Manipulating the Spin Polarization of Excitons in a Single Quantum Dot by Optical Means

Linköping University Post Print

Manipulating the Spin Polarization of Excitons

in a Single Quantum Dot by Optical Means

Arvid Larsson, Evgenii Moskalenko and Per-Olof Holtz

N.B.: When citing this work, cite the original article.

Original Publication:

Arvid Larsson, Evgenii Moskalenko and Per-Olof Holtz, Manipulating the Spin Polarization

of Excitons in a Single Quantum Dot by Optical Means, 2011, Applied Physics Letters, (98),

7, 071906.

http://dx.doi.org/10.1063/1.3554422

Copyright: American Institute of Physics

http://www.aip.org/

Postprint available at: Linköping University Electronic Press

Manipulating the spin polarization of excitons in a single quantum dot

by optical means

L. A. Larsson,1,a兲E. S. Moskalenko,1,2and P. O. Holtz1

1_{IFM, Semiconductor Materials, Linköping University, SE-581 83 Linköping, Sweden}

2_{A. F. Ioffe Physical-Technical Institute, Russian Academy of Sciences, Polytechnicheskaya 26,} 194021 St. Petersburg, Russia

共Received 6 September 2010; accepted 22 January 2011; published online 15 February 2011兲 Circular polarization studies of photoluminescence from the neutral共X0兲 and the positively charged 共X+_{兲 excitons are reported for individual InAs/GaAs quantum dots 共QDs兲. High polarization} degrees, 60% for X0and 73% for X+, were recorded without any external magnetic field applied. These studies show that the QD polarization and population dynamics are controllable either by varying the photoexcitation intensity or by using a second IR laser excitation. © 2011 American

Institute of Physics.关doi:10.1063/1.3554422兴

Studies of spin preservation of a single carrier localized in a semiconductor quantum dot 共QD兲 are of increasingly interest during the past decade due to the opening of fasci-nating physics and due to the potential applications in spin-based nanoscale devices for quantum computer operations.1 The spin of an electron is the best candidate for these appli-cations because classical spin relaxation mechanisms are canceled for an electron confined inside a QD.2 The spin state of recombining particles can be directly measured by monitoring the degree of circular polarization 共␳c兲 in

photo-luminescence 共PL兲 experiments. For the case of neutral ex-citons共X0_{兲 in QDs,␳}

cat zero external magnetic field共Bext兲

is expected to be negligible due to the strong electron-hole anisotropic exchange interaction 共␻ex兲.3–7 Conversely, for

charged exciton complexes, an essential ␳cis expected and

has been measured since ␻ex is suppressed.5,8,9 Recently,

however, a nonzero␳cof X0in InGaAs QDs was observed.10

In Ref.10, the PL spectra involve both X0_{and the positively} charged exciton共X+兲 but it is the presence of X+that leads to the appearance of nuclear polarization, while X0 _simply ex-periences the resulting nuclear polarization field共BN兲.

How-ever, in the present study, we propose that solely X0 is suf-ficient to create BN.

In this letter, ␳c of X0 in individual InAs/GaAs QDs is

monitored and manipulated by pure optical means. A surpris-ingly high␳c共60%兲 is demonstrated for X0at Bext= 0, which

is explained in terms of the generation of BNin the QD by

spin-polarized electrons. This field stabilizes the electron spin by suppressing ␻exand, hence, plays a similar role as

Bextemployed by others 6,7

to “restore”␳cof X0. The ability

to build up BN for X0 even at Bext= 0 is indeed surprising

共see, e.g., Ref.9兲 but has been ascribed to the faster capture

of electrons as compared to holes into the QD providing a time interval, when the QD is populated by a sole electron, which can then polarize the QD lattice nuclei.11,12In contrast to single laser excitation, which only results in X0, when adding a second infrared 共IR兲 laser excitation X+ _{is formed,} as was demonstrated by us earlier.13 An even higher polar-ization is measured for X+_,␳

c= 73%, which is considered to

be an upper bound for spin polarization of electrons captured into the QD from the wetting layer 共WL兲.

The sample under study was grown by molecular beam epitaxy and consists of 1.7 monolayers of InAs constituting the WL with a low density of InAs QDs 共⬇106 cm−2兲 posi-tioned between GaAs barriers. To excite and collect the PL, a conventional microphotoluminescence共␮-PL兲 setup, operat-ing at T = 3.9 K, was used. A Ti:sapphire laser with excita-tion energy h␯exc= 1.465 eV 共slightly higher than the WL

band gap兲 and a semiconductor laser with excitation energy

h␯IR= 1.17 eV共smaller than any QD related interband tran-sition兲 were used and focused to a diameter of ⬇2 ␮m on the sample surface. Detailed descriptions of the sample and of the experimental setup are given elsewhere.11–13 ␳c was

determined as ␳c=共Ico− Icross兲/共Ico+ Icross兲, where Ico 共Icross兲

corresponds to the spectrally integrated PL signal of the co-共cross-兲circular components.

Upon excitation with linearly polarized light 共␴X兲, two mutually orthogonally linearly polarized components 共␲X and␲Y兲 are recorded, since X0 is split into a pair of bright states by the anisotropic electron-hole exchange energy, ⌬Eex=ប␻ex= 23 ␮eV, as inferred from Fig.1共a兲.14When

in-stead detecting the circularly polarized ␴+ _and␴−_PL com-ponents, no splitting of X0is expected nor is observed关Fig.

1共a兲兴, since both the␴+ _and␴− _{components represent a} co-herent mixture of the two linear states. However, upon exci-tation with ␴+-light, two circularly polarized components, exhibiting an essential spectral shift,⌬E_⌺= 52 ␮eV, are ob-served 关Fig.1共a兲兴. The remarkable fact that ⌬E_⌺⬎⌬Eex

im-plies the existence of an effective magnetic field共Beff兲 in the

sample, resulting in an additional Zeeman splitting between the two exciton components. This field has been generated by the excitation since Bext= 0 in the present study. The

ori-gin of Beffis attributed to BN, which is generated in the QD.

We stress that the generation of BNat Bext= 0 is only possible

in case of an essential electron Knight field experienced by the nuclei.9Upon excitation with␴−_{, the spectral positions of} the␴+and␴−PL components are reversed共not shown here兲. This fact supports the identification of Beffas BNbecause the

orientation of the nuclear spin is determined by the direction of the optically generated electron spin. Along with the large splitting, ⌬E_⌺, the lower pair of spectra in Fig. 1共a兲 also show a large difference in amplitude, which corresponds to a high ␳c 共60%兲. This experimental observation appears

sur-prising at a first glance, since␳cis predicted to be negligible

a兲_{Electronic mail: alarsson@ifm.liu.se.}

APPLIED PHYSICS LETTERS 98, 071906共2011兲

0003-6951/2011/98_{共7兲/071906/3/$30.00} 98, 071906-1 © 2011 American Institute of Physics

for X0 _{in QDs at conditions when no charged exciton is} observed.3–7,10

The high value of␳crecorded for X0in the present study

is explained by considering the electron spin 共Se兲 within a vector model for the exciton pseudospin共Sex兲 共Refs.4and7兲

关Fig.1共b兲兴. Here,␻exis considered to behave as an effective

magnetic field共␻ex兲 directed in the plane of the sample, i.e.,

perpendicularly to the z-axis. If the sample is illuminated with a circularly polarized laser beam, excitons with Sex

par-allel to z are created. For a neutral exciton captured into a QD, Sex will start to precess around ␻ex with the period

␶b= 2␲/␻ex⬇180 ps 共for ប␻ex= 23 ␮eV兲. For the exciton

decay time␶d⬇800 ps,

15

the time averaged projection of Sex

onto the z-axis共and the measured␳c兲 is expected to be zero.

If an external field Bext is applied parallel to the z-axis, Sex

will instead rotate around the total field Bext+␻ex, which, in

turn, will raise the polarization degree ␳c from zero. In the

present case, Bext is replaced by the nuclear field BN. After

excitation, the electrons and holes propagate in the WL plane prior to capture into the QD. The electron spin does not relax during such a capture into the QD, whereas the initial hole spin is lost.5,16,17After capture, the spin of the electron in the QD共S0

e_{兲 will rotate around the total magnetic field B}

⌺= BN

+␻exwith the average value S_⌺e directed at an angle␪ with

respect to the z-axis 关Fig.1共b兲兴. Hence, S0

e

is influenced by two competing factors:␻ex, which tends to decrease its

pro-jection onto the direction of the PL detection, and BN, acting

to preserve it.␳cis entirely determined by the projection of

S_⌺e onto the z-axis 共Sz

e_{兲 and as a result}

␳c= 2 ·兩Sz e_兩.15

It also follows from Fig. 1共b兲 that 兩S_⌺e兩=兩S0

e_兩cos␪ and 兩Sz e_兩 =兩S0 e_兩cos2_␪. Thus, if 兩S0

e_{兩 could be estimated from the experiments,}

one could estimate␳c. In order to evaluate兩S0

e_{兩, one needs to}

“switch off” ␻ex, which can be realized experimentally by

employing dual laser excitation: a second IR laser was used, which has an insufficient energy to generate electron-hole pairs in the QD, but excites electrons from the valence band into deep levels in the GaAs barriers and thereby creates free holes that can be captured into the QD.13Consequently, X+is expected in the␮-PL spectra of the QD and in this case,␻ex

is switched off and a higher value of ␳c, as compared with

X0_{, is predicted.}

Figure1共c兲shows the evolution of the␮-PL spectra of the QD recorded at dual laser excitation conditions, obtained for a fixed Pex with increasing excitation power of the IR

laser 共PIR兲. Clearly, at PIR= 0 共top spectrum兲, the spectrum only consists of the X0_{-line and an increase of P}

IRresults in a progressive redistribution of the ␮-PL spectra in favor of the X+line, which dominates the spectra at highest PIRused in our experiments. Figure 1共d兲 shows the ␴+ _{and ␴}− _PL components of the ␮-PL spectrum obtained at highest P_IR = 300 ␮W, which allowed us to derive ␳c= 0.73 and ␳c

= 0.60 for the X+ _{and X}0 _{lines, respectively. Taking ␳} c

= 0.73 as the maximum degree of circular polarization 共i.e., when␻exis canceled兲 to be achieved for the QD studied and

cos2_{␪⬇0.8 from Fig.1共b兲,}18

the expected ␳cfor X0 can be

evaluated to be 0.73 cos2␪⬇0.59, which agrees well with the experimentally obtained value of ␳c= 0.60关Fig.1共d兲兴.

The spin pumping rate共WS兲 from the electrons into the

nuclear spin system 共which determines ␳c measured in our

experiment兲 is directly proportional to the fraction of time that the QD is occupied with only an electron 共⌫e兲 and

in-versely proportional to the square of the energy separation 共EZ兲 between the electron levels with spin along and opposite

to the z-axis.3,19–21 Evidently, this fraction of time is ⌫e

=⌬␶_e-h/␶r, where⌬␶e-h⬇26 ps is the difference in time

be-tween the electron and the hole capture into the QD11,12and ␶r is the “recycling” time, i.e., the averaged time between

two adjacent events of exciton formation in the QD. To ob-tain the data in Fig.1, Pexwas adjusted to be slightly smaller

than Pex= 3 ␮W共Pexⴱ兲 at which the biexciton 共2X0兲 appears

in the ␮-PL spectra. Upon excitation with Pexⴱ, one can

ap-proximate ␶r as ␶d because the observation of 2X0 should

require that a second exciton should be formed in the QD before the first exciton recombines. Consequently, one can assume ␶r⬇␶d⬇800 ps 共Ref.15兲 and hence, ⌫e⬇0.0325.

Since␶r−1is directly proportional to Pex, a strong

depen-dence of⌫eand hence␳con Pexis unambiguously predicted.

Indeed, a gradual increase from ␳c= 0 共at minimum Pex兲 to

␳c= 0.60 measured at Pex= Pexⴱ is demonstrated共Fig.2兲. This

behavior is explained in terms of a progressively increasing

BN with increasing Pex. Obviously, this should

simulta-neously result in an increase of EZ 共contributing to ⌬E⌺兲,

which is indeed in consistence with the experimental results 共Fig. 2兲. The saturation of the parameter ⌬E_⌺ recorded at

Pexⱖ Pexⴱ 共Fig. 2兲 could be understood in terms of a

“nega-tive feedback” mechanism19: an increase of 兩BN兩 and hence

of EZ should be accompanied by a decrease of WS due to

inverse proportionality of WS and EZ2.

3,19–21

These two com-peting factors共the increase of ⌫eand WSwith increasing Pex

and the decrease of WSwith increasing EZ

2_{兲 would explain the} limited value of兩BN兩 corresponding to only ⬇15% of

polar-ized nuclei achieved in our experiments.

1.354 1.356 1.3548 1.3551 Energy (eV) ρ c(X 0 )= = 0.60

(c)

(d)

(b)

det.

σ

+

det

.

_σ

-Energy (eV)

S

_Σe exc.σ+ σ+ θ ρ c(X + )= =0.73 X+ _X0

(a)

z

ω

_ex B Σ IS z e I S₀e B N

det.

σ+

k

exc.

σ+

300

210

100

65

27

0

P

_IR

,

μ

W

X

X

0 P L in tensi ty ,a rb .uni ts

det

.

σ

-

det.

σ+ Δ

E

_ex

= 23

μ

eV

Δ

E

_Σ

= 52

μ

eV

det

.

π

_Y

det.

π

_X

det

.

σ

-

det.

σ+

exc.

σ+

exc.

σX

exc.

σX PL int ens ity ,a rb .u n its + σ+

FIG. 1. 共a兲␮-PL spectra of a QD measured at different polarization con-figurations in the excitation and detection paths as indicated in the figure.共b兲 A schematic illustration of the vector model of an electron spin exposed to a nuclear magnetic field and to the effective magnetic field of the anisotropic electron-hole exchange interaction.共c兲␮-PL spectra of a QD measured at dual laser excitation and for different PIRas indicated in the figure.共d兲␮-PL

spectra of a QD measured at dual laser excitation共with PIR= 300 ␮W兲, at ␴+_{-polarized excitation, and␴}+_{-共thin兲 and␴}−_{-共thick兲 polarized detections.}

Pex= Pexⴱ= 3 ␮W in共a兲, 共c兲, and 共d兲.

071906-2 Larsson, Moskalenko, and Holtz Appl. Phys. Lett. 98, 071906共2011兲

An additional remarkable observation is the rather high value of ␳c 共40%兲 for X0 recorded at Pexⴱⴱ⬇7⫻ Pexⴱ, while

␳c= 0 is detected for 2X0共inset of Fig.2兲. This observation is

explained by the symmetry of the 2X0 _{ground state, which} consists of two electron-hole pairs having zero total spin. Consequently, the 2X0 will emit ␴+- and ␴−-polarized pho-tons with equal probabilities. The carrier-carrier scattering taking place inside the QD, when it is occupied with more than one electron-hole pair, is believed to explain the strong reduction of␳cfor X0 at Pexabove Pexⴱ 共Fig.2兲.

Finally, the difference between the results presented here and in Ref. 10 should be highlighted; in Ref. 10, the QD nuclei are polarized by an electron in the presence of two holes共i.e., during the radiative lifetime of X+_{兲, while in the} present case, the nuclei are polarized by a sole electron共i.e., without a hole兲 in the QD.11

When a hole is subsequently captured into the QD, the electron has the possibility to re-combine with it, resulting in the X0_{PL line. The larger} mag-nitudes for the nuclear and electron polarizations could be understood in terms of a different QD composition in our case 共nominally pure InAs兲 with respect to the case in Ref.

10 共InGaAs兲, since BNdepends on the value of the nuclear

spin. The spin of Ga and As is only 3/2, while the spin of In is 9/2.

In conclusion, the unexpectedly high degree of polariza-tion共␳c⬇60%兲 of X0is explained in terms of the creation of

a nuclear field, BN, in the QD by spin-polarized electrons. BN

essentially decreases the destructive role played by the an-isotropic electron-hole interaction, ␻ex, on the electron spin

preservation. For the case of X+, where␻exis naturally

can-celed, an even higher degree of polarization共␳c⬇73%兲 was

achieved and taken as the upper bound of the electron spin

for the experimental conditions with optical excitation above the band gap of the WL.

The authors thank P. M. Petroff and W. V. Schoenfeld for the samples. This work was supported by grants from the Swedish Research Council 共VR兲, the Swedish Foundation for Strategic Research共SSF兲 and the Knut and Alice Wallen-berg Foundation. E.S.M. acknowledges support from the Swedish Institute short-term scholarship.

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共2008兲. ΔE Σ (μ eV ) 50 0 10-3 10-2 10-1 100 101 102 Pex (μW) P o lar izat ion d egree, ρc 0 0.2 0.4 0.6 0.8 P_ex* P_ex** 2X0 X0 exc. σ+ det. σ+ det. σ-Energy (eV) PL int. (arb. u.) 1.350 1.355

FIG. 2. The dependence of ␳c共⌬E⌺兲 on Pex is shown by filled 共open兲

symbols. The solid 共dotted兲 vertical arrow indicates the excitation power used to obtain the data shown in Fig.1共inset in this figure兲. The inset shows

␮-PL spectra of a QD measured at␴+_{-polarized excitation, at␴}+_-polarized

excitation, and at␴+_{-共thin兲 and␴}−_{-共thick兲 polarized detections. P}

ex= Pexⴱⴱ

= 21 ␮W in the inset.

071906-3 Larsson, Moskalenko, and Holtz Appl. Phys. Lett. 98, 071906共2011兲