Table Of ContentOptical Properties of 20 Systems with Interacting
Electrons
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SeriesII:Mathematics,PhysicsandChemistry- VoI.119
Optical Properties of 2D Systems
with Interacting Electrons
edited by
Wolfgang J. Ossau
PhysikalischesInstitutder UniversitătWurzburg,
Wurzburg, Germany
and
Robert Suris
loffe Physico-Technicallnstitute, RAS,
SI.Petersburg, Russia
SpringerScience+BusinessMedia, B.V.
Proceedingsofthe NATOAdvanced Research Workshopon
Optical Propertiesof20Systemswith InteractingElectrons
St.Petersburg, Russia
13-16June 2002
AC.I.P.Cataloguerecord forthisbook isavailablefromthe LibraryofCongress.
ISBN 978-1-4020-1549-6 ISBN 978-94-010-0078-9 (eBook)
DOI 10.1007/978-94-010-0078-9
Printedanacid-freepaper
AIIRights Reserved
©2003SpringerScience+BusinessMediaDordrecht
OriginallypublishedbyKluwerAcademicPublishersin2003
Softcoverreprintofthehardcover1stedition2003
Nopart ofthis work maybereproduced, stored inaretrieval system, ortransmitted
inanyformorbyanymeans, electronic, mechanical, photocopying, microfilming,
recording orotherwise,without written permissionfrom the Publisher, withthe exception
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and executed onacomputersystem, forexclusive usebythe purchaserofthework.
Contents
Preface 3
LV.Kukushkin,J.H.Smet,K. vonKlitzing,andW.Wegscheider/Cyclotron
resonance ofcomposite fermions 5
A V. Larionov andVB.Timofeev/ Collective behaviorofinterwellexcitons
in GaAs/AIGaAs double quantum wells 13
B.D. McCombe, A.B. Dzyubenko, H.A Nickel, T.Yeo, C,J. Meining,
T. Sander, A Petrou, and AYu. Sivachenko/ Internal transitions
of negatively charged excitons and many-electron effects in GaAs
quantum wells 25
W.Ossau,G.v.Astakhov, D.RYakovlev,W.Faschinger, v.P.Kochereshko,
J. Puis,F.Henneberger, S.A. Crooker, Q. McCulloch, and A Waag/
Positively and negatively charged trions in ZnSe-basedquantum wells 41
G.Aichmayr, M.D.Martin, L.Vifia,R Andre,V.Ciulin, J.D.Ganiere, and
B.Deveaudl Non-lineareffects on the spin dynamics of polaritons in
II-VI microcavities 63
M. Senes,B.L. Liu, X. Marie, T.Amand, andJ.M. Gerard/Spin dynamics
ofneutral and chargedexcitons inInAs/GaAs quantum dots 79
M. Combescot, O.Betbeder-Matibet, and C. Tanguy/ Novel many-body
procedure for interacting close-to-boson excitons 89
A Esser and R Zimmermann! Density-matrix theory of trionic spectra in
semiconductornanostructures 99
RA. Suris/ Correlation between trion and hole in Fermi distribution in
process of trion photo-excitation indoped QWs III
v.P.Kochereshko,D.RYakovlev,RA. Suris, G.v.Astakhov,W.Faschinger,
W.Ossau, G. Landwehr, T. Wojtowicz, G. Karczewski, J. Kossutl
Combined exciton-electron optical processes in optical spectra of
modulation doped QWs 125
D.RYakovlev,G.V.Astakhov,W.Ossau, S.A CrookerandA.Waag/II-VI
quantum wells with high carrierdensities and inhigh magnetic fields 137
P.Hawrylak/ Magneto-opticsofinhomogeneous two-dimensional electron
gas 151
2
RT. Cox, Y.Huard, K. Saminadayar,C. Bourgognon, S.Tatarenko/Filling
factor dependence of optical spectra for CdTe quantum wells under
magnetic field 159
EX. BronoldlClustermeanfield approximation for the optical response of
weakly doped semiconductorquantum wells 169
M.M.Glazovand E.L. Ivchenko/D'yakonov-Perel's spin relaxation under
electron-electron collisions in QWs 181
B.M. Ashkinadze,Y.Voznyy,E.Cohen,ArzaRon, L.N. Pfeiffer/Evolution
of the 2DEG-free hole to charged exciton photoluminescence in
GaAs/AIGaAs quantum wells 193
M.T. Portella-Oberli, Y.Ciulin, J.-D. Ganiere, B. Deveaud, P. Kossacki,
M. Kutrowski, and T. Wojtowicz! Radiative decay, diffusion, lo
calization and dephasing of trions and excitons in CdTe quantum
wells 205
D. Keller, G.Y. Astakhov, D.R Yakovlev, L. Hansen, W. Ossau, and
S.A. Crooker! Optical studies of spin polarized 2DEG in modulation-
doped (Zn,Mn)Se/(Zn,Be)Se quantum wells in high magnetic fields 217
RI. Dzhioev,Y.L.Korenev,M.Y.Lazarev,Y.ESapega, R.NotzelandKPloog/
Fine structure of excitons in quantum wires 233
P. Lavallard, G. Lamouche, and S.v. Goupalov/ Electromagnetic field
resonance in semiconductornanocrystals 239
S.M. Ryabchenko, O.Y.Terletskij,Yu.G. Semenov, and EY. Kirichenko/
Co-manifestation ofinterfaces asymmetryand magneticfieldinfluence
on luminescence polarization anisotropy of [IOO]-oriented QW with
semimagnetic barriers 247
Y.R Shaginyan/Model of strongly correlated 2D Fermi liquids based on
fermion-condensation quantum phase transition 259
RA. Sergeev and RA. Suris/The heavy-hole X+ trion in double quantum
wells 279
Contributors 289
Index 291
Preface
This volume of NATO Science Series presents the Proceedings of the NATO
Advances ResearchWorkshop "OpticalProperties of2D systems with interacting
electrons"which washeld attheEducationalCenteroftheIoffe Physico-Technical
Institute in the period of June 13-16, 2002. More than 40 scientists from 14
countries participated and gave 24 lectures and 16posterpresentations.The main
goaloftheWorkshop wastobring togetherleading scientistsworkinginthefieldof
optical properties of correlated electron systems in semiconductornanostructures
and to organize a vital and informal discussions ofnewest results in the field.The
location and the format of the Workshop provided an atmosphere of friendly and
fruitful communications.
It is importantto note that the Workshop continued a series of meetings con
cerningthe same topic:Warsaw 1999,Wurzburg 2000 (NATOARW), and Berlin
2001.
The subject agendaof theARW was focused on the following topics:
Evolution of optical spectra from the excitonic peaks to the Fermi-edge
singularity
Negatively and positively chargedexcitons
Reconstructionofone-particleand collective excitationspectrawith increase
of the electrondensity (combinedexciton-cyclotron resonance and shake-up
processes)
Effect ofspatial inhomogeneity on the carrier interaction in nanostructures
Spin-sensitive interaction and spin-spin interaction in confined systems
Many-particleeffects in semimagnetic semiconductorheterostructures.
A wide spectrum of the optical methods for the analysis ofmany-body phe-
nomena in semiconductorheterostructures had been presented at theARW:
Photoluminescence spectroscopy
Raman spectroscopy
Reflectivity
Near-field spectroscopy
Magneto-optics in magnetic fields up to50T
Pico- and femto-second time-resolved spectroscopy,
Polarized light spectroscopy (including Faraday rotation effect in transmis
sion)
Optically detectedresonance spectroscopy under far-infrared and microwave
radiation.
The combination ofoptical and transport measurements was reported in some
presented papers. The technique let extract information on extended electronic
states (mainly contributing in the transport phenomena) and on localized states
(manifesting themselves in the light emission) in the same sample.
3
4
About onethirdofthepresentationshadbeengivenbytheorists, which mirrors
aratio 2:I betweenthe experimental and theoretical studies in the field.
One of the central problems discussed was the scenario of the evolution of
theenergy spectrumofthe electronicsystemwith increasingelectrondensity.The
regimes of lowand moderateelectrondensity were ofspecial interest. The optical
spectratransforms from the resonancecorrespondingto theexcitation ofthe trion
(three-particle complex) to the so-called "Fermi edge singularity". It had been
agreed that the existing concept of the resonance in the optical spectra, which is
commonly assigned to the Fermi edge singularity, should be revised, especially
in light of new experimental data for the systems based on II-VI semiconductors
with astrong Coulomb interaction.
Aconsiderableprogress hasbeen showninthefieldofspin-dependentphenom
enafor systems ofinteractingcarriers.Spin dynamicsoftrions has been examined
ingreatdetails fortwo-dimensionalsystems(quantum wells)andzero-dimensional
systems (quantum dots).A new extension ofthis field has been achieved by us
ing diluted magnetic semiconductors, e.g. CdMnTe and ZnMnSe, where strong
exchange interaction of carrier spins with the localized magnetic ions results in
a full polarization of the electronic system already at very low magnetic fields.
Ferromagneticphase formation, which iscausedbycollective effect ofthe system
of free carriers of high density on the system of magnetic ions, ha been reported
for CdMnTe quantum wells with 2D hole gas.
The Workshop topic: "the properties of many-electron confined systems" is
very wide and ofgreat interest.This iswhy we are sure thatthis workshopheld in
St Petersburg, Russia isnot last inthis field.
Westronglythank NATOScienceProgramforthefinancial support. Wewould
like to thank Dr. Mikhail Mizerov, Dr. Boris Egorov and Mrs. Elena Solovyova
who carried out the grate organization work to make the workshop successful.
The preparation of Proceedings was performed by Mr. Nikita Vsesvetskii and
Mrs. Elena Solovyova whose work is greatly appreciated. Finally, we thank the
Educational Centerstaff involved for very valuable assistance.
Winter 2002 Wolfgang Ossau
Robert Suris
CYCLOTRON RESONANCE OF COMPOSITEFERMIONS
LV.KUKUSHKINt, J.H. SMET,K. VON KLITZING
Max-Planck-Institutfiir Festkorperforschung,
D-70569Stuttgart, Germany,
t InstituteofSolidState Physics, RAS,
Chernogolovka, 142432 Russia
W.WEGSCHEIDER:j:
WalterSchottky Institut, Technische UniversitdtMilnchen,
D-85748Garching, Germany,
:j: Institutfur Experimentelle undAngewandte Physik,
UniversitdtRegensburg,
D-93040Regensburg, Germany
Abstract. The introduction of suitable fictitious entities occasionally permits to cast otherwise
difficult strongly interacting many-body systems in a single particle form. Wecan then take the
customary physical approach, using concepts and representations which formerly could only be
appliedtosystemswithweakinteractions,andyetstillcapture theessential physics.Amostnotable
recent example occurs intheconduction propertiesof atwodimensionalelectron system(2DES),
whenexposed toastrong perpendicularmagnetic field B.They aregoverned byelectron-electron
interactions,thatbringaboutthefractionalquantumHalleffect(FQHE)[1].Compositefermions,that
donotexperience theexternal magnetic fieldbutadrastically reduced effective magnetic fieldB*,
wereidentifiedasappositequasi-particlesthatsimplifyourunderstanding oftheFQHE [2,3].They
precess,likeelectrons, alongcircularcyclotronorbits,withadiameterdeterminedbyB*ratherthan
B[4-10].Thefrequency oftheircyclotronmotionremainedhitheretoenigmatic,sincetheeffective
massis nolonger related totheband massoftheoriginalelectronsand isentirely generatedfrom
electron-electroninteractions.Here,wedemonstratetheenhanced absorptionof amicrowave field
thatresonates withthefrequency oftheircircularmotion.From thiscyclotronresonance,wederive
acompositefermioneffective massthatvariesfrom0.7to1.2timestheelectronmassinvacuumas
theirdensityistunedfrom0.6x 1011/cm2to 1.2 x 1Q11/cm2.
Key words: two-dimensional electrons, fractional quantum Hall effect, composite fermions, mi
crowavecyclotron resonance,dimensional plasmaresonance,Kohntheorem
Composite Fermions (CFs) are electrons dressed with two flux quanta (more
generally an even number), that point opposite to the external B-field [2-4]. This
attachmentisanatural waytominimizetheenergy ofthe2DES,sincetheassociated
vortex expels otherelectrons from its neighbourhood and decreases the repulsive
interaction between the 2D-electrons. If two flux quanta penetrate the sample
5
Wi. OssauandR.Suris(cds.),OpticalPropertiesof2DSystems withInteracting Electrons,5-12.
©2003KluwerAcademicPublishers.
6
per electron, i.e. if the filling factor v equals 1/2, the external field is effectively
compensated and a metallic state ofthese compound particles emerges [4J. This
state can be characterized by a Fermi wavevector and energy.A deviation from
exact half filling results in the appearance of a non-zero effective field B*, that
quantizesthe CF-motionand discretizestheirenergy spectrumintoLandaulevels.
Inthis framework,the FQHE[IJ isamanifestationofthisLandauquantizationand
isequivalentto the integerquantum Hall effectofCFs.A variety ofexperimental
observations[5-10Jcanbeunderstoodinsemiclassicaltermsofnearlyindependent
CFs.
Since the kinetic energy of electrons is entirely quenched in the course of
applyingaB-field, theCFcyclotronmass isnot arenormalizedversionoftheelec
tron conductionband mass, but mustbe generatedentirely from electron-electron
interactions [4]. The search of the CF cyclotron resonance requires substantial
sophistication over conventional methods used to detect the electron cyclotron
resonance, sinceKohn'stheorem [11] mustbe outwitted. Itstatesthat in atransla
tionallyinvariantsystemradiationcan onlycoupletothecenter-of-masscoordinate
and can not exciteotherinternaldegreesoffreedom. Phenomenaoriginatingfrom
electron-electroninteractionswill thus not bereflectedinthe absorptionspectrum.
An elegant way to bypass this theorem isto imposea periodicdensity modulation
to breaktranslational invariance. The non-zero wavevectors defined by the appro
priately chosen modulation may then offer access to the cyclotron transitions of
CFs,even though they are likelytoremain very weak. Therefore,the development
ofan optical detection scheme, that boosts the sensitivity to resonant microwave
absorption by up to two orders ofmagnitude in comparison with traditional tech
niques, was aprerequisitefor ourstudies.Furthermore,we exploitedto our benefit
the accidental discovery that microwaves, already incidenton the sample, set up a
periodic modulation through the excitation of surface acoustic waves (SAW).
The 2DES, patterned into a disk with 1mm diameter [12J, is placed near the
end ofa 16- or 8-mm short-circuited waveguide in the electric field maximum of
the microwave excitation inside a He--cryostat. At a fixed B-field, luminescence
spectra with and without microwave excitation were recorded consecutively. The
differential luminescence spectrum is obtained when subtracting both these spec
tra. To improve signal-to-noise ratio, the same procedure was repeated N times
(N = 2-20). Subsequently, we integrated the absolute value of the averaged
differential spectrumoverthe entire spectralrange and hereafterreferto the value
ofthis integralasthe microwaveabsorptionamplitude.Thesameprocedureisthen
repeated for different values of B.To establish trustworthiness in this unconven
tionalscheme,weapplyitinFig.1tothe well-knowncaseoftheelectroncyclotron
resonanceWcr = eB[m", with m" theeffectivemass ofGaAs(0.067mo).Duetoits
limitedsize, the samplealso supportsadimensionalplasmamodewith afrequency
wp, that depends on boththe density n20 and diameterd ofthe sample, according
to w~ = 3rr2n2oe2j(2m*cerrd). The plasmaand cyclotron mode hybridizeand the
