Light controlled spin properties and radiative coupling of CdSe based quantum dots

phys. stat. sol. (c) 4, No. 9, 3334–3346 (2007) / DOI 10.1002/pssc.200775410

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Light controlled spin properties and radiative couplingof CdSe based quantum dots

T. Schmidt∗1, L. Worschech∗∗1, M. Scheibner1, T. Slobodskyy2, G. Schmidt2,L. W. Molenkamp2, T. Passow3, D. Hommel3, and A. Forchel1

1 Universitat Wurzburg, Technische Physik, Am Hubland, 97074 Wurzburg, Germany2 Universitat Wurzburg, Experimentelle Physik III, Am Hubland, 97074 Wurzburg, Germany3 Institut fur Festkorperphysik, Universitat Bremen, Otto-Hahn-Allee, 28359 Bremen, Germany

Received 16 February 2007, revised 28 June 2007, accepted 28 June 2007Published online 18 July 2007

PACS 73.21.La, 75.75.+a, 78.47.+p, 78.55.Et, 78.67.Hc

The authors have studied the photoluminescence of large and small ensembles of CdSe based quantum dots(QDs) in magnetic fields for different polarizations and powers of the exciting laser light. By means ofpolarization spectroscopy the g factors and spin lifetimes were determined for semimagnetic CdMnSe QDswith nominal Mn contents of 0%, 1% and 2%. Also the corresponding exciton lifetimes were analyzed.A sign reversal of the QD exciton g factor was identified comparing the polarization of QD luminescencewith 0% and 2% Mn. For small excitation powers QDs with 1% Mn have a vanishing small value of g.Interestingly, by ramping up the excitation power of the exciting laser the exciton g factor increases by upto a factor of 30. Different heating mechanism were identified by characteristic power dependencies. Forlow excitation powers indirect heating of the spin systems occurs whereas above a critical power directheating due to photoexcited carriers dominates. It is also demonstrated that in CdMnSe QDs the circularpolarization of the luminescence can be inverted solely controlled by the laser power. Applying mesatechniques, collective radiance of QDs is demonstrated. For that purpose the radiative lifetimes of QDs withsuch a density that there are many dots within an area proportional to the square of the optical wavelengthwere studied for different numbers of QDs removed from that area. A comparison of photoluminescencedecay times obtained for non-resonant and quasi-resonant excitation conditions and different mesa sizes isgiven. Radiative coupling of QDs takes place at least on the order of 150 nm. This length is comparable tothe dimensions of lithographically well definable nanostructures and may therefore provide a mechanism tocouple discrete quantum objects on a large scale.

1 Introduction Radiative couplings of QDs and optical control of well defined spin states in QDsrepresent topics of intense active research driven by the attempt to understand in more detail the physicsof light-matter interaction in semiconductor nanostructures [1]. For this reason it is not amazing thatmethods of optical spectroscopy have formed the basis for a plurality of experiments with semiconductorspin systems [2,3]. In recent years special attention was paid to the polarization dynamics of QDs subject toan external magnetic field [5]. Exploiting the carrier spins of QDs several new and innovative devices havebeen proposed [6], including, e.g. a controllable spin filter [7] or a spin memory, for which principally thespin state can be read out electrically or optically by polarized emission [8–10]. In this regard, it has beendemonstrated that circularly polarized QD emission is very useful to reveal information on the distributionand the dynamic properties of QD spins [4].

∗ Corresponding author: e-mail: [email protected], Phone: +49 931 888 5104, Fax: +49 931 888 5143∗∗ e-mail: [email protected]

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

In this field of research semimagnetic QDs play an important role due to their distinct magnetic prop-erties, e.g. the giant Zeeman splitting caused by the exchange interaction of the carrier spins with themagnetic lattice ions [13, 14]. It is clear that the semimagnetic properties depend sensitively on the con-centration of Mn. Reducing the number of Mn ions in CdMnSe QDs, a sign reversal of the exciton g factorshould occur as in strongly diluted semimagnetic QDs a positive exciton g factor exists [12, 15] whereasCdSe QDs have a negative one [16].

Recently, by means of optical polarization even spin coupling has been observed in a double layer QDstructure containing one layer CdSe QDs and one layer CdMnSe QDs [17]. In addition, control of evena single Mn atom in a CdTe QD has been demonstrated [18]. It is clear that circularly polarized opticalexcitation induces not only a preferred optical orientation of spins but also can substantially change theoccupation of spin states due to the heat which is transferred from optically excited carriers into the spinsystem, for which principally two different mechanisms are known to occur in semimagnetic nanostruc-tures referred to as direct and indirect heating of electrons and holes [19–23].

Besides the aforementioned light controlled spin properties, radiative coupling between QDs can occurif many QDs interact by their radiation field. Usually, each QD in an ensemble can be regarded as indepen-dent quantum-mechanical system as long as characteristic interaction lengths are by far smaller than theseparation between the dots. In order to use QDs for future applications much effort was spent to coupleat least two of them [24–28]. It has been proposed that there might be a long-range coupling even be-tween QDs which is based on an optical interaction [29–31]. The range of interaction is in the order of thewavelength of the emitted radiation. Superradiant coupling between QDs could be especially interestingfor quantum schemes which are based on the control and manipulation of collective emitters such as QDsstudied here.

In this paper we report on optical investigations of QDs with no or a small amount of Mn. We determinethe exciton g factor of QD excitons and we demonstrate the possibility to tune the exciton g factor eitherby variation of Mn or simply by the power of the exciting laser light. With increasing Mn content a signreversal of the exciton g factor takes place. The polarization properties of these dots as well as the g factorapproaches that of QDs without Mn when the excitation power is increased which is related to a strongheating of the Mn system.

The second part of the manuscript describes experiments performed with CdSe QDs using time-resolvedPL spectroscopy under quasi-resonant excitation. Forming a small ensemble of single QDs we observedan enhanced exciton lifetime. We relate this effect to a radiative interaction between different QDs. Dueto the coupling with the superradiant mode the radiation rate is increased. The radiative coupling can bereduced by removing QDs from the ensemble. Thus the exciton lifetime increases by forming small mesas.By analyzing the lifetime variation the range of the superradiant coupling was determined to be in the orderof 150 nm.

2 Sample preparation The investigated quantum dots were grown by molecular beam epitaxy (MBE)on the top of a GaAs substrate. The deposition of nominally 1.3 monolayers of Cd1−xMnxSe results in theformation of self-assembled QDs embedded between a 50 nm thick ZnSe buffer layer and a 25 nm thickZnSe capping layer. The typical size of such self-assembled dots was found to be about 1 nm in heightand 6–10 nm in width [32]. A set of three samples with nominal Mn concentrations of xMn = 0, 0.01,and 0.02 were grown by the described method. The samples were studied by optical spectroscopy at asystem temperature of 1.5 K. For that purpose the samples were mounted on a coldfinger and placed forall investigations in an optical LHe bath cryostat. Magnetic field dependent studies were conducted in acryostat equipped with a split coil superconducting magnet (8 T). For optical excitation the 458 nm line ofan Ar ion laser was used and the polarization of the emitted PL light was analyzed with the help of sheetpolarizers placed in front of a 0.6 m double monocromator. The monocromator was equipped with two1200 m−1 gratings. For detection a nitrogen cooled CCD camera was connected to the first exit of themonochromator. The system has a spectral solution of about 0.2 meV.

phys. stat. sol. (c) 4, No. 9 (2007) 3335

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Fig. 1 Left part: PL spectra of Cd1−xMnxSe/ZnSe QDs with xMn = 0.1, 0.01, and 0.02. The peak energies shiftslightly to lower energies with increasing Mn concentration. In the inset a FEM picture together with the correspondingPL signal is shown. Reducing the mesa size single lines appear in the spectrum associated with single QDs. Rightpart: Zeeman components (σ+ and σ−) of a single exciton line at B = 8 T. A positive gx ≈ +1.6 was determined.

The left part of Fig. 1 shows the observed PL signal of the QDs containing 0%, 1%, and 2% Mn. Broadlines with a full-width at half maximum (FWHM) of about 36 meV appear due to QD inhomogeneities. Thepeak maximum of the QD ensemble shifts with increasing Mn content slightly to lower energies by onlyabout 2%. In order to proof the zero dimensionality of the investigated nanostructures small mesa werefabricated. The PL spectra of a 200 nm mesa is shown exemplarily as inset. The QDs contain nominally2% Mn. Narrow peaks appear which are associated with an exciton in a single QD. From the number ofpeaks observed in a mesa the QD density was determined to be in the range of ρQD = 1011 cm−2.

Applying a magnetic field of 8 T in growth direction (Faraday geometry) the Zeeman splitting of theσ+ and σ− polarized components of a QD was studied (right part of Fig. 1). Semimagnetic II-VI QDswith a large content of Mn exhibit an enhanced exciton g factor due to a strong sp-d interaction betweenthe carriers and the Mn 5/2 spin system [11–13]. As shown as inset of Fig. 1 the Zeeman splitting of a QDwith nominal 2% Mn has a positive g factor of gx = +1.6, a value inverted to that (gx = −1.6) of CdSeQDs without Mn [16, 33, 34].

3 Circular polarization properties In order to analyze the spin properties of semimagnetic QDs we

studied the degree of circular polarization ρσ+/σ−

c of the luminescence of QDs containing nominal 0%,

1%, and 2% Mn for σ+ and σ− polarized excitation. ρσ+/σ−

c is determined by

ρσ+/σ−

c =I+ − I−I+ + I−

. (1)

For a better discussion of the QD polarization properties the optical orientation and the spin relaxation

ρor = 12

(ρσ+

c − ρσ−

c

)and Σρ = 1

2

(ρσ+

c + ρσ−

c

), respectively, can be distinguished, which contribute

differently to the observed polarization. In particular, the optical orientation is even in B (magnetic fieldstrength) and thus a measure of polarization transferred from the process of the polarized excitation intothe QD system. In contrast, the spin relaxation is odd in B. Therefore it reflects e.g. the spin relaxationbetween spin split states.

3336 T. Schmidt et al.: Light controlled spin properties and radiative coupling of CdSe based QDs

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-c.com

3.1 Experiment For optical excitation we used circular polarized light of a frequency doubled titanium-sapphire laser system with a repetition rate of 82 MHz and a pulse duration of 1.5 ps. The laser energy wastuned to resonant excitation below the ZnSe bandgap of the samples. The part of the polarization which isonly influenced by the Zeeman splitting of the QD eigenstates can be determined by comparing the circularPL polarization under σ+ and σ− polarization. For that purpose a 50 kHz photoelastic modulator (PEM)followed by a linear sheet polarizer was used to separate the σ+ and σ− polarized components of the PLsignal. A micro-channel plate connected to the second output of the double monocromator system wasused as detection system. The micro-channel plate was read out by a gated two-channel photon countertriggered by the operation frequency of the PEM. The circular polarized components of the PL signal weredetected at the maximum of the spectral intensity as a function of the external magnetic field applied inFaraday geometry.

3.2 Results and discussion In Fig. 2a–c the experimentally observed polarization curves ρc(B) areshown for QDs with 0%, 1% and 2% Mn. For all samples the circular polarization found for σ+ and σ−

excitation are almost pointsymmetric to ρc(0) = 0. In particular, having a look at the CdSe QDs (Fig. 2a)for σ− excitation the polarization is found to be about 15% at -5 T. With decreasing B ρc(B) decreases toabout ρc(0) = 0. For positive values of B the polarization degree decreases only slightly with increasingmagnetic field and reaches a value of -4% at B = 5 T. Doping the QDs with Mn the polarization curveschange completely. For xMn = 0.01 (Fig. 2b) the degree of circular polarization reaches for B = −5 Tonly about +10% which decreases to 0% at zero magnetic field at σ− polarized excitation. Interestinglyramping up the magnetic field to +5 T the polarization cures starts again to increase until it reaches +7%.The opposite behavior is found for σ+ excitation. Finally, increasing the Mn concentration up to 2% asign reversal of the polarization compared to the QDs without Mn was observed. The maximum of ρc wasfound to be 18% at +5 T for σ− excitation. A value of –2% was reached for the minimum at B = −2 T.

A time inversion invariance changing from σ+ to σ− polarized excitation explains the above observedpoint symmetry of the polarization degree. Such a symmetry implies the absence of an intrinsic ferro- orantiferromagnetic order of the Mn spins within the sample. As a consequnsce two mechanisms, opticalorientation and relaxation, can contribute to the observed polarization. The polarized excitation imposes(some of) its polarization on the QD excitons, ρor (optical orientation). In addition we have to account forspin relaxation Σρ. Considering both contributions the measured degree of polarization can be written asρc = Σρ ± ρor, where the sign of ρor depends on the kind of excitation. In order to determine the excitong factor of the studied QD ensemble from the degree of polarization we are further interested in Σρ whichcan be described by a model recently proposed by Mackowski et al. [39]:

Σρ =τr

(e∆E/kT − 1

)(τr + (τs + τr) e∆E/kT

) , (2)

with the Zeeman energy ∆E = gxµBB, gx the exciton g factor, µB the Bohr magneton, B the strengthof the magnetic field and the thermal energy kT . τr and τs represent the exciton lifetime and the spinrelaxation time between the upper and lower Zeeman level, respectively. By means of time-resolved mea-surements we have determined τr for the studied structures. The time evolution of the PL intensity of theQD emission is shown as inset in Fig 3. We determined the following exciton lifetimes: τr = (321 ± 20)ps, (222 ± 20) ps, and (145 ± 20) ps for Mn concentration of 0%, 1% and 2%, respectively.

By fitting Eq. (2) to the experimental data one is able to determine gx. The corresponding fit curvestogether with the experimental data are shown in Fig. 3. With increasing Mn content a sign reversal ofthe exciton g factor from negative to positive was observed with gx = −0.05 for xMn = 0.01. For QDscontaining 2% Mn an exciton g factor of gx = +1.32 and for xMn = 0.0 gx = −1.62 were found whichis in perfect agreement with the values known from the literatur [16]. The observed sign reversal of gx iscaused by a change of the sp-d exchange interaction which depends on the Mn concentration [11,12]. Fromthe theoretical point of view one would expect a sign reversal of gx in DMS QDs with a Mn concentration

phys. stat. sol. (c) 4, No. 9 (2007) 3337


of about 0.1%. Thus we conclude that only a part of the exciton wavefunction overlaps with the Mn spins.It is also possbile that due to the QD confinement the spin-spin exchange interaction is reduced [40].

Interestingly, the g factor of the QDs containing 1% Mn can be efficiently controlled [41] and manipu-lated optically. As presented in Fig. 4 by increasing the power of the excited laser light from 1mW up to 8mW a drastic increase of Σρ (filled squares) was observed. For the large excitation power we determineda g factor of gx = −1.47, which corresponds to a change of the g factor by a factor of 30.

Σρ versus excitation power is shown in Fig. 5a for a magnetic field strength of |B| = 4 T. For laserpowers ranging between 0.2 mW and 10 mW Σρ increase form 0.3% up to about 4.6% and approaches

Fig. 2 Degree of circular polarization ρc versus themagnetic field strength (Faraday geometry) for a QDensemble with (a) xMn = 0.0, (b) xMn = 0.01, and(c) xMn = 0.02. A point symmetric behavior be-tween σ+ and σ+ polarized excitation was observedas well as a sign reversal of the polarization compar-ing QDs with 0% and 2% Mn. In addition the opticalorientation (gray solid line) due to circular polarizedexcitation is shown for each sample as a function ofthe external magnetic field.



Fig. 3 Σρ(B) for CdSe QDs with 0%, 1% and2% Mn. From 0% to 2% Mn a sign change of theexciton g factor was observed. For QDs with 1%Mn a vanishing small g factor of gx ≈ –0.05 wasdetermined from the Σρ (B) function. The insetshows the PL decay obtained at the maximum of thetime-integrated PL spectra. The exciton lifetimes forQDs with 0%, 1%, and 2% Mn were determined asτr = (321±20) ps, (222±20) ps, and (145±20) ps,respectively.

with increasing power Σρ of QDs with xMn = 0.0. We have determined the exciton lifetimes of the samesample for different excitation powers (inset Fig. 5a). Up to 12 mW no change of the lifetime could beobserved which rules out the formation of multiexciton complexes and the population of excited states forwhich a change of the radiation rate is expected [42–44].

We relate the excitation power dependent changes of Σρ to an optical heating effect of the Mn system.Principally two different heating mechanism are known in the literature and of relevance for semimagneticsystems [20–23]. One is an indirect heating process mediated by nonequilibrium phonons [20, 22]. Inaddition to that photo-excited carries with an excess energy contribute to the heating of the system. Viaspin-flips these carriers can transfer their excess energy to the Mn system which is called a direct heatingmechanism [21, 22]. Such a direct heating process would result in a large spin temperature. It is clear thatdue to an energy conservation it is required that the Zeeman splitting of the hot carriers matches to thatof the Mn ions. Normally such a mechanism is not very efficient in semimagnetic QDs since the Zeemansplitting of the carriers is large compared to the Zeeman splitting of the Mn2+ ions [23]. In the studiedsample containing 1% Mn with a small exciton g factor such an obstacle is a not given anymore and bothheating processes can principally occur.

In order to analyze the different contributions of the heating, we have to deteremine the effective tem-perature of the Mn spin system. For that purpose we have to take into account Eq. (2) and the effective gfactor which can be described by [11, 12, 16, 45]:

gx =∆E

µBB= g0 + gsp−d. (3)

Fig. 4 Σρ versus magnetic field for QDs withxMn = 0.01. For high excitation power (P =8 mW) an enhanced g factor results in an increasingexciton relaxation rate.

phys. stat. sol. (c) 4, No. 9 (2007) 3339


gsp−d is the contribution to the effective g factor mediated by the sp-d interaction between the Mn system

and the photogenerated carriers with gsp−d ∝ xMnB5/2

(5µBgMnB2kBTeff

). B5/2

(5µBgMnB2kBTeff

)represents the

Brillouin function for the Mn spin-5/2 system, where gMn ≈ 2 is the g factor of the Mn2+ ions [11].Teff denotes the effctive system temperature and xMn the Mn concentration of the sudied samples. Theeffective system temperature extracted by Eq. (2) and (3) is shown for different excitation powers up to 10mW in Fig. 5b for QDs containing nominal 1% and 2% Mn.

For xMn = 0.01 (open squares) and for a low range of excitation power up to P ≈ 3 mW the tem-perature rises up weakly with the power. From the fit (solid lines) a P ∝ T 4.8 dependency was foundwhich is in good agreement with a P ∝ T 4 behaviour expected for an indirect heating mechanism [22].Therefore we conlude that for P < 3 mW mainly phonons contribute to the heating process. As it isdiscussed above and shown in Fig. 5 with increasing excitation power the effective g factor increase withnegative sign and thus at a critical excitation power the heating mechanism via photogenerated carries canoccur. Such a threshold was found for an excitation power of P ≈ 3 mW where the temperature starts toincrease rapidly which scales for P > 3 mW as P ∝ T 1.4 with an exponent more than a factor 3 smallerthan for an indirect heating mechanism. With respect to these results we conclude that for P > 3 mW adirect transfer of heat occurs which was recently analyzed for ZnMnSe/ZnBeSe quantum wells [22]. Froma simple point of view a linearly dependence between the number of photogenerated carries and the energyflux from electron and hole to the Mn system is expected. Such an assumption can be hold as long asthe number of photogenerated carries increases proportional to the excitation power. This is the case aslong as the excitation power doesn’t reach a saturation level where the probability for excited states andthe generation of multi-exciton complexes is enhanced. Such a formation can be ruled out as the lifetime

Fig. 5 Σρ for QDs with 1% Mn versus excitation power at |B| = 4 T. With increasing laser power Σρ increases andapproaches the value found for QDs with xMn = 0.0. The inset shows a constant exciton lifetime of about 220 ps fordifferent excitation powers. (b) System temperature as a function of the laser power due to optical heating. For QDswith 1% Mn (open squares) and P > 3 mW a direct carrier mediated heating effect takes place for which a P ∝ T 1.4

behavior was determined. The P ∝ T 4.8 dependency for P < 3 mW and P ∝ T 4.9 for 2% Mn (filled squares) arerelated to the generation of phonons.



in the relevant power range remains constant. Thus a P ∝ T dependency can be expected for an directheating mechanism which corresponds well to the observed P ∝ T 1.4.

In contrast to the sample with 1% Mn where both heating effects influence the system temperature, forQDs with xMn = 0.02 a different behavior was found. From the double logarithmic plot of T (P ) (Fig. 5b)we extracted a P ∝ T 4.9 dependency. Thus a indirect heating mechanism dominates for the entire rangeof the excitation powers. Such a result can be explained by a mismatch of the Zeeman splittings of thephotocarriers and the Mn system. Direct energy transfer via spin flip is not possible as the energy wouldnot be conserved.

However studying the evolution of the circular polarization degree for QDs with 2% Mn as a functionof the exciting laser power an additional possibility to tune the polarization properties was found. Fig. 6shows the degree of circular polarization for σ+ as well as for σ− polarized excitation versus the excitationpower ranging from 0.2 mW up to 9 mW at a magnetic field strength of +4 T and –4 T, respectively. Forσ− polarized excitation and B = +4 T (open circles) ρc decreases from +17% to +10%. Changing theorientation of the magnetic field (B = −4 T) and the polarization of the exciting laser, the polarization de-gree changes its sign whereas the absolute values remain for each laser power the same. On the other hand,if the polarization of the exciting laser is changed from σ− to σ+ ρc decreases by about 13% independenton the laser power. The difference of ρc induced by a change of the polarization of the exciting laser isreferred to the optical orientation ρor of excitons. In the frame of a pseudo-spin model it has been demon-strated that the optical orientation depends for instance on the anisotropic exchange splitting of excitonsand the strength of the magnetic field [5].

Most interestingly, for excitation of the QD ensemble with σ− polarized light at a magnetic field strengthof –4 T (open squares) ρc changes from –4% for P = 0.2 mW to around 3% for P = 9 mW, passing thepoint of zero polarization at approximately P = 3 mW. Also here a change of the magnetic field and thepolarization of the exciting laser leads to a change of the sign of ρc (filled circles). It should be noted thatan optical power induced change of sign in ρc represents an interesting control parameter of the excitonspin states and their occupation in a quantum dot, for which usually the magnetic field or the polarization ofthe laser serve as control parameters. In order to describe the observed ρc(P ) curves we take into account:

Fig. 6 Degree of circular polarization ρc of the QDluminescence (xMn = 0.02) as a function of thelaser power P for σ+ and σ− polarized excitationat B = ±4 T. For σ− excitation and –4 T (opensquares) as well as for σ+ excitation and +4 T ( filledcircles) ρc can be tuned to positive and negative val-ues. The solid lines were calculated by Eqs. (4) and(6).

phys. stat. sol. (c) 4, No. 9 (2007) 3341


ρc = Σρ ± ρor

and thus with Eq. (2):

ρc(∆E, T ) =τr

(e

∆E

kT − 1)

τr + e∆E

kT (τr + τs)± ρor. (4)

The optical orientation of excitons due to circular polarized excitation σ± of the laser is ρor = ∓7%.τs = 1.5 ns is the carrier spin relaxation time and τr = 145 ps the exciton lifetime. According to Gaj et al.and Eq. (3) ∆E can be described by a modified Brillouin function which is in a first order approximation[13]:

∆E ∝µBgMnB

T+ O[B2]. (5)

Taking the observed indirect heating mechanism into account the exponent in Eq. (4) reads as follows:

e∆E

kT ∼ eT−2

∼ e1√P . (6)

With the help of Eq. (6) in combination with Eq. (4) the observed power dependence of the circular degreeof polarization was calculated. The solid lines represent theoretical values of the above described model.

4 Radiative coupling of QDs Quantum dots as they were studied here are very often regarded asindependent quantum-mechanical systems. Such a treatment appears correct by comparing the as growndensity of QDs (≈ 1011 cm−2) and the wavefunction dimensions of electrons and holes captured in thesestructures. QDs are often called artificial atoms due to their discrete density of states similar to atoms. Itis well known that in a spontaneously radiating gas of atoms, the particles can interact with a commonradiation field. Thus they can not regarded as independent sources of the radiation [46]. It has beenproposed by several groups that such a radiative coupling could lead to superradiance of QDs, similar toatoms [29–31].

We have observed an indication of QD superradiance in samples containing just one single layer ofself-assembled CdSe/ZnSe QDs [1]. The experimental results suggest that the QDs do not behave likeindividual particles as long as they form an ensemble.

4.1 Sample and experiment The sample was grown by molecular beam epitaxy on top of a GaAssubstrate and a 200-nm thick GaAs buffer layer. The lateral size of the studied QDs is 6–10 nm [48] withan as grown density of 1011 cm−2 [49]. Thus the average separation between two adjacent QDs is largerthan 35 nm. Considering the bulk exciton Bohr radius the QDs behave like independent quantum objectsin terms of a quantum-mechanical tunneling coupling. The sample was structured forming square shapedmesas by electron beam lithography and dry etching. For statistical averaging the mesas were arranged inmulti-mesa-arrays (MMAs) with a size of 100 µm×100 µm and a center to center distance between singlemesas of 1 µm and 2 µm, respectively. Multi-mesa-arrays with mesa sizes from 100 µm (unstructuredpart) down to 60 nm were realized. In Fig. 7a FEM picture of a 500 nm MMA with mesa center to centerdistance of 1 µm is shown.

The sample was investigated using a pulsed and frequency-doubled titanium-sapphire laser system pro-viding 1.5 ps pulses with a repetition rate of 82 MHz. The laser energy was tuned to quasi-resonantexcitation below the ZnSe bandgap but closely above the exciton ground state energy of the QDs. With thehelp of a achromatic lens the laser beam was focused on the sample with a spot size of 60 µm in diameter.



Fig. 7 (a) Time evolution of the PL decay of CdSe QDs detected at the maximum of the time-integrated PL signal forMMAs with different mesa sizes. The exciton lifetime increases with decreasing mesa size starting with 100 µm (QDensemble) down to 60 nm (ensemble of single QDs). In the upper left a FEM picture of a 500 nm MMA is shown. (b)Spectral evolution of the exciton lifetime for quasi-resonant (τqr) and non resonant excitation (τnr). The ratio τqr/τnr

(black solid line) exhibits a minimum at the maximum of intensity (dashed line).

For studying the temporal evolution of the PL signal a streak camera in combination with a Peltier-cooledCCD camera was used. The system has a spectral and temporal resolution of about 1 meV and < 20 ps,respectively. The linear polarization of the laser beam was adjusted to πx and πy by the use of a Glan-laser-prism followed by a λ/2-rhombus. The sample was kept at a temperature of 1.5 K in a LHe bathcryostat.

4.2 Results and discussion In order to show that well separated QDs can interact with each otherthrough their radiation field, it must be demonstrated that the exciton lifetime changes with the number ofQDs, their spatial and spectral separation [30,31]. For that reason the number of excited QDs was stepwisereduced by the fabrication of MMAs of different mesa size.

As it is shown in Fig. 7b the exciton lifetime versus the spectral position has a minimum comparing thequasi-resonant (τqr) and the non-resonant (τnr) (above the ZnSe bandgap) excitation conditions. For bothkinds of excitation the PL decay time decreases from the low- to the high-energy side of the QD spectraas it is known from the literature [50–52]. The relative change of PL decay times for quasi-resonant andnon-resonant excitation conditions, τqr/τnr, has a minimum approximately at the maximum of the time-integrated PL signal. At this spectral position the radiation rate has a maximum (Fig. 7b).

In order to proof this assumption whether the studied QDs couple with each other through a commonradiation field the number of QDs was stepwise removed by fabricating MMAs with decreasing mesa size.With the as grown density of about 1011 cm−2 in average only 3 to 4 QDs are located in one single 60 nmmesa. If really a superradiant coupling between the dots exist than the observed exciton lifetime shouldchange drastically by removing more and more QDs. In Fig. 7a the temporal evolution of the PL signalof different MMAs is shown determined at the maximum of the time-integrated PL signal. Starting withthe QD ensemble represented by the 100 µm mesa the decay of the PL signal is slowed down by reducingthe mesa size to 150 nm and finally down to a MMA with containing 60 nm mesas. Thus a variation ofthe exciton lifetime from around 270 ps for the QD ensemble up to 375 ps for an ensemble of single QDs(60 nm MMA) was observed (Fig. 8). It should be noted that such a result is in contrast to an expecteddecrease of the exciton lifetime due to an enhancement of non-radiative channels at the larger surface

phys. stat. sol. (c) 4, No. 9 (2007) 3343


Fig. 8 PL radiation time as a function of the num-ber of QDs per mesa arranged in MMAs for a mesacenter-to-center distance of 1 µm (filled squares)and 2 µm (open squares) at quasi-resonant excitationconditions.

in small mesas. In Fig. 8 the increase of the of radiative lifetime with decreasing number of QDs permesa is shown. Interestingly such a variation was only found for resonant excitation conditions belowthe ZnSe bandgap. Tuning the laser energy to values above the ZnSe transition energy of ≈ 2.82 eV nosignificant change of the emission rate across the whole range of mesa size was found. As a result neitheran alteration in strain due to the formation of mesas nor a modified dielectric constant can be regarded asorigin of the lifetime variation. Evidently in the case of quasi-resonant excitation the superradiant modecouples efficiently to the optical field [1].

A close inspection of Fig. 8 gives, that even for MMAs with mesa sizes larger than 300 nm the observedexciton lifetimes continue to decrease. A lower limit for the optical coupling and the average range ofinteraction between the QDs is at least 150 nm.

5 Conclusion In summary we showed that in single and ensembled semimagnetic CdMnSe/ZnSe QDsthe spin orientation of photoexcited carriers depends sensitively on the amount of Mn incorporated in thesenanostructures. For that purpose we studied the circular polarization of the photoluminescence of QDscontaining nominal Mn concentrations between 0% and 2% under resonant excitation conditions usingcircular polarized laser light. From the observed curves of circular polarization versus the magnetic fieldstrength we were able to determine the g factors. It was found that the exciton g factor can be tuned bychanging the Mn concentration. We demonstrate a sign reversal from negative to positive of the excitong factor by increasing the Mn content from 0% up to 2% with a vanishing small value of g for QDs with1% Mn. Furthermore, it was shown that the circular degree of polarization depends sensitively on theexcitation power which we interpret in terms of a heating mechanism of the Mn spin system. Two differentheating mechanism, direct heating via spin-flip scattering and indirect heating mediated by nonequilibriumphonons were identified for QDs with xMn = 0.01. Due to the heating process an effective optical manip-ulation of the exciton g factor by a factor of 30 was observed. In contrast to that for QDs with nominal 2%Mn only the indirect heating mechanism was observed. Interestingly for appropriate excitation conditionsand a certain orientation of the magnetic filed the PL polarization can be inverted with increasing excitationpower passing the point of zero polarization at P ≈ 3 mW.

Also a radiative coupling between CdSe QDs was observed. Such a superradiant interaction was demon-strated by time-resolved PL investigations under quasi-resonant excitation conditions. In case of a radiativecoupling a shortened PL decay time was observed due to the coupling to a superradiant mode. The num-ber of QDs located within a certain area was reduced. For such a constrained ensemble of single QDs anenhanced exciton lifetime was observed which is related to a reduced superradiant coupling. This kind ofoptical coupling could play possibly a significant role for novel devices based on semiconductor nano-structures.



Acknowledgements The authors are grateful for financial support from the Deutsche Forschungsgemeinschaft(DFG) in the framework of the Sonderforschungsbereich (SFB) 410 and the state of Bavaria. We thank M. Emmerlingfor the technical assistance.

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Light controlled spin properties and radiative coupling of CdSe based quantum dots

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