INTRODUCTION TO THE ELECTRON THEORY OF METALS
CONTENTS 1 INTRODUCTION 11 WHAT IS THE ELECTRON THEORY OF METALS? 12 HISTORICAL SURVEY OF THE ELECTRON THEORY OF METALS 13 OUTLINE OF THIS BOOK 2 BONDING STYLES AND THE FREE-ELECTRON MODEL 21 PROLOGUE 22 CONCEPT OF AN ENERGY BAND 23 BONDING STYLES 24 MOTION OF AN ELECTRON IN FREE SPACE 25 FREE ELECTRON UNDER THE PERIODIC BOUNDARY CONDITION 26 FREE ELECTRON IN A BOX 27 CONSTRUCTION OF THE FERMI SPHERE EXERCISES 3 ELECTRONS IN A METAL AT ?NITE TEMPERATURES 31 PROLOGUE 32 FERMI–DIRAC DISTRIBUTION FUNCTION (I) 33 FERMI–DIRAC DISTRIBUTION FUNCTION (II) 34 ELECTRONIC SPECI?C HEAT 35 LOW-TEMPERATURE SPECI?C HEAT MEASUREMENT 36 PAULI PARAMAGNETISM 37 THERMIONIC EMISSION EXERCISE 4 PERIODIC LATTICE, AND LATTICE VIBRATIONS IN CRYSTALS 41 PROLOGUE 42 PERIODIC STRUCTURE AND RECIPROCAL LATTICE VECTORS 43 PERIODIC LATTICE IN REAL SPACE AND IN RECIPROCAL SPACE 44 LATTICE VIBRATIONS IN ONE-DIMENSIONAL MONATOMIC LATTICE 45 LATTICE VIBRATIONS IN A CRYSTAL 46 LATTICE WAVES AND PHONONS 47 BOSE–EINSTEIN DISTRIBUTION FUNCTION 48 LATTICE SPECI?C HEAT 49 ACOUSTIC PHONONS AND OPTICAL PHONONS 410 LATTICE VIBRATION SPECTRUM AND DEBYE TEMPERATURE 411 CONDUCTION ELECTRONS, SET OF LATTICE PLANES AND PHONONS 5 CONDUCTION ELECTRONS IN A PERIODIC POTENTIAL 51 PROLOGUE 52 COSINE-TYPE PERIODIC POTENTIAL 53 BLOCH THEOREM 54 KRONIG–PENNEY MODEL 55 NEARLY-FREE-ELECTRON MODEL 56 ENERGY GAP AND DI?RACTION PHENOMENA 57 BRILLOUIN ZONE OF ONE- AND TWO-DIMENSIONAL PERIODIC LATTICES 58 BRILLOUIN ZONE OF BCC AND FCC LATTICES 59 BRILLOUIN ZONE OF HCP LATTICE 510 FERMI SURFACE–BRILLOUIN ZONE INTERACTION 511 EXTENDED, REDUCED AND PERIODIC ZONE SCHEMES 6 ELECTRONIC STRUCTURE OF REPRESENTATIVE ELEMENTS 61 PROLOGUE 62 ELEMENTS IN THE PERIODIC TABLE 63 ALKALI METALS 64 NOBLE METALS 65 DIVALENT METALS 66 TRIVALENT METALS 67 TETRAVALENT METALS AND GRAPHITE 68 PENTAVALENT SEMIMETALS 69 SEMICONDUCTING ELEMENTS WITHOUT AND WITH DOPANTS 7 EXPERIMENTAL TECHNIQUES AND PRINCIPLES OF ELECTRONIC STRUCTURE-RELATED PHENOMENA 71 PROLOGUE 72 DE HAAS–VAN ALPHEN E?ECT 73 POSITRON ANNIHILATION 74 COMPTON SCATTERING E?ECT 75 PHOTOEMISSION SPECTROSCOPY 76 INVERSE PHOTOEMISSION SPECTROSCOPY 77 ANGULAR-RESOLVED PHOTOEMISSION SPECTROSCOPY (ARPES) 78 SOFT X-RAY SPECTROSCOPY 79 ELECTRON-ENERGY-LOSS SPECTROSCOPY (EELS) 710 OPTICAL RE?ECTION AND ABSORPTION SPECTRA 8 ELECTRONIC STRUCTURE CALCULATIONS 81 PROLOGUE 82 ONE-ELECTRON APPROXIMATION 83 LOCAL DENSITY FUNCTIONAL METHOD 84 BAND THEORIES IN A PERFECT CRYSTAL 85 TIGHT-BINDING METHOD 86 ORTHOGONALIZED PLANE WAVE METHOD 87 PSEUDOPOTENTIAL METHOD 88 AUGMENTED PLANE WAVE METHOD 89 KORRINGA–KOHN–ROSTOKER METHOD 810 LMTO 9 ELECTRONIC STRUCTURE OF ALLOYS 91 PROLOGUE 92 IMPURITY E?ECT IN A METAL 93 ELECTRON SCATTERING BY IMPURITY ATOMS AND THE LINDE LAW 94 PHASE DIAGRAM IN AU–CU ALLOY SYSTEM AND THE NORDHEIM LAW 95 HUME-ROTHERY RULE 96 ELECTRONIC STRUCTURE IN HUME-ROTHERY ALLOYS 97 STABILITY OF HUME-ROTHERY ALLOYS 98 BAND THEORIES FOR BINARY ALLOYS 10 ELECTRON TRANSPORT PROPERTIES IN PERIODIC SYSTEMS (I) 101 PROLOGUE 102 THE DRUDE THEORY FOR ELECTRICAL CONDUCTIVITY 103 MOTION OF ELECTRONS IN A CRYSTAL: (I) – WAVE PACKET OF ELECTRONS 104 MOTION OF ELECTRONS IN A CRYSTAL: (II) 105 ELECTRONS AND HOLES 106 BOLTZMANN TRANSPORT EQUATION 107 ELECTRICAL CONDUCTIVITY FORMULA 108 IMPURITY SCATTERING AND PHONON SCATTERING 109 BAND STRUCTURE E?ECT ON THE ELECTRON TRANSPORT EQUATION 1010 ZIMAN THEORY FOR THE ELECTRICAL RESISTIVITY 1011 ELECTRICAL RESISTIVITY DUE TO ELECTRON–PHONON INTERACTION 1012 BLOCH–GRÜNEISEN LAW 11 ELECTRON TRANSPORT PROPERTIES IN PERIODIC SYSTEMS (II) 111 PROLOGUE 112 THERMAL CONDUCTIVITY 113 ELECTRONIC THERMAL CONDUCTIVITY 114 WIEDEMANN–FRANZ LAW AND LORENZ NUMBER 115 THERMOELECTRIC POWER 116 PHONON DRAG E?ECT 117 THERMOELECTRIC POWER IN METALS AND SEMICONDUCTORS 118 HALL E?ECT AND MAGNETORESISTANCE 119 INTERACTION OF ELECTROMAGNETIC WAVE WITH METALS (I) 1110 INTERACTION OF ELECTROMAGNETIC WAVE WITH METALS (II) 1111 RE?ECTANCE MEASUREMENT 1112 RE?ECTANCE SPECTRUM AND OPTICAL CONDUCTIVITY 1113 KUBO FORMULA 12 SUPERCONDUCTIVITY 121 PROLOGUE 122 MEISSNER E?ECT 123 LONDON THEORY 124 THERMODYNAMICS OF A SUPERCONDUCTOR 125 ORDERING OF THE MOMENTUM 126 GINZBURG–LANDAU THEORY 127 SPECI?C HEAT IN THE SUPERCONDUCTING STATE 128 ENERGY GAP IN THE SUPERCONDUCTING STATE 129 ISOTOPE E?ECT 1210 MECHANISM OF SUPERCONDUCTIVITY–FRÖHLICH THEORY 1211 FORMATION OF THE COOPER PAIR 1212 THE SUPERCONDUCTING GROUND STATE AND EXCITED STATES IN THE BCS THEORY 1213 SECRET OF ZERO RESISTANCE 1214 MAGNETIC ?UX QUANTIZATION IN A SUPERCONDUCTING CYLINDER 1215 TYPE-I AND TYPE-II SUPERCONDUCTORS 1216 IDEAL TYPE-II SUPERCONDUCTORS 1217 CRITICAL CURRENT DENSITY IN TYPE-II SUPERCONDUCTORS 1218 JOSEPHSON E?ECT 1219 SUPERCONDUCTING QUANTUM INTERFERENCE DEVICE (SQUID) MAGNETOMETER 1220 HIGH-TC SUPERCONDUCTORS 13 MAGNETISM, ELECTRONIC STRUCTURE AND ELECTRON TRANSPORT PROPERTIES IN MAGNETIC METALS 131 PROLOGUE 132 CLASSI?CATION OF CRYSTALLINE METALS IN TERMS OF MAGNETISM 133 ORBITAL AND SPIN ANGULAR MOMENTA OF A FREE ATOM AND OF ATOMS IN A SOLID 134 LOCALIZED ELECTRON MODEL AND SPIN WAVE THEORY 135 ITINERANT ELECTRON MODEL 136 ELECTRON TRANSPORT IN FERROMAGNETIC METALS 137 ELECTRONIC STRUCTURE OF MAGNETICALLY DILUTE ALLOYS 138 SCATTERING OF ELECTRONS IN A MAGNETICALLY DILUTE ALLOY – “PARTIAL WAVE METHOD” 139 SCATTERING OF ELECTRONS BY MAGNETIC IMPURITIES 1310 S–D INTERACTION AND KONDO E?ECT 1311 RKKY INTERACTION AND SPIN-GLASS 1312 MAGNETORESISTANCE IN FERROMAGNETIC METALS 1313 HALL E?ECT IN MAGNETIC METALS 14 ELECTRONIC STRUCTURE OF STRONGLY CORRELATED ELECTRON SYSTEMS 141 PROLOGUE 142 FERMI LIQUID THEORY AND QUASIPARTICLE 143 ELECTRONIC STATES OF HYDROGEN MOLECULE AND THE HEITLER–LONDON APPROXIMATION 144 FAILURE OF THE ONE-ELECTRON APPROXIMATION IN A STRONGLY CORRELATED ELECTRON SYSTEM 145 HUBBARD MODEL AND ELECTRONIC STRUCTURE OF A STRONGLY CORRELATED ELECTRON SYSTEM 146 ELECTRONIC STRUCTURE OF 3D-TRANSITION METAL OXIDES 147 HIGH-TC CUPRATE SUPERCONDUCTORS 15 ELECTRONIC STRUCTURE AND ELECTRON TRANSPORT PROPERTIES OF LIQUID METALS, AMORPHOUS METALS AND QUASICRYSTALS 151 PROLOGUE 152 ATOMIC STRUCTURE OF LIQUID AND AMORPHOUS METALS 153 PREPARATION OF AMORPHOUS ALLOYS 154 THERMAL PROPERTIES OF AMORPHOUS ALLOYS 155 CLASSI?CATION OF AMORPHOUS ALLOYS 156 ELECTRONIC STRUCTURE OF AMORPHOUS ALLOYS 157 ELECTRON TRANSPORT PROPERTIES OF LIQUID AND AMORPHOUS METALS 158 ELECTRON TRANSPORT THEORIES IN A DISORDERED SYSTEM 1581 ZIMAN THEORY FOR SIMPLE LIQUID METALS IN GROUP (V) 1582 BAYM–MEISEL–COTE THEORY FOR AMORPHOUS ALLOYS IN GROUP (V) 1583 MOTT S–D SCATTERING MODEL 1584 ANDERSON LOCALIZATION THEORY 1585 VARIABLE-RANGE HOPPING MODEL 159 ELECTRON CONDUCTION MECHANISM IN AMORPHOUS ALLOYS 1510 STRUCTURE AND PREPARATION METHOD OF QUASICRYSTALS 1511 QUASICRYSTALS AND APPROXIMANTS 1512 ELECTRONIC STRUCTURE OF QUASICRYSTALS 1513 ELECTRON TRANSPORT PROPERTIES IN QUASICRYSTALS AND APPROXIMANTS 1514 ELECTRON CONDUCTION MECHANISM IN THE PSEUDOGAP SYSTEMS 15141 MOTT CONDUCTIVITY FORMULA FOR THE PSEUDOGAP SYSTEM 15142 FAMILY OF QUASICRYSTALS AND THEIR APPROXIMANTS 15143 FAMILY OF AMORPHOUS ALLOYS IN GROUP (IV) 15144 FAMILY OF “UNUSUAL” PSEUDOGAP SYSTEMS