In-plane radiative recombination channel of a dark exciton in self-assembled quantum dots

0.24 MB·English

by  Tomasz Smoleński

Radiative lifetime of dark excitons in self-assembled quantum dots
T. Smolen´ski,1,∗ T. Kazimierczuk,1 M. Goryca,1 T. Jakubczyk,1
L . Kl opotowski,2 L . Cywin´ski,2 P. Wojnar,2 A. Golnik,1 and P. Kossacki1
1Institute of Experimental Physics, Faculty of Physics, University of Warsaw,
ul. Hoz˙a 69, 00-681 Warsaw, Poland
2Institute of Physics, Polish Academy of Sciences,
Al. Lotniko´w 32/64, 02-688 Warsaw, Poland
(Dated: July 6, 2012)
2
Wedemonstrateanevidenceforradiativerecombinationchannelofdarkexcitonsinself-assembled
1
quantumdots. Thetime-resolvedmagnetospectroscopyofsingleCdTe/ZnTequantumdotswasused
0
toextractthezeromagneticfielddarkexcitonlifetime, whichvariedfordifferentdotsfrom 30nsto
2
over2µs. We found thestrong dependenceof this lifetime on thedegree of light hole admixtureto

l the excitonic ground state. This admixture creates a radiative recombination channel for the dark
u
exciton. Photonscreated from itsrecombination areemitted only in thedirection perpendicularto
J
thegrowth axis. Thiswasconfirmedbyadirectobservationofthedarkexcitonphotoluminescence
5 from a cleaved edge of the sample.

]
PACSnumbers: 78.55.Et,78.67.Hc
l
l
a
h
Self-assembledsemiconductorquantumdots(QDs)are evident in the analysis of the low temperature behavior
-
s recognized as a medium for storage and manipulation of ofthisprocess. Inparticular,turningdarkexcitonintoa
e
m quantuminformation[1]. Importantapplications,involv- brightonerequiresabsorptionofenergyfromthephonon
ing emission of single photons [2] or entangled photon bathequalto(isotropic)electron-holeexchangeconstant
.
t pairs [3, 4] rely heavily on properties of confined exci- δ [9], and therefore predicted lifetime of dark exciton
a 0
m toniccomplexes. Inparticular,thecentralpointofmany can, in principle, be infinitely prolonged by lowering the
schemes is a neutral exciton consisting of a single elec- temperature. A presence of another decay mechanism
-
d tronanda singlehole. However,the properties ofsucha wasalreadysuggestedinRef. 13,wheretheauthorscon-
n complexdependontherelativeorientationofthespinsof cluded that the lifetime of the dark exciton is limited by
o
confined carriers. An electron and a hole with antiparal- an unknown “non-radiative decay channel”, rather than
c
[ lelspinsformanopticallyactivebright exciton (Xb)with by the spin-flip process.
total angular momentum projection on the QD growth In this Letter, we demonstrate that the dark exciton
1
v axis Jz =±1, while parallel orientation of spins leads to can recombine radiatively at zero magnetic field due to
7 the formationof a dark exciton (Xd) with Jz = 2. Due anadmixtureofalightholestate. Furthermore,weshow
±
3 to the lack of dipole allowed recombination channel, the thatthisemissionisdirectedperpendiculartothegrowth
2 lifetimeofthelatteronemayextendabovemicroseconds axis, as expected from the mixing in the valence band.
1 [5]. The presence of the dark excitons is often neglected We also provide an evidence that the slow decay of the
.
7 [6], however due to their persistent nature, dark exci- brightexcitoncannotbe,inourcase,explainedbycarrier
0 tons can havedetrimentaleffect onthe properties ofQD spin-flip as usually assumed.
2
devices. On the other hand, recent findings show that
1 Our experiments were performed on samples contain-
the dark exciton can be also used as a qubit [7], which
: ing self-assembled CdTe/ZnTe QDs grown by the amor-
v turns its long lifetime into an advantage. The important
phous tellurium desorption method [14]. However, our
i
X roleofthe darkexcitons andtheir lifetime is thereforeof
findings should apply also to other systems. The mea-
principal interest for quantum information processing.
r surementswerecarriedoutinamicro-photoluminescence
a
Studies of dark excitons are hindered by their absence setup described in Refs. 15 and 16. Sample was
in the photoluminescence (PL) spectrum. They become placed inside a magneto-optical cryostat at 1.7K. Dur-
visible after introducing a mixing between bright and ing the time-resolved measurements the QDs were ex-
dark configurations,either by an in-plane magnetic field cited nonresonantly by a frequency doubled pulses from
[8, 9] or the exchange interaction with magnetic dopant a Ti:sapphire laser. The laser repetition rate was effec-
[10]. The lifetime of the dark exciton is widely believed tively reduced with a pulse picker, which enabled us to
to be determined by a spin-flip process turning a dark observelongPLdecays. ThePLwasrecordedeitherbya
excitoninto a brightone [5, 11,12]. The mainargument CCD camera or, in case of time-resolved measurements,
forsuchamechanismisabiexponentialdecayofabright byanavalanchephotodiode(APD)withsub-nanosecond
exciton,whichwasobservedinbothIII-VandII-VIQDs temporal resolution.
[5, 13]. However, the spin-flip cannot be considered the Figure 1(a) presents spectra of a single QD for differ-
soledecaymechanismofthedarkexciton. Itisespecially ent values of the in-plane magnetic field. Emission lines
2
with bright excitons. The fast decay time is related to
X with larger admixture of the bright excitons, while
d
(a) + Xd Xb the slow decay time originatesfrom PL of Xd with lower
2X X 10T bright exciton admixture. This explanation stays in an
agreement with more abrupt reduction of the fast de-
s) 8T cay time with increasing magnetic field. In the following
nit analysiswefocusonthedarkexcitonwithstrongerfield-
u
b. 6T inducedmixing. Figure1(c)showstheinverselifetime of
ar th is dark exciton as a function of the magnetic field.
(
L 4T Inordertoquantitativelyanalyzethe observeddepen-
P
denceweuseasimplemodeloftheneutralexcitoninthe
2T in-plane magnetic field given by the following Hamilto-
nian [9, 17],
0T
δ
= 2δ SzSz+ 1 S+S−+S−S+
1830 1835 1840 H − 0 e h 2 e h e h
Energy (meV) (cid:0) (cid:1)
+ g µ B~ S~ +g µ B~rˆ S~ , (1)
e B e h B 2θ h
·
0.6
(b) (c)
where S~ are the electron spin operators, S~ are the 1/2
e h
s) 2T spin operatorsin the two-dimensionalsubspace of heavy
b. unit 4T 1/ns)0.4 hQoDle).stTahteesfi(trhste tlwowoestte-remnesrgreyphreosleensttatthees icsoontrfionpeidc iannda
ar (
L ( 6T 1/ anisotropic parts of the electron-hole exchange interac-
P 0.2 tion. The remaining terms represent the Zeeman ener-
8T 0=32 3ns gies of the electron and the hole, with their in-plane g-
factorsequaltog andg ,respectively. TheholeZeeman
e h
termincludestherˆ tensor,whichistherotationmatrix
0.0 2θ
0 30 60 90 0 2 4 6 8 10 through 2θ, where θ is an angle between exchange inter-
Time (ns) B (T) actionanisotropyandthe directionrelatedto the strain-
induced valence band mixing [18]. All the parameters in
FIG.1: (coloronline)(a)PLspectraofasingleQDfordiffer-
entvaluesofthein-planemagneticfield. (b)PLdecaycurves the Hamiltonian were directly extracted from the polar-
of the dark exciton for different magnetic fields, measured ization resolved PL measurements in different magnetic
without polarization resolution. Solid lines represent the fits fields for each studied QD. In particular, exchange ener-
of biexponential decays, which are related to the presence of gieswereidentifiedasthesplittingbetweenthedarkand
two dark excitons with almost equal emission energies, but
bright states (δ ), and the splitting between two bright
0
different efficiencies of mixing with bright excitons. (c) In-
configurations (δ ), obtained in zero magnetic field [9].
verse lifetime of the shorter lived dark exciton as a function 1
Here we neglect δ splitting of the dark excitons, which
of the in-plane magnetic field. The solid line represents the 2
fitted curve described by Eq. (2). The zero magnetic field is of the order of a single µeV [7]. The carrier g-factors
lifetimeofthedarkexcitonforthisQDyieldsτ0 =32±3ns. wereextractedfromtheenergypositionsoffour-foldsplit
trion emission lines in magnetic field [17, 18]. Futher-
more, the angle θ was obtained from the polarization
wereidentifiedasoriginatingfromrecombinationofneu- resolvedX and trion PL measurements at B =0T [18].
b
tral excitons (bright and dark), positively charged exci- By diagonalization of the Hamiltonian for a given mag-
ton(X+)andbiexciton(2X).Asexpected[8,9],therela- neticfieldB,oneobtainsfoureigenstates. Twoloweren-
tiveintensityofX emissionlineincreaseswithmagnetic ergy states ψ (B) (i = 1,2) correspond to mostly dark
d i
| i
field,duetotheinducedmixingbetweenbrightanddark states. Theiroverlapwithzero-fieldbrightstates 1 is
|± i
excitons. InordertodeterminethedependenceofX life- givenbyf (B)= 1ψ (B) 2+ 1ψ (B) 2. Thisover-
d i i i
|h | i| |h− | i|
time on the magnetic field, we performed time-resolved lap is proportional to the oscillator strength of ψ (B)
i
| i
measurements. Figure 1(b) shows the time-dependent radiativerecombinationinducedbyanin-planemagnetic
PL intensity of X transition for several values of mag- field. In the case of lack of other decay mechanisms, the
d
netic field. The data was corrected for dark counts by inverselifetimeofdarkexcitonsshouldbeproportionalto
subtractionofareferencesignalmeasuredatemissionen- f (B). In particular,this implies that at B =0T the X
i d
ergycorrespondingto flat PL background. Decay curves lifetimewouldbeinfinitelylong. Thiscontradictstheex-
from Fig. 1(b) clearly show a biexponential behavior, perimentaldatafromFig. 1(c), whichclearlyshowsthat
which is due to the presence of two nearly degenerate the dark exciton lifetime is converging to a finite value
dark excitons [7, 9] with different efficiencies of mixing at B = 0T. We account for this fact by introduction of
3
Experiment
100000 6 27.8
Spin-flip model
8h)0
s/
10000 unt =117 10ns s
o
ounts/h)1000 PL (c /1 04 62.5 ns 0
c 8
(
PL 0 150 300 /12 250
100 Time (ns)
10
0
0.0 0.2 0.4 0.6
gh
0 100 200 300
Time (ns) FIG. 3: (color online) Square root of the inverse zero-field
dark exciton lifetime versus in-plane hole g-factor (each ex-
FIG.2: (coloronline)PLdecaycurveofthebrightexcitonat
perimental point corresponds to different randomly selected
B=0T.ThedashedlinerepresentsthePLdecayofthebright
QD). The solid line represents the linear fit predicted by the
excitonpredictedbythespin-flipmodelassumingequalinitial
theory.
populationsofbrightanddarkstatesafteranexcitationpulse
(which is due to independent capture of electrons and holes
under nonresonant excitation [6, 15]). Zero-field lifetime of
the dark exciton for this dot yielded 125±20ns. Inset: the totallineintensity,istentativelyattributedtotherecap-
PL decay of the dark exciton for the same quantum dot at turingofthecarriersbytheQD.Qualitativediscrepancy
B=0.5Twithexponentialfit(solidline). Forclarity,inboth between the experimental X decay and the one calcu-
b
plots theCW background was artificially set to 10.
latedinthespin-flipmodel(dashedlineinFig. 2)clearly
excludes such spin-flip scenario.
Instead, we introduce a new radiative decay mech-
a field independent decay mechanism, which determines
anism for the dark exciton. Proposed mechanism is
the dark exciton lifetime at B = 0T. Thus, the shorter
induced by the valence band mixing, which is usually
lived (i=1) dark exciton lifetime τ (B) should read
1
present in both III-V [19] and II-VI [10, 17, 18, 20]
1 1
QDs. We consider the heavy ( 3/2 ) and the light
=γf (B)+ , (2)
1 | ± i
τ1(B) τ0 ( 1/2 ) hole states, which are mixed due to the pres-
|± i
ence of strain in a QD. In the leading order, 3/2
where τ0 is its zero-field lifetime, and γ is a constant re- | ± i
states are only mixed with 1/2 [17], which yields
lated to the radiative lifetime of the bright exciton at | ∓ i
the lowest-energy hole states in a QD to be given by
B =0T.Ourcalculationsperfectlyreproducethedepen-
dence ofXd lifetime onthe magnetic field, as it is shown |φh±i=|±3/2i+ǫ±|∓1/2i (ǫ± =ǫe±2iθ, where ǫ rep-
resents the strength of the valence band mixing, and θ
in Fig. 1(c). Moreover, for the studied QD, the model
itsdirection). Thegroundstatesofthedarkexcitonsare
predicts one of the dark excitons to be much stronger
mixed with the bright ones, as it was noted during the now of the forms |↑ei|φh+i, |↓ei|φh−i, where |↑ei, |↓ei
denote the electron spin eigenstates. One can define the
analysis of decay curves from Fig. 1(b). Similar mea-
hole states using the X,Y,Z p-type orbitals and ,
surements were performed on several randomly selected | ↑hi
hole spin eigenstates [17]. Thus, each of the dark
QDs. Theobtainedzero-fielddarkexcitonlifetime τ0 for | ↓hi
exciton states can be expressed in the following way
analyzed QDs varied from about 30ns to over 2µs.
In orderto explainthe originofthe zero-fielddarkex-
1
citon decay mechanism, we first focus on the typically φ = X +iY
e h+ e h
invoked spin-flip process turning the dark exciton into |↑ i| i −√2|↑ i|↑ i| i
the bright one [5, 11–13]. In our case, the measured dy- 1 2
+ ǫ X iY + ǫ Z , (3)
namics ofthe brightexcitonPLatB =0T (Fig. 2) does √6 +|↑ei|↑hi| − i r3 +|↑ei|↓hi| i
not confirm this scenario. Although X decay has the
b
biexponential character,both lifetimes are over an order ( e φh− is given by an analogousexpression). Within
|↓ i| i
ofmagnitudeshorterthantheactuallifetime ofthedark ourconventionofthe holespin, the radiativerecombina-
exciton in the same QD. We identify the faster X de- tion requires antiparallel orientation of the electron and
b
caytimewiththeradiativelifetimeofthebrightexciton. the hole spin. Therefore, the admixtures represented by
The slower decay, which corresponds to about 5% of the the first two terms in Eq. (3) do not allow radiative re-
4
Theradiativerecombinationofdarkexcitonis relatedto
53 W (b) 90o the ǫ+ 2/3| ↑ei| ↓hi|Zi term in Eq. (3), and therefore,
o o corresppondingtransitiondipolemomentisorientedalong
0.6 W 120 60
the QD growthaxis (z). Such a dipole moment does not
(a) 9
nits) Xb 150o 30o 6 nits) ctioounp,lewthoicthhecolrigrehstpeomnditstetdoptayrpaicllaell gtoeotmheetgrryowofththdeirPecL-
arb. u 180 o Xb Xd 0o 003 arb. u saettuBp.=In0Tor,dweretpoeorbfosremrveedthaemdeaarksuerxecmiteonnteomf iassQioDnlPinLe
PL ( Xd 3 PL ( fwroavme tehxecitcaletaiovne.d Uedngdeerofsttrhoengsaemxcpilteatuionndeprocwoenrti(nsuhoourst
x50 210o 330o 6 carrierrecapturetime)thebrightexcitonPLisexpected
9 todominatethespectrum,asXb lifetimeismuchshorter
o o compared to the dark exciton one. However, in the low
240 o 300
1825 1827 270 excitation power regime (i.e., when the carrierrecapture
Energy (meV) time is comparable with the zero-field X lifetime), the
d
FIG. 4: (color online) PL of the neutral exciton measured darkexcitonemissionline shouldbe clearlyvisible. This
fromthecleavededgeofthesampleatB=0TunderCWex- predictions areperfectly fulfilled by the experimentalre-
citation. (a) PL spectra measured under different excitation sultspresentedinFigure4(a). Moreover,thepolarization
powers related to different average carrier recapture times. resolvedmeasurementsshowthat the X emissionline is
d
Relative intensity of the Xd line becomes stronger for the almostfully linearly polarizedalong the QD growthaxis
recapture time comparable to τ0. (b) Polar plot presenting (Fig. 4(b)).
the polarization of the dark and bright exciton emission for
0.6µW excitation power. The 90◦ and 270◦ directions are Thisdirectobservationofthedarkexcitonemissionat
alongtheQDgrowthaxis. Symbolsforanglesϕandϕ+180◦ B = 0T unequivocally confirms our model. We stress
correspond to thesame data points. out that such an emission is observed only for in-plane
detection, and it is not present in the standard experi-
mental configuration. We believe that our findings will
combination,astheelectronandtheholespinsareparal- stimulate the studies on the role of the dark exciton in
lel. However,theadmixturerepresentedbythelastterm the QDs. In particular, the coupling between the dark
in Eq. (3)has antiparallelcarriersspindirections,which exciton and the in-plane radiation demonstrated in our
opens the radiative recombination channel for the dark work may be used for direct optical control of the dark
exciton. The oscillator strength of this transition is pro- exciton qubit.
portional to ǫ2. On the other hand, ǫ is proportional to
This work was partially supported by the Polish
the in-plane hole g-factor g [18]. Therefore, the square
h Ministry of Science and Higher Education in years
root of the inverse dark exciton zero-field lifetime is ex-
2012-2015 as research grants “Iuventus” and “Diamen-
pected to be directly proportionalto g . This prediction
h towy Grant”, and by the National Science Centre un-
isfullyreproducedbytheexperimentaldataobtainedfor
der decisions DEC-2011/02/A/ST3/00131 and DEC-
several QDs, as shown in Figure 3.
2011/01/N/ST3/04536. L C acknowledges support from
For simplicity, we used here e φh+ and e φh− theHomingprogrammeoftheFoundationforPolishSci-
| ↑ i| i | ↓ i| i
states. At B = 0T, due to the QD anisotropy, one ence supported by the EEA Financial Mechanism.
should rather consider their linear combinations given
by e φh+ eiϕ e φh− . However, the behavior of
| ↑ i| i± | ↓ i| i
these states exhibits complex dependence on the relative
orientations of the anisotropy of the QD (δ splitting of
2
∗
the dark excitons), strain-induced valence band mixing Electronic address: [email protected]
and the external magnetic field. E.g., in the pure C [1] D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120
2v
(1998).
QD shape symmetry, only one of the dark excitons has
[2] P. Michler et al.,Science 290, 2282 (2000).
a non-vanishing dipole transition moment [21]. Detailed [3] N. Akopian et al.,Phys. Rev.Lett. 96, 130501 (2006).
discussionoftheseeffectsisbeyondthescopeofthisLet- [4] R.M.Stevensonetal.,Nature(London)439,179(2006).
ter. We note only that any givencombinationof relative [5] O. Labeau, P. Tamarat and B. Lounis, Phys. Rev. Lett.
orientationofinvolvedinteractionsleadstotheǫ2 depen- 90, 257404 (2003).
dence of zero-field dark exciton recombination rate. [6] J. Suffczyn´skiet al., Phys.Rev.B 74, 085319 (2006).
[7] E. Poem et al., NaturePhysics 6, 993 (2010).
Described mechanism entails the radiative emission of
[8] M. Nirmal et al., Phys.Rev.Lett. 75, 3728 (1995).
thedarkexciton. Suchaclaimisseeminglycontradictory
[9] M. Bayer et al.,Phys. Rev.B 65, 195315 (2002).
to the lack of the dark exciton line in the PL spectra at [10] M. Goryca et al., Phys.Rev.B 82, 165323 (2010).
B = 0T in Fig. 1(a). However, this apparent inconsis- [11] P. A. Dalgarno et al., Phys. Stat. Sol. (a) 202, 2591
tency is due to the geometry of the experimental setup. (2005).
5
[12] J. M. Smith et al.,Phys. Rev.Lett.94, 197402 (2005). (2004).
[13] J. Johansen et al.,Phys.Rev. B81, 081304(R) (2010). [19] M. Atatu¨re et al.,Science 312, 551 (2006).
[14] F. Tinjod et al.,Appl.Phys. Lett.82, 4340 (2003). [20] C.L.Cao, L.BesombesandJ.Ferna´ndez-Rossier,Phys.
[15] T.Kazimierczuk et al.,Phys.Rev.B81, 155313 (2010). Rev. B 84, 205305 (2011).
[16] T.Kazimierczuk et al.,Phys.Rev.B84, 165319 (2011). [21] M. A. Dupertuis et al., Phys. Rev. Lett. 107, 127403
[17] Y.L´eger et al.,Phys. Rev.B 76, 045331 (2007). (2011).
[18] A. V. Koudinov et al., Phys. Rev. B 70, 241305(R)