3. Giannini, S. et al. Quantum localization anddelocalization of chargecarriers in organic semiconducting crystals. Nat. Commun. 10,3843 (2019).4. Troisi, A. & Orlandi, G. Charge-transport regime of crystallineorganic semiconductors: diffusion limited by thermal off-diagonalelectronic disorder. Phys. Rev. Lett. 96, 086601 (2006).5. Hahn, W. et al. Evidence of nanoscale anderson localizationinduced by intrinsic compositional disorder in ingan/gan quantumwells by scanning tunneling luminescence spectroscopy. Phys.Rev. B 98, 045305 (2018).6. Zong, A., Kogar, A. & Gedik, N. Unconventional light-induced statesvisualized by ultrafast electron diffraction and microscopy. MRSBull. 46, 720–730 (2021).7. Hildner, R., Brinks, D. & van Hulst, N. F. Femtosecond coherenceandquantumcontrol of singlemolecules at room temperature.Nat.Phys. 7, 172–177 (2010).8. Miyata, K., Conrad-Burton, F. S., Geyer, F. L. & Zhu, X.-Y. Triplet pairstates in singlet fission. Chem. Rev. 119, 4261–4292 (2019).9. Chan, W.-L. et al. The quantum coherent mechanism for singletfission: experiment and theory. Acc. Chem. Res. 46,1321–1329 (2013).10. Rao, A.& Friend, R. H. Harnessing singlet excitonfission tobreak theshockley–queisser limit. Nat. Rev. Mater. 2, 17063 (2017).11. Smyser, K. E. & Eaves, J. D. Singlet fission for quantum informationand quantum computing: the parallel JDE model. Sci. Rep. 10,18480 (2020).12. Sung, J. et al. Long-range ballistic propagation of carriers inmethylammonium lead iodide perovskite thin films. Nat. Phys. 16,171–176 (2019).13. Bretscher, H. M. et al. Imaging the coherent propagation of col-lective modes in the excitonic insulator ta2nise5 at room tem-perature. Sci. Adv. 7, eabd6147 (2021).14. Delor, M., Weaver, H. L., Yu, Q. & Ginsberg, N. S. Imaging materialfunctionality through three-dimensional nanoscale tracking ofenergy flow. Nat. Mater. 19, 56–62 (2019).15. Pandya, R. et al. Microcavity-like exciton-polaritons can be the pri-mary photoexcitation in bare organic semiconductors. Nat. Com-mun. 12, 6519 (2021).16. Sneyd, A. J. et al. Efficient energy transport in an organic semi-conductormediated by transient exciton delocalization.Sci. Adv. 7,eabh4232 (2021).17. Schnedermann, C. et al. Ultrafast tracking of exciton and chargecarrier transport in optoelectronic materials on the nanometerscale. J. Phys. Chem. Lett. 10, 6727–6733 (2019).18. Sheik-Bahae, M., Said, A., Wei, T.-H., Hagan, D. & Stryland, E. V.Sensitive measurement of optical nonlinearities using a singlebeam. IEEE J. Quantum Electron. 26, 760–769 (1990).19. Wang, J., Sheik-Bahae, M., Said, A. A., Hagan, D. J. & Stryland, E. W.V. Time-resolved z-scan measurements of optical nonlinearities. J.Optical Soc. Am. B 11, 1009 (1994).20. Conforti, M. & Della Valle, G. Derivation of third-order nonlinearsusceptibility of thin metal films as a delayed optical response.Phys. Rev. B 85, 245423 (2012).21. Richards, B. & Wolf, E. Electromagnetic diffraction in optical sys-tems, II. structure of the image field in an aplanatic system. Proc. R.Soc. London. Ser. A. Mathe. Phys. Sci. 253, 358–379 (1959).22. Born, M. & Wolf, E. Principles of Optics: Electromagnetic Theory ofPropagation, Interference and Diffraction of Light. 7th edn. (Cam-bridge University Press, 1999).23. Gibson, S. F. & Lanni, F. Diffraction by a circular aperture as amodelfor three-dimensional optical microscopy. J. Opt. Soc. Am. A 6,1357 (1989).24. Lee, I.-B. et al. Three-dimensional interferometric scatteringmicroscopy via remote focusing technique. Opt. Lett. 45,2628 (2020).25. Wilson, M. W. B. et al. Ultrafast dynamics of exciton fission inpolycrystalline pentacene. J. Am. Chem. Soc. 133,11830–11833 (2011).26. Marciniak, H. et al. Ultrafast exciton relaxation in microcrystallinepentacene films. Phys. Rev. Lett. 99, 176402 (2007).27. Ashoka, A. et al. Extracting quantitative dielectric properties frompump-probe spectroscopy. Nat. Commun. 13, 1437 (2022).28. Mahmoodabadi, R. G. et al. Point spread function in interferometricscatteringmicroscopy (iSCAT) part i: aberrations in defocusing andaxial localization. Opt. Express 28, 25969 (2020).29. Aguet, F., Ville, D. V. D. & Unser, M. A maximum-likelihood formal-ism for sub-resolution axial localization of fluorescent nano-particles. Opt. Express 13, 10503 (2005).30. Amsterdam, S. H. et al. Tailoring the optical response of pentacenethin films via templated growth on hexagonal boron nitride. J. Phys.Chem. Lett. 12, 26–31 (2020).31. Poletayev, A. D. et al. Triplet dynamics in pentacene crystals:applications to fission-sensitized photovoltaics. Adv. Mater. 26,919–924 (2013).32. Seiler, H. et al. Nuclear dynamics of singlet exciton fission in pen-tacene single crystals. Sci. Adv. 7, eabg0869 (2021).33. Rao,A.,Wilson,M.W.B., Albert-Seifried, S.,Di Pietro, R.&Friend,R.H.Photophysics of pentacene thin films: the role of exciton fission andheating effects. Phys. Rev. B 84, 195411 (2011).34. Bakulin, A. A. et al. Real-time observation of multiexcitonic states inultrafast singlet fission using coherent 2d electronic spectroscopy.Nat. Chem. 8, 16–23 (2015).Article https://doi.org/10.1038/s41467-022-33647-5Nature Communications |         (2022) 13:5963 7https://doi.org/10.17863/CAM.8839235. Alvertis, A. M. et al. Impact of exciton delocalization on exciton-vibration interactions in organic semiconductors. Phys. Rev. B 102,081122 (2020).36. Giannini, S. et al. Exciton transport in molecular organic semi-conductors boosted by transient quantum delocalization. Nat.Commun. 13, 2755 (2022).37. Zaykov, A. et al. Singlet fission rate: optimized packing of a mole-cular pair. ethylene as a model. J. Am. Chem. Soc. 141,17729–17743 (2019).38. Refaely-Abramson, S., da Jornada, F. H., Louie, S. G. & Neaton, J. B.Origins of singlet fission in solid pentacene froman ab initio green’sfunction approach. Phys. Rev. Lett. 119, 267401 (2017).39. Deng, S. et al. Long-range exciton transport and slow annihilation intwo-dimensional hybrid perovskites. Nat. Commun. 11, 664 (2020).40. Latychevskaia, T. Three-dimensional structure from single two-dimensional diffraction intensitymeasurement. Phys. Rev. Lett. 127,063601 (2021).AcknowledgementsA.A. and C.S. thank René Lachmann for stimulating discussions onoptical modelling. A.A. acknowledges funding from the Gates Cam-bridge Trust as well as support from the Winton Programme for thePhysics of Sustainability. A.V.G. acknowledges funding from the Eur-opean Research Council Studentship and Trinity-Henry Barlow Scho-larship. C.S. acknowledges financial support from the RoyalCommission of the Exhibition of 1851. K.W. and T.T. acknowledge sup-port from JSPS KAKENHI (Grant Numbers 19H05790, 20H00354 and21H05233) andA3Foresight by JSPS.Weacknowledgefinancial supportfrom the EPSRC via grants EP/M006360/1 and EP/W017091/1 and theWinton Program for the Physics of Sustainability. This project hasreceived funding from the European Research Council (ERC) under theEuropean Union’s Horizon 2020 research and innovation programme(grant agreement no. 758826).Author contributionsA.A. conceived the project, built the optical model, performed theoptical experiments, analysed and interpreted the data and wrote themanuscript. N.G. designed the sample, exfoliated the hBN and per-formed the AFM measurements. A.V.G. and N.S. prepared the penta-cene films. A.A., A.J.S. and J.S. built the experimental setup. K.W. andT.T. provided the hBN crystals. C.S. and A.R. supervised the project. Allauthors discussed the results and contributed towriting themanuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-022-33647-5.Correspondence and requests for materials should be addressed toChristoph Schnedermann or Akshay Rao.Peer review information Nature Communications thanks the anon-ymous reviewer(s) for their contribution to the peer review of thiswork. Peer reviewer reports are available.Reprints and permission information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jur-isdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons license, and indicate ifchanges were made. The images or other third party material in thisarticle are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is notincluded in the article’s Creative Commons license and your intendeduse is not permitted by statutory regulation or exceeds the permitteduse, you will need to obtain permission directly from the copyrightholder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2022Article https://doi.org/10.1038/s41467-022-33647-5Nature Communications |         (2022) 13:5963 8https://doi.org/10.1038/s41467-022-33647-5http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Direct observation of ultrafast singlet exciton�fission in three dimensions Results and discussion Experimental setup and optical model Loss of triplet pair electronic correlation Singlet to correlated triplet transition Triplet-triplet annihilation Methods Pump-probe microscope setup Fabrication of the hBN-pentacene sample Data availability References Acknowledgements Author contributions Competing interests Additional information