Angle-Resolved Photoemission Spectroscopy Study of Spin Fluctuations in the Cuprate Superconductors PDF
Preview Angle-Resolved Photoemission Spectroscopy Study of Spin Fluctuations in the Cuprate Superconductors
Springer Theses Recognizing Outstanding Ph.D. Research Francisco Restrepo Angle-Resolved Photoemission Spectroscopy Study of Spin Fluctuations in the Cuprate Superconductors Springer Theses Recognizing Outstanding Ph.D. Research AimsandScope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent fieldofresearch.Forgreateraccessibilitytonon-specialists,thepublishedversions includeanextendedintroduction,aswellasaforewordbythestudent’ssupervisor explainingthespecialrelevanceoftheworkforthefield.Asawhole,theserieswill provideavaluableresourcebothfornewcomerstotheresearchfieldsdescribed,and for other scientists seeking detailed background information on special questions. 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Francisco Restrepo Angle-Resolved Photoemission Spectroscopy Study of Spin Fluctuations in the Cuprate Superconductors Doctoral Thesis accepted by the University of Illinois at Chicago, USA FranciscoRestrepo DepartmentofPhysics UniversityofVirginia Charlottesville,VA,USA ISSN2190-5053 ISSN2190-5061 (electronic) SpringerTheses ISBN978-3-031-10978-2 ISBN978-3-031-10979-9 (eBook) https://doi.org/10.1007/978-3-031-10979-9 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerland AG2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Tomyparents,RosaHelenaMedinaand JuanGuillermoRestrepo Supervisor’s Foreword Shortlyafterthediscoveryofthelanthanumbariumcopperoxidehigh-temperature superconductors, P.W. Anderson pointed out that the parent insulator was an odd electron state with unusual magnetic properties, an antiferromagnetic Mott insulator. Several authors considered the possibility that as the insulator is doped, antiferromagneticfluctuations,genericallyreferredtoasspinfluctuations,persisted inthedopedinsulator.Itwassuggestedthatthesespinfluctuationscouldeffectively become the glue that binds the electrons in the Fermi sea, leading to high- temperature superconductivity. The transition temperature T could be calculated c if one knew the spin fluctuation spectra, the electronic spectra, and the interaction betweenthetwo. Calculations,however,showedmixedresults:someindicatingthathighT could c originate from these interactions, while others did not produce reasonable values of T . There was also controversy over the pseudogap, the state above T in the c c optimally and underdoped materials. A large part of the problem was the fact that oneofthecomponentsneededtocalculateT wasnotknownapriori.Forexample, c theelectronspectraofsomematerialswerenotmeasuredattemperatureswherethe material would have become a superconductor, or the electron spectra would not haveshownasuperconductinggapatlowtemperatures,forexample. Morerecently,extensivedatasetsunderfarbettercontrolledconditionsbecame available. Dr. Restrepo used experimental techniques that allowed the samples to keep their surface cleanliness, and therefore their doping values, for over a month under experimental conditions. This is crucial in allowing measurements of the electronicexcitationspectraoftheentireirreducibleBrillouinzoneunderidentical conditions. He mastered the details of the entire measurement process to a point wheretheexperimentsprovidedveryreliabledata.Frompreviouswork,ageneral understanding developed, that in order to make a reasonable estimate of T , all of c the quantities entering the calculations needed to be known in the normal state at atemperaturecloseenoughaboveT ,andattheappropriatedopinglevel,soasto c leadtoareasonableestimateofT . c Perhapsamoreseriousproblemforthisentireprogramwasthefactthatthespin fluctuation spectra above T were not considered to be representative of those in c vii viii Supervisor’sForeword thesuperconductingstate.Afewyearsbeforethepresentwork,Chatterjeeetal.had shownthat,surprisingly,ARPEScouldbeusedtoderiveaverycloseapproximation tothespinexcitationspectrameasuredbyneutronscatteringmethods,eventhough ARPES only measures the single-particle scattering component of the electron- spin excitation spectra, while the neutron scattering spectra include all orders of scattering.Andapriori,onedoesnotknowifthehigherorderprocessesarecritical indescribingtheimportantconsequencesoftheelectron-spinfluctuationscattering. Nonetheless, Dr. Restrepo decided to test the spin fluctuation theory again, making use of the appropriate bosonic and fermionic functions obtained from ARPESdatainthenormalstate,andatthecorrecttemperatures.Thiswasaremark- ably brave attempt, considering that Dr. Restrepo was trained as an experimental physicist, while the calculations required some of the most advanced theoretical and calculational methods. For example, the strong interactions involved required the use of a generalization of the BCS gap equation –the Bethe–Salpeter equation (BSE)–tocalculateT .Tothisend,Dr.Restrepofirstshowedhowthevariousterms c enteringtheBSEequationcouldbeobtained,withincertainapproximations,from the spectrum of electronic excitations measured by ARPES. He then used these ARPES-derivedquantitiesasinputstotheBSEandfoundsolutionscorresponding to T values of 60–90K, in agreement with experiments. Thus, he concluded that c antiferromagnetic correlations are a viable candidate for the pairing interaction in thecupratesuperconductors. Aside from carrying out the measurements, Dr. Restrepo himself also carried out all the calculations required for this work, a rare accomplishment for an experimentally trained physicist. Moreover, I should point out that previous to the measurementsandanalysisofthedata,Dr.Restrepowasinvolvedintheconstruc- tionofthemeasurementapparatus.Thisentirebodyofworkisdescribedindetail in the PhD thesis. Chapter 1 introduces the problem of high T superconductivity c and two of the main classes of theories proposed to solve it. One such class of theories, studied in this work, explores the possibility of magnetic excitations as mediatorsofCooperpairing,asmentionedabove.Chapter2summarizesthebasic conceptsofsuperconductivityinGreen’sfunctionformalismandoffersaworking introduction to the cuprate superconductors and their anomalous characteristics. Chapter 3 introduces the experimental technique used in this work, ARPES. Chapter4coverssomeofthemoretechnicalaspectsoftheexperiment,highlighting Dr. Restrepo’s contributions to the construction of measurement instrument. In Chap.5,Dr.RestreposhowshowtheextensiveARPESdatacanbeusedtoextract thesingle-particleGreen’sfunction,aswellasconstructthespinsusceptibility,both of which are used as inputs to the Bethe–Salpeter equation. In doing so, he finds eigenvalues of this equation consistent with T values in agreement with exper- c iments and eigenfunctions—which reflect the properties of the superconducting orderparameter—withd-wavesymmetryandanenergydependenceconsistentwith theexperimentallyobservedtimeretardationofthepairinginteraction.Overall,his results represent an attempt to quantitatively reconcile observations from various experimentalprobes—likeneutronscattering,ARPES,andothers—andaccountfor thehighcriticaltemperaturesobservedinthecupratesuperconductors. Supervisor’sForeword ix Dr.Restrepohasalsostriventomakehisworkself-containedandpedagogical,as evidencedbytheextensiveintroductorymaterialcontainedinChaps.1–4,aswellas theadditionalexplanationsintheappendices.Therefore,wehopethatnewstudents in high T superconductivity and photoemission spectroscopy will find this work c original, engaging, and instructive. We wish to thank Springer for giving us the opportunitytosharethisexcitingworkwithawideraudience. UniversityofIllinoisatChicago JuanCarlosCampuzano Chicago,IL,USA May2022 Acknowledgments Iwanttofirstthankmyadvisor,JuanCarlosCampuzano,forhisunderstanding,his seemingly infinite patience, and, of course, his advice, which often went beyond the scientific. I am also indebted to professors Utpal Chatterjee and Dirk Morr for several key suggestions which helped this project come to fruition. (I am particularly grateful to Professor Chatterjee for kindly sharing a large data set analyzedinthiswork.)Imustalsothankmycolleague,HaoXu,forhisperseverance and resourcefulness in solving the many technical difficulties that plagued our experiment. IamgratefultoFanny Rodolakis andCrisAdrianoforhelpfuladvice during the many hours spent at the synchrotron facility during the first two years of my research. It is also a great pleasure for me to acknowledge the outstanding workperformedbytheinstrumentmakersatUIC;inparticular,KevinLynch,Bob Kurdydyk, Rick Frueh, and Rich Djoutrek. The many parts they fabricated for us, their aid in the design process, and the instrumentation difficulties they helped us overcome are testimony to a contribution to this work that cannot be overstated. AlsoatUIC,IwishtothankthegraduatestudentadvisorJamesNellforhispatience and his eagerness to help, not just me, but also other physics graduate students. I am equally grateful to Derrick Stanley and Brian Shim for placing orders for me in a timely fashion and keeping our accounts under control. Professors Mark Schlossman and Anjum Ansari also deserve special mention. Aside from being outstandingphysicsinstructors,theyprovidedmewithabetterappreciationofthe truenatureofscientificresearchbykindlyallowingmetoworkintheirlabsasan undergraduateassistant.Ialsowanttothankmydefensecommitteefortheirinterest inmyworkandformakingpartofanimportanteventinmycareer. Onamorepersonalside,Iwouldliketoextendmygratitudetomyfamily,espe- cially to my parents, for their unfaltering support and encouragement throughout mylife.Thisworkistheirs.Finally,IshouldverymuchliketothankthefriendsI madeduringmystayatUIC,aswellasmyoldchildhoodfriendsfromColombia.It isnoexaggerationtosaythatthroughallourbickering,arguing,joking,laughing, agreeing,anddisagreeing,theyhavelefttheirmarkinmymemoryandthought. xi
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