VOLUME 79, NUMBER 18 P H Y S I C A L R E V I E W L E T T E R S 3 NOVEMBER 1997

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Biexciton and Triexciton States in Quantum Dots in the Weak Confinement Regime

Michio Ikezawa,1 Yasuaki Masumoto,1,3 Toshihide Takagahara,2 and Selvakumar V. Nair3

1Institute of Physics, University of Tsukuba, Tsukuba 305, Japan2NTT Basic Research Laboratories, 3-1 Morinosato Wakamiya, Atsugi 243, Japan3ERATO Single Quantum Dot Project, JST, 5-9-9 Tokodai, Tsukuba 300-26, Japan

(Received 28 May 1997)

Biexciton and triexciton states in CuCl quantum dots were studied by means of time-resolvedsize-selective pump-and-probe technique. A clear induced absorption band is observed on the high-energy side of the excitation photon energy. The new induced absorption is assigned to the transitionfrom the exciton ground state to one of the weakly correlated exciton pair states which weretheoretically predicted to exist and to play an important role in nonlinear optical processes. Itspump energy dependence and temporal evolution strongly support this assignment. Under high-densityor two-color excitation condition, a triexciton state in quantum dots is observed for the first time.[S0031-9007(97)04397-4]

PACS numbers: 78.66.Li, 71.35.Gg, 78.47.+p

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Semiconductor nanocrystals dispersed in a largbandgap matrix can be treated as quantum doThree-dimensional quantum confinement of electronholes, and excitons makes it possible to observe quantsize effect in quantum dots [1–3]. We can classify thquantum confinement effects into two main categoriaccording to the ratio of the quantum dot radiusR to theexciton Bohr radiusaB. One is thestrong confinement(R , aB) where electrons and holes are quantized indvidually, and the other is theweak confinement(R . aB)where the translational motion of excitons is quantizeA CuCl quantum dot is known as a prototypical systein the weak-confinement regime because of its smexciton Bohr radius and has often been used to investigexcitons and biexcitons.

The study of the quantum confinement effect on manexciton states, e.g., biexciton and triexciton, is still in thelementary stage. There are many experimental reposhowing unique nonlinear optical properties of quantudots, for example, enhancement of the biexciton bindienergy [4], a nonmonotonic size dependence of the optinonlinearity [5], and biexciton lasing [6]. Through thesstudies, the importance of weakly correlated exciton pstates has been pointed out [7]. The weakly correlatexciton pair state is one of the excited biexciton stateRoughly speaking, that state is an antibonding state of texcitons and has a higher energy and a larger spatialtent than the biexciton ground state, leading to a largoscillator strength of transition from the exciton statThis state is of general character and is expected topresent as well in other low-dimensional structures, e.quantum wells and quantum wires. However, the actuobservation was successful for the first time in the quatum dot as reported here, because the continuum staoverlapping the weakly correlated exciton pair state ihibit clear observation of this state in other structures.far, the experimental study of the excited biexciton stathas been limited to the strong-confinement regime whe

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the excited biexciton state is blurred by the size inhmogeneity and the ground state biexciton is maskedthe broad exciton bleaching [8,9]. Therefore, it is impotant and interesting to study the excited biexciton statesthe weak-confinement regime, making use of the advangeous situation that the exciton and biexciton binding eergies are quite large. In this Letter, the excited biexcitstates are identified unambiguously in CuCl quantum dfrom comparison between theory and experiments. Fthermore, a triexciton state in quantum dots is observfor the first time. Along this line of approach, we castudy the many-exciton states in a quantum dot succsively. From details of the exciton addition spectrum, wcan clarify the exciton correlation with renewed intereand investigate, for example, the ionization thresholdexcitons and biexcitons which has been discussed soonly in the mean-field approximation. Thus, the presestudy holds a great promise of revealing new aspectsmany-body physics.

We used the time-resolved size-selective pump-anprobe method. The sample was CuCl quantum dembedded in a NaCl crystal. The absorption bandthe sample was inhomogeneously broadened becausthe size inhomogeneity of the quantum dots. The lassource was a self-mode-locked titanium sapphire laand a titanium sapphire regenerative amplifier. Aftamplification, the output pulse has a pulse duration300 fs at a repetition rate of 1 kHz, and a pulse energy200 mJypulse. The amplified laser pulses were convertto their second harmonic. The second harmonic pulswere spectrally filtered by means of a spectral filter stamade of a grating and were used as pump pulses forsize-selective excitation. Their typical spectral width wa1.7 meV. A part of the amplified laser pulse was focusin pure water to produce a white continuum which waused as a probe beam. The transient absorption spewere recorded by a spectrometer and a liquid-nitrogcooled charge-coupled device multichannel detector.

© 1997 The American Physical Society

VOLUME 79, NUMBER 18 P H Y S I C A L R E V I E W L E T T E R S 3 NOVEMBER 1997

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A solid line in the upper part of Fig. 1 shows the absorption spectrum of the sample at 77 K. TheZ3 ex-citon andZ1,2 exciton absorption structures are observeThese exciton absorption energies are shifted to the highenergy side compared to those of the bulk material dto the quantum confinement effect. TheZ3 exciton en-ergy of bulk CuCl is shown by a downward arrow. Thespectrum of the spectrally filtered pump pulse is showin the inset by a solid line together with that of the unfiltered pulse shown by a broken line. According to thwell-known relation between the quantum confined excton energy and the quantum dot radius [10], the pumpulse energy of 3.259 eV excites quantum dots of 2.3 nradius. The dashed line shows the absorption spectruat 10 ps after the excitation. The solid line in the lowepart of Fig. 1 shows the difference between two spectrathe upper part. The spectrum consists of a spectral hoat the pump photon energy and two induced absorptistructures at both sides (3.180 eV, 3.296 eV) of the spetral hole. Persistent hole burning was much smaller thathe transient hole burning at 77 K [11]. Bleaching aroun3.335 eV is related to theZ1,2 exciton.

Differential absorption spectra are shown at the lowepart of Fig. 1 for four different pump photon energiesTwo prominent induced absorption bands shift with th

FIG. 1. Upper panel: The solid line shows absorptiospectrum of CuCl quantum dots embedded in a NaCl crysat 77 K, while a dashed line represents that at 10 ps aftphotoexcitation. Lower panel: The solid line shows differentiaabsorption spectrum corresponding to the upper figure, whdashed lines are those for different excitation photon energieThe radii of quantum dots which were excited are 2.65, 2.42.32, 2.19, and 2.03 nm from top to bottom, respectivelyThick solid bars are theoretical results normalized at thspectral hole. In the inset, filtered and unfiltered pump specare shown by a solid line and a dashed line, respectively.

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change of the excitation photon energy. The energies othe spectral hole and the induced absorption bands arplotted in Fig. 2 as a function of the excitation photon en-ergy. The solid circles show spectral hole energies, andthey are on a line of slope 1.0, since their energy coincidewith the excitation photon energy. Open (solid) trianglesexhibit the energies of the induced absorption located athe higher (lower) energy side. Open circles show theenergies of induced absorption measured previously bnanosecond pump-and-probe method [4] which was identified as the transition from the exciton to the biexcitonground state. The coincidence between open circles ansolid triangles confirms the proper present measurement.

The solid line through the open triangles is a fitted lineby the least squares method. The slope of this line is2.0. This line crosses the line of slope 1.0 near theZ3

exciton energy of bulk CuCl. Furthermore, the spectralhole and the induced absorption on the higher energyside exhibit almost the same temporal evolution. Theyshow an exponential decay with a time constant of 480 pswhich almost coincides with the luminescence decay timeof excitons in CuCl quantum dots [12]. This fact indicatesthat the induced absorption on the higher energy sidearises from the excitons preexcited in the quantum dotsThese features agree well with those of the theoreticallypredicted [7] strong induced absorption transition from theexciton state to excited biexciton states.

FIG. 2. Excitation energy dependence of the structures appearing in the differential absorption spectrum. The solid cir-cles represent spectral hole energies, and they are on a linof slope 1.0. Open (solid) triangles show the energy of theinduced absorption located at the higher (lower) energy sideof the spectral hole. Open circles indicate the energy of theinduced absorption measured by nanosecond pump-and-probmethod in Ref. [4]. Solid diamonds correspond to additionalinduced absorption under high-density excitation.Eb denotesthe biexciton binding energy defined by2EX 2 EXX and EtshowsEXXX 2 EXX 2 EX . Then the triexciton binding energydefined by3EX 2 EXXX is given byEb 2 Et.

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VOLUME 79, NUMBER 18 P H Y S I C A L R E V I E W L E T T E R S 3 NOVEMBER 1997

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In CuCl where both the uppermost valence banand the lowermost conduction band are doubly degenerate, the angular momentum of the Bloch paexciton wave function is either 0 or 1. Then theangular momentum of the biexciton can be eitheof 0, 1, and 2. The explicit biexciton wave func-tion for J ­ 0 and 2 can be written asCXX0 ­p

3y2F11XX x

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22XX x

1100 , CXX2 ­ F

22XX x

112M , where

xjejh

JM denotes the Bloch part wave function which hathe total angular momentum (J, M) and is composed oftwo-electron wave function of angular momentumje andtwo-hole wave function of angular momentumjh. Inthe limit of weak confinement, it has been shown thathe weakly correlated exciton pair states may be approxmated by product states of two independent excitons [7namely,

F66XX ­

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wherefgX is the envelope function of the exciton ground

state andre1 and re2 (rh1 and rh2) denote the electron(hole) coordinates. The oscillator strengths of transitionfrom the ground state excitonX to these excited biexcitonstates are calculated asfsX ! XX0d ­ 2y3f0, fsX !

XX2d ­ 4y3f0, wheref0 is the oscillator strength of theexcitonic transition.

The theoretical induced absorption spectrum from thexciton ground state is shown by thick solid bars inFig. 1. The energy shifts of strong bands show good corespondence with experiments. Furthermore, the relatistrengths of the induced absorption lines and the specthole are reproduced quite well by the theory, althougthere is a discrepancy in the energy positions of the induced absorption lines. Hence the strong peak above tpump energy can be assigned to the induced absorpttransition toXX2 states.

Next we discuss experimental observation of triexcton states in CuCl quantum dots. At the upper part oFig. 3(A), we exhibit the excitation density dependencof the differential absorption spectrum at 10 ps after photoexcitation. Under low density excitation, spectra inFig. 3(A) are similar to those in Fig. 1, and the biexci-ton luminescence cannot be observed. Under high densexcitation condition, we observed an additional induceabsorption band which is shown by an arrow. Simultaneously the biexciton luminescence became observable.

In Fig. 3(B), the time evolution of the additional inducedabsorption is shown. Together with it, the temporal evolution of the spectral hole and the higher energy induceabsorption band are also presented in the figure, althouthe excitation density was slightly low. Two solid curvesthrough the solid circles and open triangles show an expnential decay with a time constant of 480 ps. On the othhand, the decay time constant of the additional induce

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FIG. 3. (A) Upper panel: Excitation density dependence othe differential absorption spectrum at 10 ps after photoexcittion with the excitation photon energy fixed at 3.265 eV. Additional induced absorption shown by an arrow appears withe increase of the excitation. Lower panel: Experimentaresults of the two-color pump-and-probe measurement. Thphoton energy of the first (second) pump pulse is indicateby an upward (a downward) arrow. (i) Shows the differential absorption spectrum induced by both the first and seconpulses. (ii) Exhibits the sum of differential absorption spectrinduced by the first pump pulse and by the second one alonsiii d ­ sid 2 sii d. (B) Time evolution of the additional inducedabsorption under high-density excitation together with the spetral hole and the higher energy induced absorption. Symboare the same as in Fig. 2.

absorption is less than 100 ps and corresponds to the lumnescence lifetime of biexciton which is known to be 70 pfor CuCl nanocrystals [13]. If a triexciton state consists oa biexciton and an exciton, the intensity of the induced asorption transition from a biexciton to a triexciton shouldbe proportional to the number of biexcitons. Therefore thtime evolution and the excitation density dependence sugest strongly that the additional induced absorption canassigned to transition from the biexciton ground state totriexciton state.

We examined this assignment by the two-color pumpand-probe method. The energy of the second pumpulse is tuned to the induced absorption caused by t

VOLUME 79, NUMBER 18 P H Y S I C A L R E V I E W L E T T E R S 3 NOVEMBER 1997

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first pump pulse. This combination produces biexcitoeffectively only in quantum dots of particular size andenables us to observe the induced absorption to triexcitstates. At the lower part of Fig. 3(A), results of theexperiment are shown. Photon energy of the first osecond pump pulse is represented by an upward ordownward arrow, respectively. Time delay between twpump pulses was 5 ps, and the probe pulse delay tosecond pump pulse was also 5 ps. The solid line (shows the differential absorption spectrum induced btwo successive pump pulses, while the dotted line (iexhibits the sum of differential spectra induced by thfirst pump pulse and by the second one alone. Spectru(iii) shows the difference between two spectra. If thsecond pump pulse increases (decreases) the absorpof the quantum dots excited selectively by the first pulswe would observe negative (positive) signal in spectru(iii). In fact, we observed an increased absorption regiobetween the spectral hole and the induced absorptionspectrum (iii). The relative peak position is similar tothat of the additional induced absorption in the uppepart of Fig. 3(A). Hence both structures should be othe same origin. Excitation energy dependence of thinduced absorption is shown in Fig. 2 by solid diamondThe fitted line has a slope of 1.7, and this line also crossthe other two lines near the bulkZ3 exciton energy.

In addition to an increased absorption region, wobserved two decreased absorption regions in spectr(iii). The lower or higher energy one indicates thedecrease of the transition from the exciton statethe biexciton ground state or excited biexciton statrespectively. This can be explained by noticing that thbiexcitons are produced size-selectively by the secopump pulse.

The linear proportionality of the induced absorptionenergy to the exciton confinement energy suggests ththe exciton addition energy is primarily determined bthe increase in the kinetic energy proportional to thinverse square of the quantum dot radius. As propospreviously [7], since the weakly correlated exciton pastate (XX2) is an antibonding state of two excitons, itskinetic energy can be assumed to be equal to that of twexcitons independently confined in a region of half thvolume of the quantum dot. Then its energy is written aEXX2 ­ 2Ebk 1 2 3

p4 sEX 2 Ebkd, whereEXsEbkd is the

exciton energy in a quantum dot (bulk material) and thslope in Fig. 2 is estimated as2 3

p4 2 1 > 2.2 in good

agreement with the experiment. The observed triexcitostate has an energy greater than that of an independbiexciton-exciton pair but smaller than that of threexcitons. Thus, while this state is a bound state, it mabe regarded as an antibonding combination of a biexcit

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and an exciton. Therefore the above argument may bextended to the case of exciton addition to the biexcitoground state assuming the added exciton to occupy hathe volume of the quantum dot without affecting thebiexciton ground state. Then we haveEXXX 2 EXXg ­3

p4 sEX 2 Ebkd 1 Ebk with EXXXsXXgd being the energy of

the triexciton (biexciton ground) state, and this gives theslope in Fig. 2 as3

p4 > 1.6, again in good agreement with

the experiment. These qualitative arguments providestrong support to the identification of the newly observedinduced absorption as the transition from the biexciton toa triexciton state.

In conclusion, we studied biexciton and triexcitonstates in quantum dots in the weak-confinement regimby using the time-resolved size-selective pump-and-probtechnique. One of the observed induced absorption banwas unambiguously identified as the transition from theexciton state to the weakly correlated exciton pair statwhose presence was theoretically predicted. We observea triexciton state in quantum dots for the first time by twoindependent methods employing high-density excitatioand two-color excitation scheme. These experiments opea new direction of research and hold a great promise orevealing new aspects of many-exciton states in confinesystems.

[1] A. I. Ekimov, A. L. Efros, and A. A. Onushchenko, SolidState Commun.56, 921 (1985).

[2] A. D. Yoffe, Adv. Phys.42, 173 (1993).[3] L. Bányai and S. W. Koch,Semiconductor Quantum Dot

(World Scientific, Singapore, 1993).[4] Y. Masumoto, S. Okamoto, and S. Katayanagi, Phys. Rev

B 50, 18 658 (1994).[5] T. Kataoka, T. Tokizaki, and A. Nakamura, Phys. Rev. B

48, 2815 (1993).[6] Y. Masumoto, T. Kawamura, and K. Era, Appl. Phys. Lett.

62, 225 (1993).[7] S. V. Nair and T. Takagahara, Phys. Rev. B53, R10 516

(1996);55, 5153 (1997).[8] Y. Z. Hu, S. W. Koch, M. Lindberg, N. Peyghambarian,

E. L. Pollock, and F. F. Abraham, Phys. Rev. Lett.64,1805 (1990).

[9] Y. Z. Hu, M. Lindberg, and S. W. Koch, Phys. Rev. B42,1713 (1990).

[10] T. Itoh, Y. Iwabuchi, and M. Kataoka, Phys. Status SolidiB 145, 567 (1988).

[11] Y. Masumoto, J. Lumin.70, 386 (1996).[12] T. Itoh, M. Furumiya, T. Ikehara, and C. Gourdon, Solid

State Commun.73, 271 (1990).[13] Y. Masumoto, S. Katayanagi, and T. Mishina, Phys. Rev

B 49, 10 782 (1994).

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