NANOSCALE APPLICATIONS OF QED - U.TORONTO

8/6/2019 NANOSCALE APPLICATIONS OF QED - U.TORONTO

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nature materials| VOL 5 | SEPTEMBER 2006 | www.nature.com/naturematerials 683

Excitons in nanoscale systemsNanoscale systems are forecast to be a means of integrating desirable attributes of molecular and

bulk regimes into easily processed materials. Notable examples include plastic light-emitting devices

and organic solar cells, the operation of which hinge on the formation of electronic excited states,

excitons, in complex nanostructured materials. The spectroscopy of nanoscale materials reveals

details of their collective excited states, characterized by atoms or molecules working together to

capture and redistribute excitation. What is special about excitons in nanometre-sized materials? Here

we present a cross-disciplinary review of the essential characteristics of excitons in nanoscience.

Topics covered include confinement effects, localization versus delocalization, exciton binding energy,

exchange interactions and exciton fine structure, excitonvibration coupling and dynamics of excitons.

Important examples are presented in a commentary that overviews the present understanding

of excitons in quantum dots, conjugated polymers, carbon nanotubes and photosynthetic light-

harvesting antenna complexes.

GREGORY D. SCHOLES*1 ANDGARRY RUMBLES2

1Department of Chemistry 80 St George Street, Institute for

Optical Sciences, and Centre for Quantum Information andQuantum Control, University of Toronto,

Toronto, Ontario M5S 3H6, Canada2National Renewable Energy Laboratory, Chemical and

Biosciences Center, MS3216,

1617 Cole Boulevard, Golden, Colorado 80401-3393, USA

*e-mail: [email protected]

An exciting aspect o nanoscience is that relationshipsbetween structure and electronic properties arebeing revealed through a combination o synthesis,structural characterization, chemical physics andtheory. Spectroscopy is a tool that is sensitive toaspects o the electronic structure o materials. As

such, spectroscopic studies o nanoscale systemsofen provide insights into the collective absorptionand redistribution o excitation energy. Tis vibranteld is the study o excitons in nanoscale systems.Tese electronic excitations dier rom excitonsin bulk materials, and represent a distinct class oexciton that can be thought o either as a connedbulk-type exciton or a molecular excitation. In thisreview or the non-specialist, our aim is to capturethe essence o the eld and highlight areas o currentinterest. For the expert, we aim to provoke cross-disciplinary discussion and emphasize some o thechallenges at the leading edge o the eld. Overall weaim to identiy and discuss characteristic eatures oexcitons in materials with nanometre-size dimensions

or organization. Part o our emphasis is to highlighttopics at the oreront o the eld, and to suggestquestions that should be asked in uture work.

Excitons can be ormed by association o

electrical charge units (ree carriers) or by directphotoexcitation. Te exciton luminescence that canollow this charge association underlies organic light-emitting diode technologies1. Conversely, excitons thatare ormed readily by photoexcitation can dissociateinto ree carriers (unbound electrons and holes) andthus play a central role in photovoltaic and solarcell devices2. Excitons that remain bound and emitlight can be used as laser media3. Tese observationshelp to illustrate the concept o excitons comparedwith ree carriers in bulk materials4. Photoexcitationcreates an electron in the conduction band, leaving ahole in the valence band. I the interaction betweenthe electron and hole is assumed to be negligible

justied when each waveunction is spread over anexpanse o atomsthen the pair are ree carriers. Onthe other hand, an attractive coulombic interactionbetween the electron and hole quasi-particles bindsthem into an exciton. A distinguishing eature oexcitons is that the spatial extent o an electronicexcited state is increased through coherent sharing othe excitation among subunits o the material. Tatcharacteristic is determined by electronic couplingamong the repeat units that make up the material58.

Excitons in nanoscale systems are ormed bylight absorption in molecules such as polyacenesand polyenes, conjugated polymers, quantum dots,molecular aggregates, carbon nanotubes and so on.Te new aspect o excitons that is prevalent in, or


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684 nature materials| VOL 5 | SEPTEMBER 2006 | www.nature.com/naturematerials

even denes, nanoscience is that the physical size andshape o the material strongly inuences the natureand dynamics o the electronic excitation. Tereore, adeciding property o excitons in nanoscale systems isthat the exciton size is dictated not by the electronholeCoulomb interaction, but by the physical dimensionso the material or the arrangement o distinctbuilding blocks. Tat interests the chemist because

excitons can be engineered in a material accordingto structure. It is o interest to physicists because thespatial connement o the exciton accentuates manyo its interesting physical properties, exposing themor examination. Te theorist may conclude thatperhaps we should not try to orce-t existing theoriesto model excitations in nanostructures as they ofencarry with them assumptions that we have orgotten,or that we erroneously ignore. Nanoscale materialsthus provide both a testbed and an inspiration or newquantum mechanical approaches to the calculationo electronic properties o large systems. Trough thestudy o excitons in nanoscale systems we are learningsome general rules dening how size and shape tunes

electronic structure and dynamics. In Fig. 1a summaryo excitons in bulk materials (adapted rom re. 6) isextended to indicate how excitons in nanoscale systems

dier. An overview and introduction to elements oexcitons in nanoscale systems is given in Box 1.

A challenge in this eld is that the materialsunder investigation are ofen complex; they containmany atoms, they can be structurally disorderedor inuenced by surace eects, and samples ofenhave an inhomogeneous composition in terms ostructural disorder and size polydispersity. We

attempt below to provide some insights into howsuch hurdles have been overcome. Questions beingaddressed include: can the properties o connedexcitons be used to change the way that solar cellsor lasers operate? How should we transer thelanguage o solid-state physics to organic systems9,and vice versa?

A uniying theme in nanoscience is that size andshape are important. How best can we understandand compare nanomaterials and the implicationso size-tunable properties or excitons? A powerulapproach is to combine experiment and theory.However, owing to the intermediate length scalescharacteristic o many nanomaterials, unique

challenges or theory are presented. For example,the huge number o electrons presents di cultiesor molecular-type electronic structure calculations,

Box 1: An introduction to excitons in nanoscale systems

1. Bands and molecular orbitals or extended systemsPeriodic, strongly coupled molecular or atomicsystems are characterized by a high density odelocalized orbitals that orm the valence (VB)and conduction (CB) bands. Tose bands can berepresented in real space as shown on the lef side

o the diagram, or equivalently, the energy o eachband can be plotted against its wave vector k, as inthe right schematic. Excitation o an electron romVB to CB creates ree carriers. Te minimumenergy required is that o the bandgap, Eg.

k= 1k= 0

k= 0k= 1

Eg

CB

VB

0k

/a

2. Excitons in extended systems: bound electronhole pairs

Te language that describes the eatures o thequasi-particle approach is nicely intuitive. Anexciton in a spatially entended system is describedas a neutral excitation particle:an electronholepair. In an exciton the electron and hole are boundby the electron-hole Coulomb interaction. In thechemists electronelectron language, the attractionderives rom decreased electronelectron repulsionintegrals in the excited state conguration comparedwith the ground state, thus lowering the energyo that conguration relative to the continuum bythe exciton binding energy, Eb = Eg Ex. Relatedelectronhole exchange interactions mix theHartreeFock (single particle) congurations, sothat the exciton states are nally obtained througha conguration interaction (CI-singles) calculation.Correct spin eigenstates can only be obtainedby antisymmetrizing waveunctions and mixingcongurations through exchange interactions.

Photoconduction band

Exciton bands

Ground state

Ex


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which scale steeply with the number o electrons,

yet the importance o atomic-scale details needsto be captured. Great progress has been madein solving such problems, as has been reviewedelsewhere1013. In this review we will cover ourbroad topics o importance in the spectroscopyo excitons in nanoscale systems. o illustrate theways in which excitons in nanoscale systems areunique or interesting, and to ormulate some generalobservations that may stimulate cross-disciplinarydiscussion, we will describe examples pertainingto quantum dots, conjugated polymers, carbonnanotubes and photosynthetic light-harvestingantenna complexes within each o these subjectareas. We begin by providing some background oneach material.

OVERVIEW OF THE MATERIALS

PHOTOSYNTHETIC LIGHT-HARVESTING COMPLEXES

Proteins organized in the photosynthetic membraneso higher plants, photosynthetic bacteria and algaeaccomplish the capture o incident photons (light-harvesting), subsequent spatial redistribution othat excitation energy, and the ultimate trappingo the energy via photo-induced electron transer,with remarkably high e ciencies14. Suspensions osuractant-isolated light-harvesting complexes (knownas LH2) rom purple bacteria provide a good example.Tey show two absorption bands (Fig. 2), attributedto two distinct arrangements o bacteriochlorophyll-a(Bchl) molecules. Te B800 absorption band is due to

3. Molecular orbital picture or confned systems

Occupied (in the ground state) and virtualmolecular orbitals or a series o polyacenes. As theconjugation size increases, the bandgap decreases

and the density o states increases. Tese quantumsize eects derive rom changes in electronelectron interactions that are proportional tomolecular orbital waveunction delocalization. Asingle-excitation conguration is constructed byexcitation o an electron rom an occupied to a

virtual orbital. Tat conguration is delocalizedover the extent o the molecule. However, to beconsistent with the denition o an exciton in anextended system, the change in electronelectroninteractions afer excitation needs to be consideredto describe the exciton. Te single-excitationcongurations are mixed by exchange interactionsso that each excited state exciton state is

a linear combination o the single-excitationcongurations. A maniold o singlet and tripletexcitons are thus obtained.

4. Spectroscopy o molecular excitons

Absorption spectra o a series o naphthyl dimermolecules117 compared with a monomeric modelchromophore (dashed line). Te dimer spectraconsist o two bands, with a splitting equal to theelectronic coupling HLRbetween the naphthylgroups on the lef (L) and right (R), indicatingthat the excitation is shared between the twochromophores: a molecular exciton. A schematic

diagram o the relative energies and waveunctionso the napthyl moieties compared to the dimer isgiven below. Te redshif o the centre o gravity othe exciton bands is due to orbital mixing eects.Tese interactions induce the electron and hole todelocalize over the subunits. Model dimers suchas shown here allow or detailed examination ointerchromophore interactions, including realistictreatment o solvation118. (Spectra reprintedwith permission rom re. 117. Copyright (1993)American Chemical Society).

Extinctioncoefficient

(mol1dm3cm1)

38 42 46 50

Energy (103 cm1)

2HLR

2 L* LR*)R1 =1

2 (

1 L* LR*)R+1 =1

2 (

2

1

0

1

2

Eigenvalue

Box 1: Continued


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a ring o essentially non-interacting Bchl molecules(nearest-neighbour electronic coupling ~30 cm1). TeB850 band, however, is the absorption into the opticallybright exciton states characteristic o the ring ostrongly interacting Bchl molecules (nearest-neighbourelectronic coupling ~300 cm1). Here is an example oelectronic coupling among molecules that creates a newchromophore: a Frenkel exciton. Te excitons that areo interest in these systems include Frenkel excitons,but are primarily weakly coupled localized excitations15.

Relatively weak electronic coupling amongst the manyhundreds o chromophores that are bound in light-harvesting proteins enables the excitation energy tobe unnelled e ciently through space to reactioncentre proteins16.

In Fig. 2 a simple light-harvesting antennaprotein, PE545, is shown together with a sketch othe organization o the photosynthetic membrane o

a type o cryptophyte algae17. Each PE545 antennaprotein binds eight chromophores, as seen in thestructural model. Such model systems, where weknow the precise arrangement o light-absorbingmolecules, have provided superb model systemsor learning about molecular excitons (also knownas Frenkel excitons; see Fig. 1) and electronic(resonance) energy transer. Electronic energy transerallows excitation energy absorbed by an antennaprotein to migrate rapidly (over a ew picoseconds)to the peripheral chromophores, circled in thegure, then transer into the core antenna o one othe membrane-bound photosystems, PS I or PS II(50100 ps). In most organisms the antenna protein

is also membrane-bound. Te unnelling o excitationenergy to the photosynthetic reaction centres involvesmany tens o hops, occurring on timescales o100 s to 100 ps. Tese ast, light-initiated processesoccurring in proteins isolated rom photosyntheticorganisms have been studied in great detail overthe past years14,17. It has become evident that theorganization o light-absorbing molecules (usuallychlorophylls and carotenoids) on the nanometrelength scale provides importantsometimes subtleand ingeniousoptimizations that control lightcapture and unnelling18.

CONJUGATED POLYMERS

Conjugated polymers are highly conjugated linearmacromolecules that are o great current interestbecause o their semiconductor-like propertiesand ease o processing. Excitons in conjugatedpolymers such as unctionalized poly(phenylene

vinylene) (or example MEH-PPV, poly[2-methoxy-5-(2-ethyl)hexyloxy-1,4-phenylene

vinylene]) and alkyl polyluorenes have beenintensively studied rom both experimentaland theoretical viewpoints to understand theirnature and dynamics. wo basic types o excitonhave been identiied: intrachain and interchain.he ormer are ormed by the extended -

conjugation along sections o the polymerbackbone. Interchain excitons orm when twochain segments couple through space, eitherbecause the chains are near to each other in a solidilm, or because the chain is olded back on itsel.hus optical properties depend strongly on theaggregation state o the polymer. Details can beound in recent reviews1922.

Conjugated polymer excitons play importantroles in electroluminescent and photovoltaic devices,and some intriguing properties relevant to deviceoptimization have been reported. For example, theobservation o wavelength-dependent photocurrentgeneration in MEH-PPV was explained by analysiso quantum chemical calculations that revealed

Bulk materials Nanomaterials

Electron,hole

Bloch functions

delocalized bands

WannierMott

exciton model

Frenkel

exciton model

A general

exciton model

Atomic ormolecular basis

localized excitations

}

}

Confinement

Delocalization

Discrete optical

transitions

Increased excitonbinding energy

Enhanced singlettriplet

exchange interaction

Increased absorption

coefficient and nonlinear optical

properties

Decreased exciton

binding energy

Diminished singlettriplet

exchange interaction

Dielectricconstant

High

Low

*

*

*

*

*

*

Figure 1 Excitons in nanoscale systems. The diagram

relates the Wannier and Frenkel exciton models and sketches the

basis for describing excitons. The description may proceed from

delocalized bands, wherein the electron and hole may move freely

throughout the material. Such a model can be used to model

excitons in crystalline materials with high dielectric constant,

such that electronhole Coulomb interactions are small compared

with the bandgap of the material. One may also develop a model

starting from a localized basis set. The tight-binding model is

an example of this approach. In their usual implementation,either approach contains approximations or limitations that

restrict its application. A general exciton model overcomes

such limitations, and contains all the key features necessary to

describe the excited states of a molecule as well as an infinite

system. Nanoscale excitons can be described starting from the

point of view of either a delocalized or a localized excitation. In a

delocalized representation of the problem, nanoscale excitons are

subject to quantum confinement, and their spectroscopy becomes

richer. With respect to a model based on localized functions,

nanoscale materials can sustain more delocalized excitations.

The Frenkel model uses the point of view, particularly useful for

molecular aggregates, that the wavefunction is separable into

distinct electron groups tightly associated with each repeat unit.

Such an approach is applied to molecular excitons, such as a

photosynthetic excitons or J-aggregates.


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signicant changes in mixing o congurationwaveunctions o the polymer23. Tat is, the electronicmake-up o higher-energy excitons diers romexcitons at the optical gap in such a way that mixingwith extended charge-separated states is increased. Achallenge now is to elucidate a microscopic picturethat explains observations o interacial excitons inheterojunction polymer blends24. Evidence suggests

that such excitons can reversibly dissociate intoan exciplex (an excited-state hetero-complex)25,in which the electron and hole become spatiallyseparated. In that case the Frenkel exciton modelbreaks down because in the excited state electrondensity is transerred rom one molecule to the other.Dissociation o an exciplex produces geminate ionpairs that might play important intermediate roles inelectronhole dissociation or capture processes26.

SEMICONDUCTING SINGLE-WALL CARBON NANOTUBES

Te spectroscopy o semiconducting carbonnanotubes (CNs)27 has been o great interest

in the last ew years. CNs are ormed in a greatvariety o sizes and types, and typically aggregateinto macroscopic bundles. Until recently, theaccepted description o their electronic states andspectroscopy was a simple model that neglectedinteractions between electrons. However, that

viewpoint changed as a result o the report obandgap uorescence or CNs28, made possibleby suractant isolation o individual tubes or smallbundles o tubes, thus providing samples withoutlarge bundles and ropes in which uorescenceis quenched. Although it was not immediatelyrecognized, that observation provided clear evidenceor excitons in CNs, supporting the earlier

predictions o Ando29

.Not surprisingly, the key advance underpinningthe observation o CN exciton uorescence wasmaterial preparation. Nonetheless, optical spectraare highly inhomogeneously broadened, as shown inFig. 3, by a sum o contributions rom a series o CNmacromolecules. A plot o excitation energy versusuorescence emission, Fig. 3b reveals distinct peakscorresponding to a series o individual tube types30,which in combination with simple theory has allowedassignment o the spectral eatures to the variouschemical types and sizes o CNs. Nanotube typesare designated by the chiral index (n,m), accordingto how the parent graphene sheet is rolled up to orm

a tube31

. Te uorescence data30

made it possible toassign the optical transitions and elucidate their size-evolution. An interesting observation rom inspectiono the uorescence spectra is that spectral linewidthsare narrow, being ~30 meV at room temperature32;this is probably a result o exchange narrowing33,whereby the linewidth is reduced because thedelocalized exciton states average over disorder in thesite energies o primitive cells.

SEMICONDUCTOR QUANTUM DOTS

Semiconductor quantum dots (QDs), or nanocrystals,are nanometre-sized crystallites that can be preparedwith great tunability o size and shape through

colloidal routes3438. Sel-assembled QDs can be ormedspontaneously in a semiconductor heterostructuregrown using molecular beam epitaxy39,40. ypically,sel-assembled QDs are lens-shaped, having a diametero tens o nanometres and a height o a ew nanometres,whereas colloidal QDs are usually spherical with radiio 1 to 4 nm and contain around 200 to thousandso atoms. Te most common materials studied withrespect to excitons include CuCl, CdSe, CdS, Cde, InP,PbSe and PbS. In the early 1980s it was predicted thatQDs should possess discrete electronic energy levels,more like molecules than bulk semiconductors41,42.

ATPasePS ll

PS l

Chl a/c

PE545

B800

B850

700 750 800 850 900

Wavelength (nm)

Absorbance

Figure 2 Frenkel excitons in photosynthesis. Left, the structure of a simple light-harvesting

protein PE545 isolated from a marine cryptophyte algae. It binds eight light-absorbing molecules

(blue). A cascade of electronic energy transfer steps equilibrates excitation, over timescales of tens

of femtoseconds to a few tens of picoseconds, to the periphery of the protein, onto the encircled

chromophores17. Ultimately that excitation is transferred into core antenna complexes associated with

the reaction centres, photosystems I and II (PS I and PS II), organized in the thylakoid membrane as

indicated schematically. (Bottom left image adapted from C. D. de Witt et al., submitted to J. Phys.

Chem B.)PE545, unlike the peripheral light-harvesting complexes of higher plants (LHC-II) or purple

bacteria (LH2), is not membrane-bound. Right, the light-harvesting antenna of purple bacteria, LH2,

is an example of a system whose spectroscopy is characteristic of a molecular exciton. The structural

model shown at the top emphasizes the -helices serving as a scaffold binding the light-absorbingmolecules. These molecules are shown in the simplified structural model below, indicating the

B850 ring (red), B800 ring (yellow) and cartenoids (blue). The absorption spectrum clearly shows

the marked distinction between the B800 absorption band, arising from essentially monomeric

bacteriochlorophyll- a(Bchl) molecules, and the redshifted B850 band that is attributed to the optically

bright lower exciton states of the 18 electronically coupled Bchl molecules.


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Tat idea was conrmed through an accumulation oexperimental work34. QDs are clearly dierentiatedrom molecules in that many properties have analoguesin those o bulk semiconductors, spinorbit couplingcan be signicant, and they have large dielectricconstants. An important consideration in decidingconnement o the exciton to the QD, in particular thesize o the waveunction compared to that o the QD,is the dielectric medium surrounding the QD40,43. Inthe coming years, shape-dependent photophysics oQD excitons will be topical, driven by recent syntheticbreakthroughs44. Electron micrograph images o a

range o CdSe QD shapes are shown inFig. 4c.Nanoscale exciton engineering epiaxial growtho one semiconductor over another opens urtherpossibilities or improving surace passivation, changingexcited state dynamics o the exciton, or manipulatingwaveunctions, thereby increasing the diversity oexciton photophysics that can be examined36.

SIZE-TUNABLE SPECTROSCOPY AND EXCITONS

What are the unique aspects o excitons innanometre-sized materials? Certainly theprevalence o size-dependent properties is notable.A myriad o electronic properties are governed bysize, including the bandgap, the exciton binding

energy, and the exchange interactions. hesequantities determine the spectroscopic stateso the material and its (photo-)electrochemicalproperties. he goal o this section is to establishthe spectroscopic signatures o excitons innanoscale systems and to suggest notable aspectso their spectroscopy.

Size-tunable spectroscopic properties have been

o great interest or over hal a century45, althoughrecent interest has centred on QDs. Te Bohr radiuso a semiconductor exciton provides a reerence as tothe exciton size in the bulk. Size-tuning o propertiesin QDs is attributed to connement o the excitonin a nanocrystal signicantly smaller than the bulkexciton. For example, the exciton Bohr radius o PbSis ~20 nm and its bulk bandgap is 0.41 eV. Absorptionspectra or PbS QDs46 o radii ranging rom ~1.3 to~3.5 nm are shown in Fig. 5, revealing QD excitonenergies in the range 0.7 to 1.5 eV.

Te spectroscopic properties o molecularmaterials that scale in size can be elucidated ingreat detail, thus providing a oundation or a

deeper understanding o spectroscopic measureso excitons in nanoscale materials. Te sizedependence o exciton transition energies or arange o organic30,45 and QD4649 materials is plottedin Fig. 5. Measurement o the exciton energy doesnot directly reveal inormation that allows usto learn generally about excitons by comparingdierent materials. For example, size-tunable opticalproperties derive primarily rom the bandgap, notthe exciton. Te bandgap is the energy dierencebetween occupied and unoccupied orbitals. Tatprovides only a starting point or establishing theexcitation energy because, rst, the electronicexcited-state waveunction is not accurately written

as a one-electron excitation between these orbitals.For example, to develop a theory or calculatingelectronic spectra Pariser and Parr50 decided thata method involving antisymmetrized productwaveunctions and conguration interaction wasessential. Second, the interactions between electronsin the excited state dier rom those or ground-statecongurations. Tere is lower repulsion betweenelectrons in an excited state than in a closed-shellground state because a pair o electrons can occupydierent orbitals. Tat decreased electronelectronrepulsion gives the exciton binding energy. Inaddition, an associated quantum mechanical eectarises, known as the exchange interaction. Both o

these eects are intimately tied to the size o theexciton because that parameter dictates the averageelectronelectron separation.

Te exchange interaction plays a central role indetermining the ordering o electronic spin statesin any material. An exchange interaction raises theenergy o each singlet state and lowers the energy othe three corresponding triplet spin eigenstates. Sucha distinction between singlet and multiplet statesis a traditional backbone to atomic and molecularspectroscopy. Similarly, the exchange interactionmixes the single-excitation congurations in a QD,evident as a splitting between the bright and darkexciton states at the band edge47,51,52 (Fig. 6). QDs withwurtzite structure are complicated by crystal eld

Excitationenergy(eV)

2.3

2.2

2.1

2.0

1.9

1.8

1.7

1.60.9 1.0 1.1 1.2 1.3

Emission energy (eV)

550

600

650

700

750

Excitationwavelength(n

m)

1,400 1,0001,1001,2001,300

Emission wavelength (nm)

0.5 1.0 1.5 2.0 2.5

Energy (eV)

Absorbance

(0,0) (3,0) (4,0) (5,0) (6,0) (7,0)

(1,1) (2,1)

(2,2)

(3,3) (4,3)

(4,4)

(5,3)

(3,2) (4,2) (5,2) (6,2)

(3,1) (4,1) (5,1) (6,1) (7,1)

a1

a2

a

c

b

(9,2)

(8,4)(6,5)

(8,3)

(11,0)

(7,5)

(10,2)(9,4)(8,6)

(8,7)

(9,5)

(10,3)

(11,1)

(12,2)

(7,6)

Figure 3 Excitons in single-

wall carbon nanotubes.

a, The absorption spectrum

of an aqueous suspension of

CNTs made by high-pressure

CO conversion (HiPco),

showing inhomogeneous

line broadening. A single-

wall CNT structural modelis inset. b, CNT size and

wrapping determine the

exciton energies. Samples

contain many different kinds

of tubes, as evident from the

absorption spectrum. However,

by scanning excitation

wavelengths and recording

a map of fluorescence

spectra30, the emission bands

from various different CNTs

can be discerned (see text).

Assignments of the major

emission peaks for this sampleare indicated (T. McDonald, M.

Heben & M. Jones, unpublished

work; cf. ref. 32). c, The index

(n,m) is used to define the

vector Cn = na1 + ma2, which

in turn determines the direction

that the graphene sheet is

rolled to form a particular CNT.

The sheet is rolled so that a

particular lattice point (n,m) is

superimposed with (0,0).


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eects, otherwise the exciton ne structure splitting isdetermined by the same kind o exchange interactionthat splits singlet and triplet states o molecules. Asan exciton is spatially compressed by connement,exchange interactions are increased, as evidenced bylarger singlettriplet splitting. Te distinct manioldo states provides an opportunity in spectroscopy tolearn about the excited states and electronic structure

o nanoscale systems. Te challenge, however, ormaterials such as QDs is that the spectrum is obscuredby inhomogeneous line broadening, so specializedtechniques are required to probe these states.

Te singlettriplet splittings or the conjugatedoligomers5356 are closely comparable to those or thearomatic57 molecule and polyene series58. Te long-range character o the exchange interaction is evidentin the attenuation o the exchange interaction inthe polyenes, polyacenes and conjugated oligomersplotted in Fig. 6. I only one-centre exchangeintegrals contributed to the singlettriplet splitting,it would diminish as the inverse o the length L othese quasi-one-dimensional excitons (that is the

approximation ofen used or solid state materials).It turns out that the splitting alls o approximatelyas L1/3 or each o these materials, which is a result olong-range exchange interactions, clearly signicantover 3 nm. Te polyacenes and conjugated oligomersare less linear than the polyenes: in other wordsthe exciton is about twice as wide (compare thechemical structures). Tat extra width is maniest inthe delocalization o the exciton, through molecularorbital coe cients, hence reducing the magnitudeo the exchange interaction or any length byapproximately a actor o two compared with thecorresponding polyene. One can see, thereore, howthe exchange interaction (singlettriplet splitting)

is a good measure o exciton size, regardless o thechemical structure o a material. It is in that waythat one should think about the CN data59 plottedin Fig. 6. Te exciton is very long, but an increase inCN diameter urther delocalizes the exciton aroundthe tube, reducing the exchange interaction.

We see that nanoscale materials provide aascinating intermediate ground between molecularand bulk materials. Interesting spectroscopicproperties o excitons, which are ofen minuscule inbulk materials, are greatly accentuated in nanometre-sized materials and molecules. For example, theelectronhole exchange interaction is o the order omillielectronvolts in bulk semiconductor materials,

but is increased 1,000-old in QDs51,6065

. Tat isstill several hundred times smaller than exchangeinteractions in organic materials that are


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organic materials, long-range exchange interactionsmay modiy that predicted size-dependence andmagnitude. Experimental observation o this splittingseems to be an important next step.

Te basic size-scaling o the dark state/brightstate splitting or the range o QDs ollows a similartrend to that seen or the organic materials, but themagnitudes o the splitting are substantially smaller.

Te main reason or that is that the high dielectricconstant o QDs attenuates the long-range electronelectron repulsion compared with these organicmaterials. It is striking that the exchange interactionsover the range o materials plotted in Fig. 6 aresimilar in magnitude or each QD size. Connemento the QD exciton is in three dimensions, thereorethe exchange is predicted to scale as R3, where R isthe QD radius. Tat is the case or some o the dataplotted here, which include a range o experimentalobservations and good quality calculations. A scalingo ~R3 is ound or brightdark splitting o CdSe,Cde and GaAs QDs. Silicon QDs are calculated toshow R2.6, whereas the splitting or AgI, InAs and InP

scales as R2, or slightly more weakly. Future work mayexpose more details o the spectroscopic signatureso the exciton rom beneath the inhomogeneouslybroadened absorption band. An example was reportedrecently where the dynamics associated with ippingbetween two QD ne-structure states was measured67.

A concluding message is that nanoscale materialso vastly dierent structure and composition can bedirectly compared through spectroscopic signatures oexciton delocalization. Any eect that is determinedby a two-electron integral involving orbitals thatconstitute the exciton is appropriate, although theexchange interaction seems the obvious choice.Finally we note that in this section we have ocused on

strongly delocalized excitons. Te discussion becomesmore complex or consideration o Frenkel excitons.

EXCITON BINDING ENERGY

Te exciton binding energy in a quantum connedsystem can be taken to be the energy dierencebetween the exciton transition energy (optical gap)and the electronic bandgap, as shown in Box 1. Teelectronic bandgap can be written as the dierencebetween the ionization potential and electrona nity, assuming no structural relaxation o thematerial or its surroundings68. Tis Coulomb energy,thought o as electronhole attraction, assumes

marked signicance in nanoscale materials. In thissection we discuss the binding energy o excitonsin various materials, aiming to understand how tothink about connement in terms o the prevalenceo excitons as elementary excitations. We give urtherexamples that illustrate how the size and bindingenergy o an exciton can be dynamic, changingconsiderably rom optical absorption to equilibrationprior to photoluminescence emission.

In a bulk semiconductor material with highdielectric constant, the exciton binding energy istypically small: 27 meV or CdS, 15 meV or CdSe,5.1 meV or InP and 4.9 meV or GaAs. Excitons arethereore not a distinctive eature in the spectroscopyo such materials at room temperature, making them

5

4

3

2

1S

0

S1

excitationenergy(eV)

Conjugated oligomers

Catacondensed

polyacenes

Semiconducting

single-wall CNTs

0.1 1 10 100 1,000

Confinement length (nm)

Quantum dot radius (nm)

0.1 1 10

Ge

CdS

CdSe

lnP

CdTe

PbS

10

1Excitontransitionenergy(eV)

1PV

2PV

3PV

4PV

Fluorescencein

tensity

20,000 30,000 40,000

Energy (cm1) Wavelength (nm)

Absorbance

600 900 1,2001,5001,800

b

d

a

c

Figure 5 Size dependence of exciton transition energies. Loglog plots of excitation energy

versus confinement length (dimension) of the ground and first excited states. For CNTs, the confinement

dimension is taken to be the tube diameter. For the other organic materials it is the approximate

conjugation length from end to end. a, Organic materials. Squares show data for the series of aromatic

molecules45 naphthalene, anthracene, naphthacene, pentacene and hexacene. Triangles indicate data

for some oligomers that serve as models for conjugated polymers: methyl-substituted ladder-type

poly(p-phenylene) (MeLPPP), poly(2,7-(9,9-bis(2-ethylhexyl)fluorene)) (PF2/6)53,54, oligofluorenes56 and

oligothiophenes55. Data were typically recorded for samples at 80 K. The filled circles show CNT data

recorded at ambient temperature30. b, Size-tuning of excitation energies for various QD materials: Ge49,

calculated using ab initiodensity functional theory using SCF, CdSe, CdS and CdTe (ref. 48), measuredat 250 K, PbS (ref. 46), measured at 293 K, and InP (refs 47,61)measured at 10 K. c, The size-scaling

of conjugated molecules, for example phenylenevinylene (PV) oligomers120, derives from size-limited

delocalization of the molecular orbitals. Absorption and fluorescence spectra are shown as a function of

the number of PV repeat units. d, In semiconductor QDs, the small size of the nanocrystal compared with

the exciton in the bulk material confines the exciton. A result is size-dependent optical properties, as

shown for the absorption spectra of PbS quantum dots46.


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ideal or photovoltaic applications. On the other hand,in molecular materials, the electronhole Coulombinteraction is substantiala ew electronvolts. Innanoscale materials we nd a middle ground whereexciton binding energies are signicant in magnitudethat is, excitons are importantand they are size-tunable. As a consequence o the size-dependence othe binding energy, delocalization versus localization

o the exciton complicates matters. For example,exciton sel-trapping (see the ollowing section) inorganic materials, such as conjugated polymers, leadsto a strongly bound (hundreds o millielectronvolts)exciton. Hence the need to dope conjugated polymersolar cells with electron acceptors, such as otherpolymers69, ullerenes70 or quantum dots71, to promotecharge separation. In a strongly delocalized exciton,ree carriers could be photogenerated directly uponexcitation o conjugated polymers. Te extent to whichthat occurs is still a matter or debate.

Te exciton binding energy in QDs o radiiR 12 nm is in the range 20050 meV, scalingapproximately as 1/R, according to the size-

dependence o the electronhole Coulombinteraction60. A key dierence between theseinorganic materials and organic materials isdielectric constant. Dielectric constant is central indetermining the exciton binding energy because itshields electronelectron repulsions, or equivalentlyelectronhole interactions. Interestingly, it has beenreported that dielectric constant diminishes withsize or QDs, urther increasing the size eect o theexciton binding energy60.

Te importance o electronelectron interactionsin determining the properties o excitons in CNs hasbeen revealed by quantum chemical calculations7274.Te most striking result is the large binding energy,

ound to be between ~0.3 and 1.0 eV, depending onthe chiral index and computational methodology.Te remarkable nding is that they are o theorder o hal the bandgap. Zhou and Mazumdar74report the scaling o the binding energy or variousCN types, indicating that the binding energy isgreater or smaller tube diameters, as expected.Compelling experimental evidence or a signicantexciton binding energy in CNs has been recentlycommunicated75,76. In each case, experimentalstudies suggested that the exciton binding energy in(8,3) CNs is ~0.4 eV. Evidence or the existence oexcitons in CNs can also be inerred rom a reporto phonon sidebands in uorescence data32. In the

work reported by Wang et al.75

the energy o the one-photon allowed exciton absorption was comparedwith the two-photon allowed absorption into a secondexciton state and nearby continuum absorption. Tatdirect observation o the exciton transition and thecontinuum provides a clean measure o the excitonbinding energy. In the report o Ma et al.76 the one-exciton state and continuum were detected usingultraast transient absorption spectroscopy, similarlyenabling the exciton binding energy to be deduced.

Te situation becomes less clear when thematerial is disordered or when there is strongcoupling between electronic and nuclear degreeso reedom. Organic materials typically exhibitstructural disorder and tend to contain torsional

motions and related low-requency vibrationsthat couple to the exciton. Such a combination ostatic disorder and electronvibration couplingdisrupts delocalization. Tat is the trade-o orthe great structural diversity in both repeat unitsand extended bonding patterns ound in organicsupramolecular assemblies and macromolecules.Tese ideas have been elucidated in detail orJ-aggregates 77, which are well known linearassemblies o dye molecules.

It has taken many years to develop an acceptableunderstanding o excitons in conjugated polymers that

CdSe

lnP

CdTe

Si

GaAs

Agl

10

1.0

0.1

0.01

Singlettripletsplitting(eV)

Polyenes

Catacondensed

polyacenesConjugated

ogliomers

Semiconducting

single-wall CNTs

1 10

Confinement length (nm)

0.5 0.7 1 2 3 4

Quantum dot radius (nm)

100

10

1

Brightdarkexcitonsplitting(meV)

S2

T2

T1

S1

ST splitting= 2 exchange interaction

0

0

1

12

F

Brightdark

exciton splitting

a b

c d

Figure 6 Size dependence of exchange interactions. Loglog plots of singlettriplet splitting

energy versus size. As in Fig. 5, for CNTs the confinement dimension is taken to be the tube diameter;

for other organic materials it is the approximate conjugation length from end to end. a,The organic

materials from Fig. 5, together with calculated singlettriplet splitting for a series of all-transpolyenes. The diamonds show the results of these time-dependent density functional calculations of

polyene excited states58. b, A typical Jablonskii diagram, indicating that the singlettriplet splitting is

determined by an exchange interaction. That diagram is compared to that for a CdSe quantum dot,

shown in d, where one considers a manifold of eight statesthe exciton fine structurerather than

just four. The splitting between the lowest bright and dark exciton fine structure states is analogous

to the singlettriplet splitting of the organic materials when crystal field splitting is negligible

compared with the electronhole exchange interaction. That is usually not the case for materials

with a wurtzite structure, such as CdSe. c, Data showing reported brightdark exciton splitting for

a selection of quantum dots: Si (ref. 62; tight-binding calculations), InP (ref. 47; fluorescence line

narrowing, measured at 10 K), GaAs (ref. 60; pseudopotential calculations of rectangular nanocrystals),

CdTe (ref. 64; fluorescence line narrowing, 10 K, of colloids in glass), AgI (ref. 65; fluorescence line

narrowing, 2 K), InAs (ref. 63; fluorescence line narrowing, 10 K), and CdSe(ref. 51; fluorescence line

narrowing, 10 K). These data are a combination of experimental results and calculations.


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explains molecular and semiconducting aspects othe materials in the context o their highly disordered

structure20

. Te binding energy and precise nature othe excited state (exciton versus polaron-exciton) arestill a matter or discussion. We note that coupling tophonons, exciton sel-trapping and energy migrationcan inuence the observed binding energy. Electronicstructure calculations in conjunction with experimenthave proven central or elucidating the propertieso excitons in conjugated polymers78. Moses et al.79report that the exciton binding energy can be as low as60 meV or excitons in poly(phenylene vinylene). Tereport o Silva et al.80 on poly-6,6,12,12-tetraalkyl-2,8-indenouorene and that o Arkhipov and Bssler81should be considered in conjunction with those results.Many other experimental and theoretical reports

conclude that the exciton binding energy is 0.3 to0.6 eV or a range o conjugated polymers. Films dierrom isolated polymers owing to interchain interactioneects. Te reader is reerred to the article by Brdaset al.82 or detailed discussion o the binding energy inconjugated polymers. An important message o thatpaper is that an interplay between electronelectronand electronlattice interactions is important indetermining a description o conjugated polymerexcitons, and hence their binding energies.

Te binding energy o the exciton in the B850 ringo LH2 is apparently lowered by 90 meV relative to thatin monomeric Bchl, as can be inerred rom the energydierence between the 800-nm and 850-nm absorptionbands (Fig. 2). Note that B850 is a Frenkel exciton, so

the electron and hole are closely associated on eachmolecule in the aggregate. I the molecules in B850were su ciently closely spaced, then charge transerbetween Bchl molecules would become importantthat is, electronhole separation. Te consequencewould be a substantially increased exciton bindingenergy or essentially the same-sized aggregate.

DISORDER AND COUPLING TO VIBRATIONS

Te purely electronic models or describing excitonsare modied by the coupling between the excitonand the bath o nuclear motions.Tat couplingis maniest in spectroscopy as line broadening,Stokes shif and vibronic structure in absorptionand photoluminescence spectra83,84. Te aim othis section is to categorize the important elementso line broadening in nanomaterials, highlighttheir size dependences and provide some specicexamples that give an overall picture o the diverseconsequences o disorder and excitonbath coupling.

Any model or the eigenstates and energies

o excitons contains the energy at each repeatunit (molecule, unit cell, atom), known as thesite energy, and inormation on how those repeatunits are coupled. In the most general model,each site can accommodate an excitation, anelectron or a hole85. Clearly both the compositiono the eigenstates and the corresponding energieswill be aected by energetic disorder in the siteenergies or couplings. Such disorder is caused byrandom uctuations in the positions o atoms84.Te timescale o those uctuations is important indelimiting the eects as static (on the timescale othe measurement) or uctuating. Te ormer givesrise to inhomogeneous line broadening, the latter

to homogeneous line broadening86

. Static disorderis seen as a temperature-independent gaussian lineshape in absorption or photoluminescence, whereashomogeneous line broadening can play an importantrole in trapping an exciton on a ast timescale87(emtoseconds to picoseconds).

Te interaction between excitons and nuclearmotions can introduce time-dependent connementeects, known as exciton sel-trapping, where theexciton becomes trapped in a lattice deormation87.Tose nuclear motions are contributed byintramolecular vibrations and the environment.Exciton sel-trapping occurs through a local collectivestructural change, connected to random nuclear

uctuations by the uctuation-dissipation theorem.Te resultant exciton is also called a polaron-exciton.Hence the size and electronic make-up o an organicexciton can change markedly on short timescalesafer photoexcitation (tens o emtoseconds)13,88.Tat is understood as the tendency o molecules tochange their equilibrium geometry in the excited statecompared with the ground state, which is observed,together with solvation86, as spectral diusion. Teassociated reorganization energy is equal to hal theStokes shif. A very small change in the equilibriumcoordinates o many vibrational modes can inspiresurprisingly rapid localization o the exciton. Inother words, exciton sel-trapping is induced by theamplitude o uctuations as well as their characteristic

Poly(phenylene vinylene) chain

Conformational disorder

breaks conjugation

A conformational

subunit

Electronic coupling

between subunits

(~100 cm1)

Conjugation

break

Figure 7 Conformational subunits of conjugated polymers.A typical defect cylinder

conformation of a conjugated polymer, poly(phenylene vinylene), is shown in red. Zooming in on a small

part of the chain, it is evident that the -bonds extending over the phenylene vinylene repeat units arefrequently disrupted by rotations of sufficient angle to break the conjugation. The result is a series of

conformational subunits, outlined conceptually by boxes. This ensemble of chromophores makes up

the zero-order picture of the conjugated chain exciton. Long-range Coulomb interactions couple the

conformational subunits, as indicated. After light-absorption, energy migration transfers the excitation

to a narrow distribution of conformational subunits, from which fluorescence emission is observed.


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timescales. Te precise excited state dynamics aredictated by competition between the delocalizingeect o electronic coupling and the localizinginuence o electronphonon coupling.

Te LH2 antenna protein (Fig. 2) rom purplebacteria provides a clear example o the implicationso static disorder at each site in a Frenkel exciton. ounderstand the optical properties, one must consider

the importance o static disorder in the transitionenergy gaps rom ground state to excited state o eachBchl molecule and/or in the electronic coupling8991.Te result is that each LH2 complex in an ensemblehas a unique absorption spectrum, as shown strikinglyin the low-temperature uorescence excitationspectra o individual LH2 complexes reported by

van Oijen et al.92. Implications are that ensemblemeasurements must be careully unravelled toexpose the properties and dynamics characteristic oindividual light-harvesting complexes. Although staticdisorder is important, particularly in determiningthe temperature dependence o spectroscopic data,dynamic electronvibration coupling also needs to be

considered to predict electronic energy transer ratesand to understand ultraast exciton dynamics. Someinsight into the role o electronvibration couplingcan be gathered rom the observation that the entirering o Bchl molecules needs to be considered in atheoretical model to predict correctly the absorptionor circular dichroism spectra o B85017. Nonetheless,excitation is sel-trapped in just tens o emtosecondsso that the exciton size determined by experimentssuch as pump-probe93 and time-resolved uorescencespectroscopy94 is small enough to cover just small parto the ring, typically three to our Bchl molecules only.Te size o an exciton thereore can depend on thetimescale on which it is probed.

Conjugated polymers provide another goodexample where static disorder is signicant. Byconsidering single-molecule studies and simulationso the polymer chain it was established that MEH-PPV adopts a airly ordereddeect cylinder chainconormation95, illustrated in Fig. 7. Tat workprovides an important low-resolution picture ochain disorder. Te -electron system o conjugatedpolymers is disrupted on shorter length scales byconormational disorder20. It has been thought thatthis disorder impacts the spectroscopy by disruptingthe -electron conjugation along the backboneo the polymer, giving a chain o chromophoresknown as conormational subunits (Fig. 7). Tus, the

optical properties o conjugated polymers are highlydependent on the polymer chain conormation20,22,96.Single-molecule studies and site-selective uorescencestudies together provide clear evidence that energyabsorbed by a polymer chain is e ciently unnelledto low-energy chromophores along the chain byelectronic energy transer97.

Recent work has aimed to understand betterhow to think about conormational subunits andhow they dene conjugated polymer excitons.Simple considerations o electronic coupling (orexample, dipoledipole coupling) suggest thatconormational subunits should be electronicallycoupled, meaning that a delocalized exciton mightbe ormed by photoexcitation98100. Careul quantum

chemical investigations urthermore reveal that itis di cult to dene conormational subunits withrespect to torsional angles: there is no clear pointwhen the strong interactions that depend on overlap switch o and, even when weak, thoseinteractions are important or dening the nature othe excited states. Beenken and Pullerits101 concludethat conormational subunits arise concomitantly with

dynamic localization o the excitation102 (exciton sel-trapping). An interesting contrast is contributed bythe highly ordered polydiacetylene chains investigatedby Schott and co-workers103. Tose moleculesresemble an organic semiconductor quantum wirein many respects, thereore sustaining a highlydelocalized one-dimensional exciton. Key propertiesthat dierentiate these chains rom many otherconjugated polymers are their structural order on alllength scales, their rigid, crystalline environment, andweaker electronphonon coupling.

QD excitons couple relatively weakly to nuclearmotions and the homogeneous line broadeningis consequently narrow compared with organic

materials, suggesting possible applications o QDsas single-photon sources and qubits or quantumcomputation. Tat is perhaps because QDs, andindeed also CNs, are considerably more rigidand ordered than the exible structures o organicmaterials. Tere are two characteristic types o

vibrations in a QD104. Te higher-requency modeis that o the longitudinal optical (LO) phonon,which has a requency that is typically very similarto the requency known or the correspondingbulk material. For CdSe the LO-phonon moderequency is 207 cm1. Te radial breathing modes oCNs105 are conceptually similar kinds o vibrations.Te requencies o radial breathing modes,

however, scale with the CN diameter d(in nm),according to the empirical relation106 = (214.4/d) + 18.7 cm1. Coupling o the exciton to vibrationswith requencies greater than thermal energiesleads to phonon sidebands in requency-resolvedspectroscopies and quantum beats (oscillations) inultraast time domain experiments.

Te principal vibrations that contribute to QDline shape are acoustic phonons. In the bulk theseare analogous to sound waves travelling through thecrystal. Owing to the small size o QDs, the acousticphonon modes are quantized torsional and spheroidalmodesthe motions o an elastic sphere that leaveits volume constant. Te requencies o these phonon

modes lie in the range 5 to 40 cm1

, depending on theQD size. Te excitonphonon coupling scales as 1/R2,where R is the QD radius104. Models or phonons inbulk crystals assume the displacements o the modesare small. Tat makes sense or an innite-sizedcrystal, in which coupling between many oscillatorslimits the amplitude o motion. On the other hand,or nanoscale materials such as QDs, excitonphononcoupling may be better described by consideringaspects o theories developed or molecules.

DYNAMICS OF EXCITONS

Te dynamics o excitons have been o interest ormany years. Here we give only a glimpse o some


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areas topical in nanoscience that characterize eachparticular material. Photosynthetic proteins providewonderul model materials or the measurementand investigation o electronic energy transer.Energy migration in conjugated polymers has beenextensively studied, particularly with respect toelucidating the essential dierences between dilutesolutions and lms97. Exciton dynamics in CNs

have recently been exposed, so this area is only nowemerging. Relaxation dynamicsradiationless as wellas radiative relaxationo highly excited excitons andmultiexcitons are a topic o continued interest in QDs.

As introduced in Fig. 2, the light-harvestingcomplexes in photosynthesis gather incident solarenergy and transer that excitation energy to reactioncentres using a series o electronic energy transersteps. Te B850 unit plays an important role in theintra-complex energy unnel or purple bacteria.Examination o B800B850 resonance energy transerrevealed that excitons are unique in the way theytrap excitation energy17,18. A surprisingly large spatialand spectral cross-section or donor quenching is

achieved through the physical arrangement o theacceptor molecules, together with the act that theull extent o the exciton density o states can beharnessed to optimize spectral overlap between donoremission and acceptor absorption, regardless othe distribution o oscillator strength. Tis secondpoint is rather subtle, as it is not captured by thedipole approximation or donoracceptor electroniccouplings. Te way that a delocalized exciton acts asa unique acceptor in resonance energy transer maybe understood in terms o coupling between excitontransition densities1618.

Exciton states are used in photosynthetic lightharvesting and redistribution because they substantially

increase the absorption cross-section or incident lightwithout the cost o dissipative processes that mightresult rom diusive trapping o excitation energyabsorbed by a weakly coupled aggregate o molecules.Once captured by the exciton maniold, excitation israpidly trapped in the lowest state. Recent work revealsthat such exciton trapping and relaxation is not a simplecascading relaxation process, but can actually involvespatial redistribution, a new picture that was discoveredthrough two-dimensional photon echo spectroscopy107.Tis method opens the possibility o new insights intomechanisms underlying ultraast dynamics o excitons,because inormation about electronic couplingsbetween exciton states can be captured in addition

to populations.Similar to conjugated polymers, CN excitonsmay migrate along the length o the tube. A possibleimplication o energy migration is that trap anddeect sites along the tube may quench excitation,contributing to the low uorescence yield. At higherexcitation intensities, two excitons on the sameCN may encounter each other and annihilate108.Tus multiexciton states are typically short-lived(300% when the pump energy is tuned to greaterthan three times the bandgap115,116.

OUTLOOK

We emphasize the great strides that have been gainedrom elucidating size-dependent properties withineach class o materials we have reviewed. What are

the signatures o nanoscale exciton spectroscopy?As an example we looked at singlettriplet splittingand its relationship to exciton delocalization (orconnement). Te properties o quantum dots stoodout rom those o the other materials examined; therelatively small magnitude o properties such as theexchange interaction highlights the role o dielectricconstant in screening long-range interactions. It isclear, however, that size plays an important role herealso, as can be concluded by comparing the singlettriplet splitting o the majority o organic materialssurveyed in Fig. 6 with those calculated or CNs.

We conclude that an opportunity ornanoscience is that solid-state materials acquiremolecular-like spectroscopic eatures: discrete


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transitions, spin state maniolds and so on, allowingor a more detailed examination o the excitedstates. Tat, in turn, will provide inspiration ortheory, which in the past has ocused mostly onbandgaps. Future work will examine more closelyhow spectroscopy can reveal properties uniqueto excitons in nanoscale systems. It is likely thatour understanding o excited electronic states

characteristic o nanomaterials will evolve in asimilar manner to our present understandingo the excited states o molecules. Standardapproximations and concepts relevant to bulkmaterials may need to be reconsidered in light othe signicant exciton binding energies, exchangeinteractions, and excitonvibration couplingsapparent in the spectroscopy o nanoscale excitons.Perhaps we need to look back beore we go small?

doi: 10.1038/nmat1710

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AcknowledgementsG.D.S. thanks G. J. Wilson or introducing him to excitons. He acknowledgesunding rom the Natural Sciences and Engineering Research Council oCanada and the A. P. Sloan Foundation. G.R. acknowledges unding through thePhotochemistry and Radiation research program o the US Department o Energy,O ce o Science, O ce o Basic Energy Sciences, Chemical Sciences , Geosciencesand Biosciences (DoE contract DE-AC36-99G010337).Correspondence should be addressed to G.D.S.


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CORRIGENDUM

EXCITONS IN NANOSCALE SYSTEMS

GREGORY D. SCHOLES AND GARRY RUMBLES

Nature Materials5, 683696 (2006).

In this Review Article, the spelling o the frst authors name in re. 74, and in the citation o this reerence within the text on page 691, was

incorrect. It should have read Zhao.

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