Linköping University Post Print
Spin polarization of the neutral exciton in a
single InAs quantum dot at zero magnetic field
Evgenii Moskalenko, L A Larsson and Per-Olof Holtz
N.B.: When citing this work, cite the original article.
Original Publication:
Evgenii Moskalenko, L A Larsson and Per-Olof Holtz, Spin polarization of the neutral
exciton in a single InAs quantum dot at zero magnetic field, 2009, PHYSICAL REVIEW B,
(80), 19, 193413.
http://dx.doi.org/10.1103/PhysRevB.80.193413
Copyright: American Physical Society
http://www.aps.org/
Postprint available at: Linköping University Electronic Press
Spin polarization of the neutral exciton in a single InAs quantum dot at zero magnetic field
E. S. Moskalenko,1,2L. A. Larsson,1 and P. O. Holtz11IFM, Material Physics, Linköping University, S-581 83 Linköping, Sweden
2A. F. Ioffe Physical-Technical Institute, Russian Academy of Sciences, Polytechnicheskaya 26, 194021 St. Petersburg, Russia
共Received 24 September 2009; published 30 November 2009兲
A high degree of spin polarization for the neutral exciton in individual quantum dots, at zero external magnetic field, is monitored. While a high polarization degree is commonly observed for the charged ex-citon, a negligible polarization has been predicted for the neutral exciton. The exceptionally high polarization 共⬎60%兲 observed here is explained in terms of a dynamical nuclear polarization field, stabilizing the electron spin. Such polarization of the quantum dot nuclei, in case of the neutral exciton, is possible due to unequal capture time of electrons and holes.
DOI:10.1103/PhysRevB.80.193413 PACS number共s兲: 78.67.Hc, 71.70.Gm, 72.25.Fe, 73.63.Kv
The spin of a single carrier localized in a semiconductor quantum dot共QD兲 has been suggested as a building block for future memory and quantum computer operation.1In particu-lar, the spin of an electron confined in a QD is a good can-didate for these applications because of cancellation of clas-sical spin-relaxation mechanisms.2 The state of the spin of recombining particles can be directly measured by monitor-ing the degree of circular polarization共c兲 in
photolumines-cence 共PL兲 experiments. For the case of neutral excitons in QDs, a negligiblechas been predicted at zero external
mag-netic field 共Bext兲 due to strong anisotropic electron 共e兲-hole
共h兲 exchange interaction.3–7 Conversely, for the case of charged excitons, the anisotropic e-h exchange interaction is suppressed5,8 and an essential
c is expected and has been
confirmed in experiments on individual In共Ga兲As/GaAs QDs. Up to now, a very low cwere recorded at Bext= 0 for
the neutral exciton in experiments with QD ensembles6,9 or individual QDs.3,8,10–12
In the present report, a high degree 共c⬇60%兲 of spin
polarization is achieved for the neutral exciton at Bext= 0 in
individual InAs QDs, studied by micro-photoluminescence 共-PL兲. The anomalously highcis explained by a separate
capture of e’s and h’s into the QD. This provides a time interval, when the QD is occupied with solely an electron, which can polarize the lattice nuclei. In turn, a nuclear mag-netic field 共BN兲, called the Overhauser field, acting upon
electrons will effectively stabilize the electron spin and result in the highcobserved in the experiments. Further, the
elec-tron magnetic field 共Be兲, the Knight field, acting upon the
nuclei in the QD has been directly measured to be⬇13 mT. These experiments demonstrate a possible way to bypass the anisotropic e-h exchange interaction in QDs and thereby al-lowing spin conservation of the neutral exciton
The sample studied was grown by MBE with self-assembled InAs QDs positioned between GaAs barriers.13To create spin-polarized carriers, the sample was excited with circular-polarized light共+and/or−兲. The degree of circular polarization of the PL is given by: c=共Ico− Icross兲/共Ico
+ Icross兲, where Ico共Icross兲 is the spectrally integrated PL
com-ponent of co共cross-兲circular polarization, with respect to the helicity of the excitation light.
Figure 1共a兲shows a -PL spectrum of the wetting layer 共WL兲 emission. In the same panel,cof the neutral exciton
as a function of excitation energy 共hex兲 is presented. It
should be stressed that for all hex, the excitation power was
tuned in order to maintain at the same integrated PL intensity from the QD 共to compensate for the change in sample ab-sorption兲. When hex is varied, c remains positive 关Fig.
1共a兲兴, in striking contrast to negatively charged excitons in
1.42 1.44 1.46 1.48 0.2 0.3 0.4 0.5 0.6
a
Bext= 0b
WL po lar izat ion d egree ρ c Energy (eV) z ωex BΣ IS z ex I S 0 ex B ext 1.3548 1.3552 B ext= 0 det.σY det.σX exc.σX exc.σX det.σ+ det.σ -det.σ -det.σ+ exc.σ -det.σ- det. σ+ exc.σ+c
P L intensity (C C D counts) Energy (eV)FIG. 1. 共a兲 The symbols show c as a function of excitation energy measured at + cw excitation, with Pex= 2 W for hex
⬎EWLand with increased Pexfor hex⬍EWL共see text兲. The line
shows a-PL spectrum of the WL measured at hex= 1.684 eV and
at Pex= 40 nW. 共b兲-PL spectra 共symbols兲 of a QD measured at
hex= 1.463 eV, Pex= 2 W and at different polarization
configu-rations in excitation and detections paths as indicated in the figure. The solid lines are fit with Lorentzian curves to the measured-PL spectra.共c兲 A schematic illustration of the pseudospin model of a neutral exciton exposed to an external magnetic field, as explained in the text. All data in 共a兲 and 共b兲 were recorded at T=4.2 K and
QDs, which exhibit a negative c.9,12,14–17 A set of typical
-PL spectra of the neutral exciton18for h
exin the range of
the WL emission energy共EWL兲, and for different polarization configurations, is shown in Fig. 1共b兲. At circular-polarized excitation, the integrated PL intensity of the cocircular-polarized component appears much stronger than the cross-circular one, illustrating a high and positive degree of c.
The highcobserved here is remarkable, since the bright
states 共兩+1典 and 兩−1典兲 of the heavy-hole neutral exciton is known to be mixed due to the in-plane asymmetry of a QD 共兩+1典 and 兩−1典 correspond to spin projections onto the z axis, which are chosen along the growth axis of the sample兲. This mixing creates two linearly polarized dipoles 兩X典=2−1/2共兩 +1典+兩−1兩兲 and 兩Y典=2−1/2共兩+1典−兩−1典兲/i, which in case of InAs/GaAs QDs emit light along the 具110典 and 具11គ0典 crys-tallographic directions.19,20 兩X典 and 兩Y典 are split by the an-isotropic e-h exchange energy共បex兲 共Ref.21兲 and the bright
states are separated in energy from the dark states. Thus, at
Bext= 0 the neutral exciton is expected to reveal two
orthogo-nal linearly polarized components and only at an elevated external magnetic field共Bext 储z兲, the mixed states 兩X典 and 兩Y典
will transform into “pure”兩+1典 and 兩−1典 states, giving rise to circular-polarized emission. Upon excitation with linearly polarized light 共X兲 at Bext= 0, two orthogonal and linearly
polarized PL lines, separated by បex⬇25 eV, are indeed
monitored关Fig.1共b兲兴.
To explain the highcobserved here, we adopt the vector
model for the exciton pseudospin developed in Refs.4and7 关see Fig.1共c兲兴. Here the anisotropic e-h exchange interaction is viewed as an in-plane magnetic field共ex兲 and the vector
S0 ex
corresponds to the initial exciton spin. Since the preces-sion time关b= 2/ex⬇165 ps 共Ref.6兲兴 of S0
ex
aroundex
is smaller than the exciton decay time 关d⬇800 ps 共Ref.
19兲兴, the exciton spin 共S0
ex兲 will accomplish many turns
around ex before recombination.20 Hence c共proportional
to the projection of the exciton pseudospin onto the z axis, 兩Sz
ex兩兲 is predicted to be negligible.4,6,7
However, as stated above, an external magnetic field of sufficient strength 兩Bext兩Bgex⬎បex 共B⬇58 eV/T is the Bohr magneton
and gex is the neutral exciton g factor兲 applied in Faraday
geometry 共Bext 储z兲 “restores” the polarization of the neutral
exciton because of decoupling of the兩+1典 and 兩−1典 states.6,7 At increasing兩Bext兩, the 兩+1典 and 兩−1典 states are separated in
energy by ⌬E=兵共兩Bext兩Bgex兲2+共បex兲2其1/2,21 which gives
rise to a nonvanishing value of c. In the vector model, an
application of Bext initiates the precession of the exciton
pseudospin around the total magnetic field B⌺= Bext+ex
leading to a nonzero value of 兩Sz
ex兩 and hence of c.
From the -PL spectra 关Fig. 1共b兲兴, an obvious energy separation 共⬇50 eV兲 is recorded between the − and + components at circular-polarized excitation despite Bext= 0.
This is the signature of an effective magnetic field 共BN兲 in
the sample with a projection共BN
z兲 onto the z axis. When the
excitation helicity is reversed, the polarization-resolved PL components exchange their spectral positions, clearly dem-onstrating that BN
z
has reversed its direction. The contribution of兩BN
z兩 to ⌬E, the Overhauser shift 共OHS兲, can be estimated
from OHS=兵共⌬E兲2−共ប
ex兲2其1/2⬇42 eV.
To further elucidate the existence of a magnetic field in the sample at+and/or−cw excitation and to measure the build-up time of BN
z
, the QD was excited by a beam with alternating+and−polarization with frequency, f. The QD was accordingly exposed to + light during the time, ⌬t = f−1, followed by−light共of the same power兲. Detection of the two circular-polarized PL components was performed within the time intervals corresponding to only + 共or −兲 excitation windows共see the lower inset of Fig.2兲.
The polarization degree c, recorded with+ excitation,
remains approximately the same for f⬍100 Hz, but de-creases progressively for f⬎100 Hz to stabilize at a few percent at f⬎1000 Hz 共Fig. 2兲. ⌬t⬇10 ms is accordingly sufficient for BNto buildup, while for⌬t⬍1 ms, BNis
neg-ligible. The dependence of the averaged polarization degree 共具c典兲 共Ref.22兲 on the external magnetic field Bext 储z共upper
inset in Fig. 2兲 shows that 具c典 changes symmetrically to
reach about 55% at 兩Bext兩⬇1.5÷2 T. Based on this
experi-ment,兩BN
z兩 determining
cat cw excitation is predicted to be
of the same order. To understand the origin of BN, a concept
of dynamic polarization of lattice nuclei by optically oriented electrons is employed.23This effect originates from the cou-pling of electron and nuclear spins through the hyperfine Fermi interaction, while the corresponding interaction of nuclear spins with a hole is considerably weaker.23 Hence, the nuclear-hole interactions will be excluded from further discussion. The interaction between a single electron and a large number共104– 105兲 of nuclei 共N兲 in the QD results in a dynamical nuclear spin polarization leading to the appear-ance of spin-oriented nuclei, which is equivalent to building up an effective magnetic field acting upon the electron local-ized in the QD. Nuclear fields as large as several Tesla have been detected for In共Ga兲As/GaAs QDs.3,24,25The rise time of
FIG. 2.cas a function of the alternating frequency, f, measured during the time windows corresponding to an excitation with+, at
Pex= 2 W, hex= 1.463 eV, T = 4.2 K, and at Bext= 0. The upper right inset shows 具c典 as a function of Bext 储z measured at Pex
= 2 W, hex= 1.463 eV, T = 4.2 K, and at f = 1050 Hz. The lower left inset illustrates the excitation procedure with light pulses of alternating helicity. The PL signal is only accumulated within the detection time windows corresponding to+共or−兲 excitation.
BRIEF REPORTS PHYSICAL REVIEW B 80, 193413共2009兲
the nuclear polarization at Bext= 0 in In共Ga兲As/GaAs QDs
has earlier been experimentally determined to be 9.4 ms.26 This value agrees well with the time scale for the buildup of
BNin our experiments.
Accordingly, the field BN introduced above is identified
as a nuclear field grown up in the QD upon cw excitation with circular-polarized light, which injects spin-oriented electrons into the QD. Consequently, no BN is predicted
in the QD under linearly polarized excitation共i.e., photoex-cited electrons appear nonpolarized兲. Hence, the + and − PL components are not expected to be split nor exhibit any measurable value of c, as consistent with our
experi-mental observations 关Fig. 1共b兲兴. Since BN influences only
electrons, the Overhauser shift should be defined as OHS =兩BN
z兩
B兩ge兩,25,27 where ge is the electron g factor. Adopting
兩ge兩=0.5÷0.6 共Refs.3 and24兲 and OHS⬇42 eV, one can
evaluate 兩BNz兩⬇1.2÷1.4 T, in satisfactory agreement with the predictions made above. The experimentally estimated exciton polarization, c, is entirely determined by the
aver-aged electron spin 共S兲 according to c= 2兩Sz兩,19 where Sz is
the projection of S onto the z axis. This is in agreement with the assumption that, for excitation into the WL, the electron spin is preserved during the capture and relaxation processes in the QD, while the hole spin orientation is lost.5,9,15 It should be emphasized that a buildup of nuclear polarization has been demonstrated earlier for the case of the neutral exciton.27 However, this was achieved at a nonzero field,
Bext, and the nuclear polarization was determined by spin flip
assisted radiative recombination of dark excitons.
To explain the experimentally observed fact that a rela-tively strong nuclear magnetic field共1.2÷1.4 T兲 is builtup in the QD even for the case of a neutral exciton at Bext= 0, the
preceding step to the formation of the exciton is considered as a process of separate capture of e’s and h’s as was dem-onstrated in our previous studies on QDs共Ref.13兲 as well as by others共e.g., Refs.28–30and references therein兲. The pa-rameter,⌬e-h, is the difference in capture times between e’s
共e兲 and h’s 共h兲 into the QD. Since both e’s and h’s are
excited into the WL, these times could be estimated as e共h兲
⬇Le共h兲/Ve共h兲. Here Le共h兲corresponds to the collection length
for individual e’s共h’s兲 into the QD and Ve共h兲is the e’s 共h’s兲
velocity in the WL plane, as was earlier deduced to be 1.6 ⫻107 共3.1⫻106兲 cm/s for the same sample.31 For our ex-perimental conditions共with one QD located within the area of the laser spot兲 Le= Lh⬇1 m can be assumed 共i.e., half
the diameter of the laser spot兲 and, hence e 共h兲
⬇6共32兲 ps resulting in ⌬e-h=h−e⬇26 ps. It should be
noted that ⌬e-h represents an expected PL rise time for a
QD, experimentally determined to be 30÷ 50 ps共Refs.9and 32兲 in reasonable agreement with our estimate, ⌬e-h ⬇26 ps. Accordingly, before the recombination of an exci-ton, the QD is assumed to be populated with only an electron for ⬇26 ps. The fraction of time 共⌫e兲 with single electron
occupancy in the QD, is defined as⌫e=⌬e-h/r, whereris
the average time between two subsequent exciton formation events. For an excitation power slightly below the biexciton formation level, one can estimatedⱖrbecause to form the
biexciton, the formation of a second exciton in the QD is required before the first exciton recombines. Hence, r⬇d
⬇800 ps is used giving ⌫e⬇0.0325 which is in reasonable
agreement with other reports.3,25
To check the idea on separate carrier capture times,⌬e-h,
determining the possibility for BN to buildup, ⌬e-h is
de-creased. This is achieved by exciting directly into the QD, i.e., hex⬍EWL, resulting in a considerable decrease in the
length Le共h兲. The results demonstrate a gradual reduction in
c, down to⬇0.25 共in the range 0.05–0.25 for different QDs兲
upon decreasing hexdown to ⬇1.41 eV 关Fig. 1共a兲兴.
Addi-tionally, experiments on QD ensembles show a monotonous decrease incwith an increasing QD density共i.e., when Le共h兲
is no longer determined by the laser spot size, but rather by the averaged interdot distance兲. These observations support our model with separate carrier capture into the QD deter-mining the nuclear field buildup.
The nuclear magnetic field BNacting upon an electron in
the QD and the electron field Beacting upon each nucleus
are consequences of the same process of dynamical polariza-tion of nuclei by spin-oriented electrons. This circumstance allows BNz to be expressed in the following form:33–35
BN z =␣兵共Bext+ Be兲 · S其兵共Bext+ Be兲2+ BL 2其−1共B ext z + Be z兲 共1兲
where ␣ is a proportionality constant, Be= beS, Bext
z 共B
e
z兲 is
the projection of Bext共Be兲 on the z axis, beis to be evaluated
below, and BL is the effective magnetic field caused by the
nuclear spin-spin interactions 关estimated to be ⬇0.3 mT for InAs/GaAs QDs共Ref.14兲兴. Beis related tocin the
follow-ing way: 兩Be
z兩=兩b
e兩·兩Sz兩=1/2兩be兩·c. The average interaction
energy of an electron spin S with N nuclei of the same spe-cies, assuming that their mean spins 共Iav兲 are equal, is
ex-pressed as: AIavS,23 where A is the hyperfine constant. Tak-ing this quantity as the nuclear spin energy in an electron field, Be, one obtains: AIavS = −Nប␥IavBe and, hence Be=
−SA/共Nប␥兲, where␥is the nuclear gyromagnetic ratio. A/␥ is estimated as 1/2⌺j共Aj/␥j兲, where j numerates In and As.
The number of nuclei in a QD is assumed to be N⬇5 ⫻104.3,5,25,26,36With ␥In共␥As兲=5.86共4.58兲⫻107 rad T−1s−1 共Ref. 37兲 and AIn 共AAs兲=56共46兲 eV,3 b
e⬇−30 mT is
-40 -30 -20 -10
0
10
20
30
40
0.1
0.2
0.3
0.4
0.5
0.6
exc.
σ
-exc.
σ
+po
lar
izat
ion
d
egree
ρ cB
ext(mT)
z sample Sz Bez k z sample Sz Bez kFIG. 3. cas a function of Bext共Bext 储z兲 measured at cw
excita-tion with+共black兲 and−共gray兲 at P
ex= 2 W, hex= 1.463 eV,
and T = 4.2 K. Positive 共negative兲 Bext correspond to Bextparallel
共antiparallel兲 to the direction of the laser beam. The arrows indicate the directions of the vectors k, Sz, and Be
z
derived. Hence for fully polarized electron spin共c= 1兲 兩Be
z兩
⬇15 mT and for our experimental conditions 共c= 0.55兲 兩Be
z兩
is estimated as⬇8.3 mT.
It follows from Eq.共1兲 that at Bext= 0,兩Be兩 should
consid-erably exceed BLto achieve a significant value of兩BN兩.
Sec-ond it follows that 兩BN
z兩 should vanish 共and accordingly
c
should decrease兲 at Bext z
= −Be z
. To check this idea, Bext 储z was
applied共see Fig.3兲. In this dependence of con兩Bext兩=Bext
for − and+ excitations, distinct minima in c are
moni-tored at兩Bext兩 from 8 up to 18 mT. Thus, the average value
兩Be
z兩=13 mT is chosen as the strength of the electron field, in
satisfactory agreement with the predictions for 兩Be z兩 made
above. It should be noted that the dips incare observed at
opposite directions of Bext when the excitation is changed
from+to−and that the compensation of Be z
by Bext z
takes place at the predicted directions of Be
z
. The+共−兲 excitation creates Sz pointing antiparallel 共parallel兲 to the direction of
the laser beam共k兲, accordingly Be
z↑ ↑共↑↓兲k for these
excita-tion condiexcita-tions. Finally, the experimental observaexcita-tion that 兩Be
z兩ⰇB
Lsupports the idea that an essential nuclear magnetic
field BNcould be achieved even for zero external magnetic
field, as evidenced by the high degree of circular-polarization measured for the neutral exciton.
To conclude, we report on a high degree of circular po-larization for the neutral exciton upon circular-polarized ex-citation, without any external magnetic field applied. This is explained in terms of the buildup of a nuclear magnetic field in the QD, which stabilizes the electron spin. The possibility to polarize the QD nuclei is shown to be due to the unequal capture times of electrons and holes.
The authors would like to thank P. M. Petroff and W. V. Schoenfeld for providing the samples. Acknowledgments also go to V. L. Korenev, V. K. Kalevich, A. S. Yurkov, and K. F. Karlsson for stimulating discussions. This work was supported by grants from the Swedish Research Council 共VR兲 and the Swedish Foundation for Strategic Research 共SSF兲 funded Nanopto consortium.
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BRIEF REPORTS PHYSICAL REVIEW B 80, 193413共2009兲