QUANTUM STATISTICAL THEORY OF SUPERCONDUCTIVITY
CONTENTS CHAPTER 1 INTRODUCTION 11 BASIC EXPERIMENTAL FACTS 12 THEORETICAL BACKGROUND 13 THERMODYNAMICS OF A SUPERCONDUCTOR 14 DEVELOPMENT OF A MICROSCOPIC THEORY 15 LAYOUT OF THE PRESENT BOOK REFERENCES CHAPTER 2 FREE-ELECTRON MODEL FOR A METAL 21 CONDUCTION ELECTRONS IN A METAL; THE HAMILTONIAN 22 FREE ELECTRONS; THE FERMI ENERGY 23 DENSITY OF STATES 24 HEAT CAPACITY OF DEGENERATE ELECTRONS 1; QUALITATIVE DISCUSSIONS 25 HEAT CAPACITY OF DEGENERATE ELECTRONS 2; QUANTITATIVE CALCULATIONS 26 OHM’S LAW, ELECTRICAL CONDUCTIVITY, AND MATTHIESSEN’S RULE 27 MOTION OF A CHARGED PARTICLE IN ELECTROMAGNETIC FIELDS CHAPTER 3 LATTICE VIBRATIONS: PHONONS 31 CRYSTAL LATTICES 32 LATTICE VIBRATIONS; EINSTEIN’S THEORY OF HEAT CAPACITY 33 OSCILLATIONS OF PARTICLES ON A STRING; NORMAL MODES 34 TRANSVERSE OSCILLATIONS OF A STRETCHED STRING 35 DEBYE’S THEORY OF HEAT CAPACITY CHAPTER 4 LIQUID HELIUM: BOSE–EINSTEIN CONDENSATION 41 LIQUID HELIUM 42 FREE BOSONS; BOSE–EINSTEIN CONDENSATION 43 BOSONS IN CONDENSED PHASE CHAPTER 5 BLOCH ELECTRONS; BAND STRUCTURES 51 THE BLOCH THEOREM 52 THE KRONIG–PENNEY MODEL 53 INDEPENDENT-ELECTRON APPROXIMATION; FERMI LIQUID MODEL 54 THE FERMI SURFACE 55 ELECTRONIC HEAT CAPACITY; THE DENSITY OF STATES 56 DE-HAAS–VAN-ALPHEN OSCILLATIONS; ONSAGER’S FORMULA 57 THE HALL EFFECT; ELECTRONS AND HOLES 58 NEWTONIAN EQUATIONS OF MOTION FOR A BLOCH ELECTRON 59 BLOCH ELECTRON DYNAMICS 510 CYCLOTRON RESONANCE CHAPTER 6 SECOND QUANTIZATION; EQUATION-OF-MOTION METHOD 61 CREATION AND ANNIHILATION OPERATORS FOR BOSONS 62 PHYSICAL OBSERVABLES FOR A SYSTEM OF BOSONS 63 CREATION AND ANNIHILATION OPERATORS FOR FERMIONS 64 SECOND QUANTIZATION IN THE MOMENTUM (POSITION) SPACE 65 REDUCTION TO A ONE-BODY PROBLEM 66 ONE-BODY DENSITY OPERATOR; DENSITY MATRIX 67 ENERGY EIGENVALUE PROBLEM 68 QUANTUM STATISTICAL DERIVATION OF THE FERMI LIQUID MODEL REFERENCE CHAPTER 7 INTERPARTICLE INTERACTION; PERTURBATION METHODS 71 ELECTRON–ION INTERACTION; THE DEBYE SCREENING 72 ELECTRON–ELECTRON INTERACTION 73 MORE ABOUT THE HEAT CAPACITY; LATTICE DYNAMICS 74 ELECTRON–PHONON INTERACTION; THE FRÖHLICH HAMILTONIAN 75 PERTURBATION THEORY 1; THE DIRAC PICTURE 76 SCATTERING PROBLEM; FERMI’S GOLDEN RULE 77 PERTURBATION THEORY 2; SECOND INTERMEDIATE PICTURE 78 ELECTRON–IMPURITY SYSTEM; THE BOLTZMANN EQUATION 79 DERIVATION OF THE BOLTZMANN EQUATION 710 PHONON-EXCHANGE ATTRACTION CHAPTER 8 SUPERCONDUCTORS AT 0 K 81 INTRODUCTION 82 THE GENERALIZED BCS HAMILTONIAN 83 THE COOPER PROBLEM 1; GROUND COOPER PAIRS 84 THE COOPER PROBLEM 2; EXCITED COOPER PAIRS 85 THE GROUND STATE 86 DISCUSSION 87 CONCLUDING REMARKS CHAPTER 9 BOSE–EINSTEIN CONDENSATION OF PAIRONS 91 PAIRONS MOVE AS BOSONS 92 FREE BOSONS MOVING IN TWO DIMENSIONS WITH ? = CP 93 FREE BOSONS MOVING IN THREE DIMENSIONS WITH ? = CP 94 B–E CONDENSATION OF PAIRONS 95 DISCUSSION CHAPTER 10 SUPERCONDUCTORS BELOW TC 101 INTRODUCTION 102 ENERGY GAPS FOR QUASI-ELECTRONS AT 0 K 103 ENERGY GAP EQUATIONS AT 0 K 104 ENERGY GAP EQUATIONS; TEMPERATURE-DEPENDENT GAPS 105 ENERGY GAPS FOR PAIRONS 106 QUANTUM TUNNELING EXPERIMENTS 1; S–I–S SYSTEMS 107 QUANTUM TUNNELING EXPERIMENTS 2; S 1–I–S2 AND S–I–N 108 DENSITY OF THE SUPERCONDENSATE 109 HEAT CAPACITY 1010 DISCUSSION CHAPTER 11 SUPERCURRENTS, FLUX QUANTIZATION, AND JOSEPHSON EFFECTS 111 RING SUPERCURRENT; FLUX QUANTIZATION 112 JOSEPHSON TUNNELING; SUPERCURRENT INTERFERENCE 113 PHASE OF THE QUASI-WAVE FUNCTION 114 LONDON’S EQUATION AND PENETRATION DEPTH; FLUX QUANTIZATION 115 GINZBURG–LANDAU WAVE FUNCTION; MORE ABOUT THE SUPERCURRENT 116 QUASI-WAVE FUNCTION: ITS EVOLUTION IN TIME 117 BASIC EQUATIONS GOVERNING A JOSEPHSON JUNCTION CURRENT 118 AC JOSEPHSON EFFECT; SHAPIRO STEPS 119 DISCUSSION CHAPTER 12 COMPOUND SUPERCONDUCTORS 121 INTRODUCTION 122 TYPE II SUPERCONDUCTORS; THE MIXED STATE 123 OPTICAL PHONONS 124 DISCUSSION CHAPTER 13 HIGH-TC SUPERCONDUCTORS 131 INTRODUCTION 132 THE CRYSTAL STRUCTURE OF YBCO; TWO-DIMENSIONAL CONDUCTION 133 OPTICAL-PHONON-EXCHANGE ATTRACTION; THE HAMILTONIAN 134 THE GROUND STATE 135 HIGH CRITICAL TEMPERATURE; HEAT CAPACITY 136 TWO ENERGY GAPS; QUANTUM TUNNELING 137 SUMMARY CHAPTER 14 SUMMARY AND REMARKS 141 SUMMARY 142 REMARKS