Somal, Herpertap Singh

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Dissertations of the University of Groningen

   University of GroningenPolarized angle resolved infrared spectroscopy of high temperature superconductors.Somal, Herpertap SinghIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:1998Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Somal, H. S. (1998). Polarized angle resolved infrared spectroscopy of high temperature superconductors.s.n.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 03-06-2022r Single Layer HTSC's,rong, Science 261, 337J. van der Eb, ín 10th,nd Applications, editedcser, and K. A. Miiller,cGraw-Hill, New York,Ed. D. Gi.nsburg (WorldW. Kress, Phys. Rev. BUarel, W. Y. Lee, A. M.)s4).r, Phys. Rev. B 51, 3312Rev. B 41,307 (1990).)95.HTSC's Eds. J. Bok, G.rse 1-13 Sept, 1997 to beSummarySpectroscopic ProbesIn order to investigate the properties of a material one must use an experimentalprobe, which will interact with the material. It is by examining the effect ofthis interaction that one is able to deduce or calculate a physical property of thematerial. There are two types of probe commonly used to investigate a material,transport and spectroscopic. A transport probe such as resistivity gives infor-mation about the density of electrons and the average time between electroniccollisions as a function of temperature. A spectroscopic probe excites the mate-rial, and by varying the temperature one can investigate the superconducting andthe normal state. Each different type of spectroscopic probe, probes a differentaspect of the material, so that all of them together provide a complete picture.Some examples of spectroscopic probes are FIR (Far Infrared), Raman, AngleResolved Photo Electron Spectroscopy (ARPES), Inelastic Neutron Scattering(lNS), Muon Spin Resonance (pSR) and Nuclear Magnetic Resonance (NMR).A spectroscopic probe can produce an electronic excitation, a collective excita-tion or a nuclear excitation. One can either measure the incoming and outcomingbeam or the excitation produced. In Nuclear Magnetic Resonance (NMR) oneexcites the oxygen and copper nuclei, which before relaxing interact with thevalence electrons. Inelastic Neutron Scattering (INS) provides information aboutthe magnetic excitations such as magnons. In Inelastic Neutron Scattering abeam of monochromatic neutrons impinges upon the material and one meàsuresthe scattered beam. Having measured the energy and momentum (E,k) of theincoming and outcoming neutrons one can calculate the dispersion relationshipfor the excitations. These may be phonons or magnons. In Photo Electron Spec-troscopy (PES) the material is excited by a beam of photons but one meàsuresthe outcoming excited electrons. Here the exciting particle (photons) are not thesame as the measured particle (electrons). Very often a model will be used topredict the outcome of an experiment. By comparing theory with experiment abetter understanding of the material is obtained.In Far Infrared Spectroscopy (FIR) we excite the material with photons (elec-tromagnetic waves) of different energy and measure the rate of absorption. Inthis thesis we use reflectivity as a measure of the absorption. In order to ob-tain the absolute reflectivity, a perfectly reflecting mirror is used as a reference.Wherever the absolute reflectivitv deviates from one, the material has absorbed1 1 3\ 1 4 Chapter 5. Excitation of c-Axis LO Modes in Sing).e Layer HTSC'sor transmitted photons at this frequency. The conservation of energy holds sothat R*T*A:1, where R is the absolute reflectivity, T is the transmisssion andA is the absorption.The normal approach to determining whether a material is a metal, insulator ora semiconductor is to examine the frequency dependence of the reflectivity. Ametal has a high reflectivity upto the plasma frequency, a semiconductor has asmall and an insulator has a large energy gap with ciear phonons.For simplicity one often uses the independant particle approximation for the the-oretical description of solids, even though electrons interact both directly (viaCoulomb interaction) and indirectly (via electron-phonon interaction) with eachother. This approach breaks down when the interaction energy of the particles islarger than the kinetic energy. This situation occurs in strongly correlated elec-tron systems (SCES) and the HTSC's are considered to fall into this category.Single electron band calculations predict the parent compound La2CuOa to be ametal whereas it is an insulator. Not only are the HTSC's strongly correlated,but also anisotropic which means their optical and transport properties dependupon which optical axis is being excited or along which axis the transport takesplace. The cuprates are therefore complex materials for which the current solidstate theory is inadequate.Far infrared spectroscopy is the probe used in this thesis to investigate theHTSC's. The measurements were performed over a temperature range of 4Kto 300K in a 113v Bruker Fourier Transform Infrared (FTIR) spectrometer. Thisspectrometer allows the material to be probed over a range of frequencies inone or two seconds. Repeating this measurement improves the noise statisticsof the spectrum. For weak signals or small samples several hundred scans arenormally performed. FIR spectroscopy measures the dressed electronic excita-tions (usually called quasiparticles), both in-phase (real part of o) and out ofphase (imaginary part of o) values of the conductivity are obtained. The energyrange of the spectrometer \4/as 10 - 8000 cm-1. The superconducting energy gapfor all HTSC's falls well within this range. If one uses the BCS weak couplingrelationship 2Lf kTc:3.5, then for La1.s5Sr6.15CuOa ( T" x32K) the gap energy2A is = 82 cm-1 (10 meV). For HgBaCaO ( T" = 132K) the gap is = 340 cm-1(41 meV). Even if \'r'e assume the case of extremely strong coupling eg. 2A,f kT"=7, then the superconducting gap still falls within the measurement range of thespectrometer.Symmetry of the Order ParameterNear normal incidence, when the angle of incidence 0 of the incoming beam isry 5o - 7", FIR spectroscopy has a limitation when measuring the spectrum ofmaterials which are highly reflecting i.e. R * 1. The resulting optical conductiv-ity then depends upon the noise level in the reflectivity measurements. Certainly5.5. Conclusiotif small changestcvel they will brreflectivity is onthen the analysirsuch a measuremincidence d is nolby l/cos 0. If 0 iTherefore small srThis novel techni<:lRIl (potarizedrne shape of  o1( ,ranreter. By mooparameter, one caiupon the symmetr.measurements of L?9K) rho* thuinurmplies that the orto_l.v:ve order pararrvarldjty of the Ginz,lective number of cht::.: ro rhe overdoperlrgn accuracy meastnumber of charge carfhe c Axis Electrc,t ne HTSC,s are charrar,or l ike c_axis condr,wo.dimcnsional metirncrdence FIR rneasurrnat  the conduct iv i tvthe Motr_Iofle l imit r,which normally denotexceeds the thcoret ic ;srruation. Below T" arr s lreqrrenc.v is beiovcollective excitation.:jto\{' a large irrcreasetnc NÍott_Ioffe l irnit, ometali jc, T. ck,r.reases.Ireqllency dorrblcs i.c.Single Layer HTSC'son of energy holds sothe transmisssion ands a metal, insulator orof the reflectivity. Aa semiconductor has arhonons.roximation for the the-ract both directly (viainteraction) with eachnergy of the particles istrongly correlated elec-fall into this category.pound La2CuO4 to be aC's strongly correlated,rport properties dePendaxis the transport takeswhich the current solidhesis to investigate thermperature range of 4KfIR) spectrometer. Thisrange of frequencies inoves the noise statisticsveral hundred scans areressed electronic excita-rl part of o) and out ofre obtained. The energYerconducting energy gaPthe BCS weak couPling" x32K) the gap energy.) the gap is ry 340 cm-lrg coupling eg. 2L'f kT":Leasurement range of theof the incoming beam is:asuring the sPectrum ofiulting optical conductiv-measurements. CertainlY5.5. Conclusions 1 1 5ifsmall changes induced during the phase transition are of the order of the noiseIevel they wil l be lost. Considering a BCS superconductor, if o1(o) :0 then thereflectivity is one. However, if due to noise the measured value is R : 0'995,then the analysis will produce an artificially large value of oi(c,.'). The error ofsuch a measurement would make the interpretation of o1 dubious. If the angle ofincidence d is now increased, the absorption and the sensitivity rvill be increasedby l/cos 0. If 0 is increased to 80' the sensitivity is increased by a factor of 6.Therefore small superconductivity induced changes are amplified by a factor of 6.This novel technique is the basis of this thesis and is referred to by the acronymPARIS (Polarized Angle Resolved Infrared Spectroscopy).The shape of ola) contains information about the symmetry of the order pa-rameter. By modelling the conductivity based upon a s and a d-wave orderparameter, one can compare the calculations with measurements and commentupon the symmetry of the order parameter for that particuiar material. PARISmeasurements of La1.65Sr6.15CuOa (T" : 32K) and for La1.66Srs.2eCuO4 (T" :29K) show that no clear gap develops in the conductivity spectrum at 4K. Thisimplies that the order parameter cannot be s-wave. Model calculations using ad-wave order parameter show a reasonable agreement. This does not affect thevalidity of the Ginzburg-Landau theory. It had long been asssumed that the ef-fective number of charges continued to increase in going from the optimally dopedcase to the overdoped situation. But it was never understood why T" decreased.High accuracy measurements of La1.seSr6.26CuOa show in fact that the effectivenumber ofcharge carriers decreases and so tracks T" (see chapter 3).The c Axis ElectrodynamicsThe HTSC's are characterized by a metallic ab-plane conductivity and a insu-lator like c-axis conductivity. Within a simple picture they may be I'iewed astwo dimensional metallic sheets separated by insulating material. Near normalincidence FIR measurements of La1.s5Sre.15CuOa (optimally doped crystal) showsthat the conductivity in the normal state is 8 (f2 cm)-1 at 40K which is belowthe Mott-Ioffe limit of 100 (flcm)-l for a metal. There is no zero crossing of e 1which normally denotes the plasma frequency. Furthermore the scattering rateexceeds the theoretically calculated plasma frequency *,hich is a lrer"v unusualsituation. Below T" a plasma edge appears at 50 cm -I. This is unusual in thatit 's frequency is below the BCS gap value of 82 cm-1, therefore it is a sub-gapcollective excitation. N'Ieasurements on the overdoped crystal La1.ssSr0.26CuOashow a large increase in the conductivity o1 at 40Ii but the r':rlue is still belorvthe N{ott-Ioíïe l imit of 100 (Ocrn)-r. As the c-axis conductivit l 'bec-omes rnoremetallic, T. decreases. For a change of 3Ii in the critical tenrperatrtre, the plasnrafrequency doubles i.e. it bccomcs 100 crn-r rvhich is trnexpected(see chapter'-l).1 1 6 Chapter 5. Excitatjon of c-Axis LO Modes in Single Layer HTSC,sExperimental Test of the Anderson fnterlayer Tunnelling ModelP. w. Anderson and coworkers proposed that the frequency of the c-axis plasmaedge was the ,losephson plasma frequency cuy. Furthermore that the critical tem-perature T" rvas directly proportional to c,.:"7. This was a consequence of theInter Layer Tunneliing (ILT) model. Due to the complicated coupling structurein a material lvith more than one copper-oxygen plane per unit cell, this modelwas applicable only to single laver compounds. The Josephson plasma frequencycan be calculated, as it is based upon physical parameters. The calculated andmeasured value of c,-,"7 for La1.65516.15CuOa are in reasonable agreement with eachother. The question remained as to whether it was valid for other single layercompounds. The concept had not been tested due to the lack of availability ofcrystals with sufficient c-axis dimensions to perform optical measurements. Crys-tals of rl2Ba2cuo6, Ndl.s5ces.15cuoa and Bi2sr2cuo6 were available but onrywith c-axis dimensions of 50 - 100pm. However as the plasma edge is a longitu-dinal excitation it may be detected using the PARIS technique. The assumptionwas tested and verified on a crystal of La1.65Srs.15Cuoa where the plasma edge wascorrectly detected. Reflectivity measurements on Tl2Ba2Cu06, Nd1.s5Ce6.15CuOaand Bi2sr2cuo6 did not show a plasma edge near the predicted value. In factno plasma edge was measured within the measurement range. The ILT modelprediction for r..,"7 appears to be incorrect (see chapter 5).Spectroscopische,^r,:..rnun de eigensc.Keluk een probe temateriaal. Door besrergenschappen van hegen worden gewoonlispectroscopie. Voorbspecifieke warmte, getetectronische eigenschine[ materiaal, en doorqende als de normaleverschillend aspect vangeven. Voorbeelden varflot..oniu;. Raman, AF(lnelastische neutronenronanties en I\IMR (nuclr.r,en. spec^troscopische pr,cl[atte of een nucleairemeten ofwel de excitatic_qe zuurstof en koperkerrvur)roát ze relaxeren. loe mag,netische excitatretng (INS), wordt een bungeschoten en meel men d1ri,KJ van de ingaande en1,1 0," exciraries berekene:::: ,1" Foro_Elecron Spee_en bundel fotonen en merngaande deeltjos (fotonennen) In de meeste g"uufi;,net experimenr te àorspe,ment, rvaardoor een betere_rl Uu.. Infrarood Specrosc,tonen (clectromagnetischr, 1

Polarized angle resolved infrared spectroscopy of high temperature superconductors.

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Polarized angle resolved infrared spectroscopy of high temperature superconductors.

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