Table Of ContentFESTKORPERPROBLEME
ADVANCES IN SOLID STATE PHYSICS 31
FESTK()RPER
PROBLEME
ADVANCES IN
SOLID STATE
PHYSICS 31
Plenary Lectures of the Divisions
Semiconductor Physics
Thin Films
Dynamics and Statistical Physics
Magnetism
Metal Physics
Surface Physics
LowTemperature Physics
of the German Physical Society (DPG),
M~nster, April 8 to 12, 1991
Edited by
Ulrich R6ssler
vleweg
Editor:
Prof.Dr.Ulrich R6ssler
Institut tVtirTheoretischePhysik
Universit~it Regensburg
P.O.Box397
D-8400 Regensburg, FRG
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Festkiirper-Probleme =Advances in solidstate physics. -
Braunschweig; Wiesbaden: Vieweg, 1991
Bis Bd. 15 (1975) aul]erdem im Verl.PergamonPress,
Oxford,Elmsford,Toronto,Sydney
ISSN 0430-3393
NE:PT
31.PlenarylecturesoftheDivisionsSemiconductorPhysics...
oftheGermanPhysicalSociety (DPG): Mt~nster, April8to12,
1991.- 1991
ISBN 3-528-08039-6
NE:DeutschePhysikalischeGesellschaft /FachausschuB
Halbleiterphysik
Vieweg i¢a subsidiary company oftheBertelsmannPublishingGroupInternational.
Allrightsreserved
© Friedr. Vieweg& SohnVerlagsgesellschaft mbH, Braunschweig 1991
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ISSN 04030-3393
ISBN 3-528-08039-6
Preface
The annual conference 1991 of the SolidStatePhysics Division (Arbeitskreis Fest-
kOrperphysik) washeldtogetherwiththe55thGeneralMeetingofthe GermanPhysical
Society inMUnster.Thisvolumecontains a selection ofplenary and invitedtalksdevoted
tothe physics ofsolids,whichhave been presented duringthis conference.
Some emphasis isput ontwo groups oftopics: surface and interface properties andlow-
dimensional semiconductor structures. Theformer demonstrates the capability ofdiffer-
ent experimental techniques ofanatomicscaleresolution andan improved understanding
of hetero-interfaces in combination witha microscopic theoretical description. Thelatter
covers optical and transport studies ofconfinedelectrons.
Two contributions arerelatedtophonons inhigh-Tc superconductors:their detection by
Raman scattering(byCh.Thomsen,the recipient ofthe Walter-Schottky prize1991)and
the relevancefor superconductivity oftheir couplingwith electrons.
Transport in amorphous solidsand ffactal systems,spectroscopic characterization ofthin
layers, laserdiodes for optical communication, time-resolved spectroscopy and non-
linear properties of excitons, dilutemagnetic semiconductors instrongmagneticfields,
and transport ofhot electrons complete the wide spectrum oftopics.
Theauthorsofthisvolumehave been requested todeliver camera-ready manuscripts.
Slight inhomogeneities dueto different text processingsystems have beentoleratedin
order to keep the production costs as lowas possible.Theevergood cooperation with
BjOrn Gondesenfrom the Vieweg publishing househelpedto make the work for this
volumeaneasy one.
Regensburg,May 1991 Ulrich R6ssler
Contents
Christian Thornsen
Raman Scattering in High-Tc Superconductors .............................. 1
RolandZeyher
How Relevantis the Electron-Phonon Coupling inHigh-Tc Superconductors? ... 19
Walter Schirmacher and Michael Wagener
Anomalous Diffusion and AnomalousSound Propagation in Amorphous Solids . 39
Gilnter Dumpich
AnomalousElectron Diffusion in Fractal Systems at LowTemperatures ........ 59
PeterGrosse
Characterization ofThin Solid Films and Surfaces by Infrared Spectroscopy .... 77
AbbasOurrnazd,Frieder H. Baurnann, Michael Bode, and YoungKirn
Mapping the Composition of Materials at theAtomicLevel .................. 99
Robert L.Johnson
X-Ray Diffraction at Surfaces ............................................ 115
PeterKrfiger
On the Theory of Adsorption on Semiconductor Substrates ................... 133
Mario Prietsch
Spectroscopic Studies of Metal/Semiconductor Interfaces ..................... 153
J~rk Hebenstreit
Calculated Atomic Structures and Electronic Properties ofClean and Alkali
Covered GaAs (110) Surfaces ............................................ 165
JeanGeurts
Raman Spectroscopy at lll-V Semiconductor Surfaces and Overlayersin the
MonolayerRegion ...................................................... 177
Ulrich Memmert and RolfJiirgen Behm
Scanning Tunneling Microscopy Investigations of Corrosive Processes on Si (Ul)
Surfaces ............................................................... 189
Markus-Christian Amann
WavelengthTunableSingle Mode LaserDiodes ............................. 201
Heinrich Stolz
Picosecond Time-Resolved Light Scattering from CoherentExcitonStates ...... 219
Stefan Schrnitt-Rink
Optical Propertiesof Magnetically Confined Excitons ....................... 243
VII
Michaelyon Ortenberg
SemimagneticSemiconductors inHigh MagneticFields ...................... 261
MarionAsche
Hot Electrons - Electron-Phonon Interaction ............................... 279
Edwin Batke
Intersubband Excitations ofInversion Electronsin GaAs ..................... 297
ThomasEgeler
Resonant RamanScatteringbyQuasi2-and1-dimensional ElectronSystems ... 315
L.P. Kouwenhoven, N.C. van tterVaart,A. T Johnson, C.J.P.M. Harmans,
C.T.Foxon,J.G. Williamson, andA.A. M. Staring
ChargingEffectsin Quantum Dots ........................................ 329
DieterWeiss
Lateral Superlattices:Magnetoresistance,Hall Effect andCommensurate
Orbits ................................................................. 341
G~inter Mahler,HartmutKOrner,and Werner Teich
Optical Properties ofQuasi-molecular Structures: From SingleAtomsto
Quantum Dots ......................................................... 357
VIII
Raman Scattering in High-Tc Superconductors
Christian Thomsen
Max-Planck-Institut ffirFestktrperforsdmng,
Heisenbergstr. 1, D-7000 Stuttgart 80, FederalRepublicofGermany.
Summary: Experimental self-energies ofopticalphononsin thehigh-Te supercon-
ductors turn out to be important for tile characterization of the supercol~ducting
energy gap. Through electron-phonon coupling,whichcauses frequency, lincwidth
and intensity changes - so-called anomalies - ofRaman and fir-active phonons at
T~, a gap valuein Rl3a2CusOT_6 of2A/kT¢ =5.04-0.1was determined. Tltisvalue
may correspondtoa minimum in an anisotropic gap in this material. We show that
a slight admixture of Auappearstoreduce tile anisotropy.
1 Introduction
Ever since tile discovery of high-To superconductivity by Bednorz and Miiller[1]
there has been an intenseresearch effort, both experimentally and theoretically,
to understand how transition teml~eratures around 100 I( can be explained. TILe
traditional izmchanisnz - clectron-I)honon coupling - is not thought to be solely
responsible, as thereis only a very small isotope effect (a) in tile high-To materials
[2-5]. A reduction or even cancellation of tile isotopeetfect through tile Coulomb
repulsion(~*),as isbelievedtooccurfor some classical superconductors [7,8],is only
possible for low-Tosubstances;for large Tc/J*would have to be unphysically large
to be consistent with tile observed a, as Allea has shown[9I. On the other haad,
recent experiments find thatc~is afunctionoftile traalsitioa temperaturein agiven
material class. IfTcis reduced e.g. in thesystem Y'Ba2-~La~CusOT-s by increasing
z, c~(T~) grows; for Te = 38 K corresponding to x = 0.5, a = 0.38, a perfectly
acceptable value for a phonon-coupled superconductor [1% Other systems have
been found to behavesimilarly [11,12], mad we believe this to be a genetic feature
of tile high-T¢ superconductors: at low trausitiontemperatures, phonon mediated
couplingis predominaatt, at high Te's an additionalmechanismwhich suppresses
comes into play. Hence, eleetrou-phonon mediatedcouplinge~stsevenat high T~'s
[~(Tc) # 0].
We present here astudy of thecouplingtophononsin theRBa2CusO7 system (12
= rare earth). In particular,we will show how, from a study of tile k"= 0phonons
by Raman scatteringandfar-infrared reflectivity measurements,onemaydeterufine
a valuefor thesuperconductinggap.
Let usfirstdiscussthe physical principle which tile measurements are based on. A
phonon in the normal state of a superconductor, say at 100 K in YBa2Cu3OT-6,
has a given energy aald lifetime, which in the Raman spectra appear as a peak at
a corresponding frequency and its linewidth. In addition, tile peak may be charac-
terized byits intensity (relative and absolute)and by lfigher moments, asymmetries
etc. Effects ofsuperconductivity on thephononsmay thusbe studied by comparing
normal-state Raman spectra with thosetaken in tile superconducting state; signifi-
cant changes in the two spectra axe generally referred to as anomalies. The lifetime
of a phonon in tile normalstate, for example, is given by anharmonicities and in-
teraction ofphonons with normal-state carriers. In tile superconducting state,say
at 10 K, the interaction with tile superconducting carriers, i.e. the Cooper pairs,
changes the phonon lifetime in one oftwo ways:ifthe phononhas an energy larger
than a gap in the electronic system, the phonon can break a Cooper pair; hence it
has an additional decay channel compared to tile normalstate and should broaden.
Ifit has an energylessthawthe gap,it cannot break Cooper pairs and the linewidth
remains unaffected by the Cooperpairs. However, the normal-state interaction will
be reduced through a reduceddensity ofstates in the gap and thephononmight ex-
perience a net increasein lifetime overthe normalstate (phonon sharpening). This
assumes that the anharmonic contribution to the lifetime remains approxinmtely
constant between 10 and 100 K, a reasonable assumption for most solids. If we
thus vary thephonon frequency in the vicinity ofthe superconducting gap, we may
find from the observed broadenings and sharpenings a value for the gap. These
anomalies have also been found forseveral ofthe IR-active phonons [13-18].
The plausibility arguments given abovehave been fornlalized ill a strong-coupling
approach by Zeyher and Zwicknagl [19,20] (ZZ) and, in the weak-coupling linfit by
Klein and Dierker [21]. In theseapproadles, the linewidth corresponds to the imag-
inary part of the self-energy ImP, the real part Re~ being the phonon frequency
which can thus be understood in a sirnilar picture. The strength ofthe inter;lotion
is given by tile electron-phonon coupling constant Ai (for mode i), which h~s been
calculated forvarious modes in a local-density approach(LDA)by Rodriguez et al.
[22]and Cohen and Pickett [23]. The experimental frequency and linewidth changes
ofphouonsin the superconducting state are thus qualitatively described by the ZZ-
theory, the absolute magnitudes of the changes may be used to find tile coupling
constants of certain modes. The agreement oftheseAi-values with tile calcttlatcd
ones is good, as we shall showbelow.
A further anomaly has been noticed recently in the Raanan intensities. Friedl ct
al. [24] found that the intensities, particularly of phonons near the energy gap
,as determined by the self-energies,increaseby up to a factor of two upon cooling
from the normal to the superconducting state. These anomalies are interpreted
as resonant-enhanced gap scattering and are - like the fxequency and linewidth
anomalies - due to the opening of a gap at the Fernfi surface. We will also show
that the anisotropies whidt most certainly exist in thegap canbe smeared out bythe
addition of impurities like Au, Pr, andF'e,which makes the mixtureYBazCu3O7-6
+ impurities appear as a dirty superconductor [25]. This result is particularly
important when considering that many crystals grown by the CuO-fluxmethod [26]
contain impurities from the crucible material, andany information about the Fermi
surface and the gap may stem from the mixed, dirty superconductor rather than
from a pure phase.
There are other aspects ofRamauscatteringon high-T~ superconductors which we
shMl not discuss in detail here. These are asymmetries in some of the phonon
lineshapes, so-called Fano lineshapes, which have best been seen in RBa2CuaOr-6
[27,28] and originatefrom a coherent interaction of tile phononwith a continuous
background in tilelight-scatteringspectra. For a reviewoftheFano lineshapes, see
Refs. [29-31].
The continuous background is "also a peculiarity of the high-Te materials. It has
definite selection rules, it extends to very high energies (> 1 eV), aud it is com-
mon to all classes of high-To materials. Yet its microscopic origin is not known,
any temperature dependence in the normM stateappears to be absent and, most
importantly, in the superconductingstate its intensity decreases linearly below a
ccrtain energy (around 300 - 500 cm-~ or 40 - 60 meV) [32-36]. This has been
intcrpretcd as the signatureof an energy gap. The anisotropies in the contimmm
scattcring data, e.g. inYBa2Cu4Os, reflect the anisotropies in theFcrmisurfaccin
the normal and superconductingstate (see e.g. [36]). For a comparisonwith data
on conventional superconductors sec Dicrker ctal. [371 (NbzSn) and Itackl et al.
[38] (VaSi). For morc details on electronic-continuum scattering and for possible
thcoreticalinterprctations and implications the reader is referred to the original
literature or to reviews [31,39] whcre also the topic of scatteringby spin-waves is
covered.
We will now briefly describe the experimental setup used in this work and then
return to the eigenmodes of the RBa2CuzOT-8 unit cell. Specifically, we present
the most important experimented results and discuss thephonon anomalies which
led to the determinationof~superconductinggap value in RBa~Cu~OT-6.
2 Experimental Procedure
Tile Ramanspectra were excited by variouslines ofargon and krypton ionlasers,
focussed to a point of ~50 tLmdiameter with average power below3 roW, leading
to a power density of ~150 W/cm". Tile geometry was exact backscattering with
au aperture of the collectinglens of f = 1:1.2. The monochromator used was an
astigmaticallycorrectedtripleDILORXY with 1800 lines/ramholographicgratings
[40]. Tilefirsttwo gratings were used in asubtractiveoperationalmode, typical for
multichannel applications. As a detector we used a charged-coupled device (CCD);
inherent spikes forlongintegrationtimes wereeliminatedwithaspecial software [41].
The data weretransferredtoapersonalcomputerandfurtheranalyzedona/~VaxII.
Line fits to obtain precise frequency and linewidthinformation were performed to
standard Lorentzian or Fano lineshapes as appropriate for the various phonons.
Typical integrationtimes were 30 nfinutes toone hour. Tile samples were held in
a closed-cycle cryostat [42]evacuatedby a turbo-pump. The absoluteexperimental
accuracy is about 1.5 cm-1, the relative one for a given experiment where one
parameter, say thetemperature,is variedis about 0.2 cm-1.
Tile samples used in this study, for the most part, were ceramics and thin films
which allowed great flexibility for the replacement of the rare-earth atom or tile
oxygen isotope. All discussedeffects have also been varified on single crystals of
R = Y and Er. No detectable impurities were found by chemical analysis ofthe
ceramics, an advantage overflux-grown samples, which tend to incorporate more of
the crucible material due to higher reaction temperatures.
3 Phonon Eigenvectors
A detailed knowledge oftilephononsin the normal state ofa newmaterialis funda-
mentalforthe studies ofeffects ofsuperconductivityon thosephonons. The analysis
of the phonons of RBa2Cu~Or_6 experimentally, group-theoretically, and through
lattice-dynamical calculations and total-energy calculations has been accomplished.
Theree~stanumberofreviewson this topic,which we refer the reader to [31,39,43-
45]. Through the similarity in the crystM structure between tile different high-Te
materials, the eigenmodes are similar in thevarious families, and weshowas a rep-
resentative example thoseof RBazCu3Or (see Fig. 1 [39]). Tile Raman modes are
in theupperhalf, the strongestmodes are thosein the first row. The assignment of
Ag
116 157 355 378 508
x: 73 142 356 429 564
y: 92 137 496 412 544
9._.55|122} 15.5{184) 199(209) 312{312} 36.~3(417} 509(519) 556(557)
x: 79(80) 121(121) 197(203} 35._.66[366J 367(415) 565(565) ~63(167)
y: 1030041 727(140) 191(193) 350(358) 36.~5{447) 545(545) 5~9(5~9)
Fig. 1 Calculated eigenmodes and frequencies at/~ = 0 of the optical modes of
RBa2Cu307-6. Only the upper half ofa unit cellis showal, the displacements ira the
lower half follow by symmetry. Raman-active modes are even (A~, 029, and/Ts~),
m-activeones odd (Bt,, O2,, B3u). From [39].
4
