ebook img

Electron correlation in metals PDF

257 Pages·2004·2.501 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Electron correlation in metals

This page intentionally left blank ELECTRON CORRELATION IN METALS Since the discovery of high T superconductivity, the role of electron correlation c insuperconductivityhasbeenanimportantnewissueincondensedmatterphysics. Heretheroleofelectroncorrelationinmetalsisexplainedindetailonthebasisof theFermiliquidtheory.Thebookdiscussesthefollowingissues:enhancementsof electronicspecificheatandmagneticsusceptibility;effectsofelectroncorrelation ontransportphenomenasuchaselectricresistivityandHallcoefficient;magnetism; Motttransitionandunconventionalsuperconductivity.Theseoriginatecommonly from the coulomb repulsion between electrons. In particular, superconductivity in strongly correlated electron systems is discussed with a unified point of view. Thisbookiswrittentoexplaininterestingphysicsinmetalsforundergraduateand graduatestudentsandresearchersincondensedmatterphysics. Kosaku Yamada has been a professor in the Department of Physics at Kyoto Universitysince1995. ELECTRON CORRELATION IN METALS K. YAMADA DepartmentofPhysics,KyotoUniversity,Japan cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521572323 © K. Yamada 1993 English translation Cambridge University Press 2004 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2004 isbn-13 978-0-511-22958-9 eBook (EBL) isbn-10 0-511-22958-5 eBook (EBL) isbn-13 978-0-521-57232-3 hardback isbn-10 0-521-57232-0 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface page vii 1 Fermigas 1 1.1 Metals 1 1.2 FreeFermigas 2 1.3 ElectronicspecificheatandPaulisusceptibility 4 1.4 Many-bodyeffectofelectrongas 7 1.5 Exchangeenergy 10 1.6 Screeningeffect 13 1.7 Plasmaoscillation 16 1.8 Groundstateenergy 18 1.9 Wignercrystal 20 2 Fermiliquidtheory 22 2.1 Principleofcontinuity 22 2.2 Landau’sFermiliquidtheory 25 3 Anderson’sorthogonalitytheorem 29 3.1 Friedelsumrule 29 3.2 Orthogonalitytheoremonlocalperturbation 33 3.3 Photoemissioninmetalsandtheorthogonalitytheorem 36 3.4 Diffusionofchargedparticlesinmetals 41 4 s–d HamiltonianandKondoeffect 49 4.1 Spinsusceptibilityofconductionelectrons 49 4.2 s–d Exchangeinteractionandspinpolarization 51 4.3 Kondoeffect 54 4.4 Groundstateofdilutemagneticalloysystem 60 4.5 Scalinglawofthes–d system 63 4.6 Wilson’stheory 67 4.7 FermiliquidtheorybyNozie`res 68 v vi Contents 5 AndersonHamiltonian 72 5.1 Hartree–Fockapproximation 72 5.2 Perturbationexpansionwithrespectto V 76 kd 5.3 Green’sfunction 79 5.4 PerturbationexpansionwithrespecttoU 87 5.5 ExactsolutionoftheAndersonHamiltonian 99 6 HubbardHamiltonian 103 6.1 Basicproperties 103 6.2 Theoryofelectroncorrelation 106 6.3 Infinite-dimensionalHubbardHamiltonian 112 6.4 Motttransition 117 6.5 One-dimensionalHubbardmodel 119 6.6 Ferromagnetismoftransitionmetals 120 6.7 SuperconductivityintheHubbardHamiltonian 121 7 Fermiliquidtheoryofstronglycorrelatedelectronsystems 122 7.1 Heavyfermionsystems 122 7.2 Heavyfermions 123 7.3 Kondotemperatureincrystallinefields 124 7.4 Fermiliquidtheoryonheavyfermionsystems 127 7.5 SpinfluctuationandFermiLiquid 141 8 TransporttheorybasedonFermiliquidtheory 147 8.1 Conductivity 147 8.2 Opticalconductivity 148 8.3 Hallconductivity 152 8.4 Cyclotronresonance 153 8.5 Magnetoresistance 157 8.6 Concludingremarks 158 9 Superconductivityinstronglycorrelatedelectronsystems 159 9.1 Cupratehigh-temperaturesuperconductors 159 9.2 Anisotropicsuperconductivityduetocoulombrepulsion 172 9.3 Electron-dopedcuprates 206 9.4 TripletsuperconductorSr RuO 210 2 4 9.5 Conclusion 218 AppendixA.Feynmanrelation 223 AppendixB.Secondquantization 224 AppendixC.Interactionrepresentationandthermal Green’sfunction 226 AppendixD.Linearresponsetheory 233 AppendixE.TransportequationderivedbyE´liashberg 238 Index 243 Preface P.W.Andersonhasachievedmanybrillianttheoriesinthewidefieldofcondensed matter physics. His book titled Basic Notions of the Condensed Matter Physics waspublishedin1984.InthisbookAndersonstressestwobasicprinciplesofcon- densedmatterphysics.Oneoftheprinciplesis‘brokensymmetry’.Thismeansthat condensedmattersystemsundergophasetransitiontotakeastatepossessinglower symmetrythanthatoftheHamiltonian.Thisstatementcorrespondstotheappear- anceofaferromagneticstateandasuperconductingstate,etc.atlowtemperatures. Thisprinciplemanifestsdiscontinuouschange. Anotherbasicprincipleistheprincipleof‘adiabaticcontinuity’.Thisprinciple tells us that when we study a generally complicated physical system we can refer to a simple system that contains the essential nature of the real system and un- derstand thecomplicated system onthe basis ofknowledge of thesimple system. Anderson stresses that the most beautiful and appropriate example showing the importanceofthecontinuityprincipleisLandau’sFermiliquidtheory.Following the continuity principle, we start from a non-interacting Fermi gas and introduce interactions among particles gradually. There exists a one-to-one correspondence betweenthefreeparticlesystembeforetheintroductionoftheinteractionsandthe Fermiliquidaftertheintroduction.ItisthebasiccharacteroftheFermiliquidatlow temperaturesthatwecanintroduceinteractionsasslowlyaspossibleowingtothe longlifetimeofquasi-particles.Eventhoughmany-bodyinteractionsexistamong particles, by considering quasi-particles renormalized by the interactions we can treatthemasiftheyarefreeparticles.BythisprocedurestronglyinteractingFermi systems are much simplified. Strictly speaking, however, the systems cannot be completelyfreeparticlesystemsevenafterrenormalization;thereremaindamping effects giving a finite lifetime and weak renormalized interactions among quasi- particles. In particular, since attractive forces make the Fermi surface unstable, it is only the repulsive force that can be continuously renormalized on the basis of theFermiliquidtheory.Thisfactplaysanimportantroleinmany-bodyproblems. vii viii Preface Afterreducingsystemstoweaklyinteractingquasi-particlesystemsfollowingthe Fermiliquidtheory,wecanthendiscussphasetransitionssuchassuperconductivity, inducedbytherenormalizedinteractionsamongquasi-particles. Fermi liquid theory, which was introduced by Landau for liquid 3He, has been applied to electrons in metals and developed. Along with progress in the electron theory of solids, strongly interacting electron systems have been studied actively for various metals. By this development, the Fermi liquid theory has been made profound and based on microscopic foundations. After completion of the many- bodytheoryofelectrongasandtheBCStheoryofsuperconductivity,inthe1960s magnetism of transition metals and Mott transitions of their oxides were studied asmainissuesofelectroncorrelation.Then,thediscoveryoftheKondoeffectand the study of the Anderson Hamiltonian relating to the appearance and disappear- ance of localized moments in metals followed. Recently, we have studied heavy electrons whose masses are thousands of times as large as the free electron mass. Theseelectronsarenothingbutthequasi-particlesintheFermiliquidtheory.Our presentsubjectinelectroncorrelationisthestudyofcopper-oxidesuperconductors as metallic systems near the Mott insulator. These are called strongly correlated electron systems. The normal state of strongly correlated electron systems can be describedastheFermiliquid.InrecentyearsithasbeenmadeclearthattheFermi liquid theory contains various fruitful physical properties. At present the Fermi liquidtheoryisinthecourseofdevelopment. The Hubbard Hamiltonian contains a wealth of physics, such as metal– insulatortransitionsandmagnetictransitions.AlthoughthetheoryoftheHubbard Hamiltonianhasbeengreatlydeveloped,asseeninthestudyoftheMotttransition usinganinfinite-dimensionalmodel,wearestillfarfromacompleteunderstanding. Recently, the new problem of whether the Hubbard system can exhibit supercon- ductivity has been added, as an important problem to be solved. In this book we showthatsuperconductivityisactuallyrealizedowingtoelectroncorrelationinthe HubbardHamiltonian. ThepurposeofthisbookistointroducetheFermiliquidtheoryandtodescribe the physics of strongly correlated electron systems. I intend to introduce unique and rich physical phenomena in each system mentioned above; I would like to describe the universality of the Fermi liquid and the basic principles common to various systems. At this point, I believe there exists a powerful theory that is not changed by details of experimental data. Nature is much more complicated than wecanimagine,butitisnotcapricious. To accomplish the purpose of this book, I intend to introduce the microscopic Fermi liquid theory developed by Luttinger et al. and describe the concepts con- firmedthroughitsdevelopment,althoughIamnotsurewhetherIhavesucceeded inthistaskornot.

See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.