Superconductivity

Superconductivity covers the nature of the phenomenon of superconductivity. The book discusses the fundamental principles of superconductivity; the essential features of the superconducting state-the phenomena of zero resistance and perfect diamagnetism; and the properties of the various classes of superconductors, including the organics, the buckministerfullerenes, and the precursors to the cuprates. The text also describes superconductivity from the viewpoint of thermodynamics and provides expressions for the free energy; the Ginzburg-Landau and BCS theories; and the structures of the high temperature superconductors. The band theory; type II superconductivity and magnetic properties; and the intermediate and mixed states are also considered. The book further tackles critical state models; various types of tunneling and the Josephson effect; and other transport properties. The text concludes by looking into spectroscopic properties. Physicists and astronomers will find the book invaluable.

Preface 1 Properties of the Normal State I. Introduction II. Conduction Electron Transport III. Chemical Potential and Screening IV. Electrical Conductivity V. Frequency Dependent Electrical Conductivity VI. Electron-Phonon Interaction VII. Resistivity VIII. Thermal Conductivity IX. Fermi Surface X. Energy Gap and Effective Mass XI. Electronic Specific Heat XII. Phonon Specific Heat XIII. Electromagnetic Fields XIV. Boundary Conditions XV. Magnetic Susceptibility XVI. Hall Effect Further Reading Problems 2 The Phenomenon of Superconductivity I. Introduction II. A Brief History III. Resistivity A. Resistivity above Tc B. Resistivity Anisotropy C. Anisotropy Determination D. Sheet Resistance of Films: Resistance Quantum IV. Zero Resistance A. Resistivity Drop at Tc B. Persistent Currents below Tc V. Transition Temperature VI. Perfect Diamagnetism VII. Fields inside a Superconductor VIII. Shielding Current IX. Hole in Superconductor X. Perfect Conductivity XI. Transport Current XII. Critical Field and Current XIII. Temperature Dependences XIV. Concentration of Super Electrons XV. Critical Magnetic Field Slope XVI. Critical Surface Further Reading Problems 3 The Classical Superconductors I. Introduction II. Elements III. Physical Properties of Superconducting Elements IV. Compounds V. Alloys VI. Miedema's Empirical Rules for Alloys VII. Compounds with the NaCl Structure VIII. Type .415 Compounds IX. Laves Phases X. Chevrel Phases XI. Heavy Electron Systems XII. Charge-Transfer Organics XIII. Chalcogenides and Oxides XIV. Barium Lead-Bismuth Oxide Perovskite XV. Barium-Potassium Bismuth-Oxide Cubic Perovskite XVI. Buckminsterfullerenes XVII. Borocarbides Further Reading Problems 4 Thermodynamic Properties I. Introduction II. Specific Heat above Tc III. Discontinuity at Tc IV. Specific Heat below Tc V. Density of States and Debye Temperature VI. Thermodynamic Variables VII. Thermodynamics of a Normal Conductor VIII. Thermodynamics of a Superconductor IX. Superconductor in Zero Field X. Superconductor in a Magnetic Field XI. Normalized Thermodynamic Equations XII. Specific Heat in a Magnetic Field XIII. Evaluating the Specific Heat XIV. Order of the Transition XV. Thermodynamic Conventions XVI. Concluding Remarks Further Reading Problems 5 Ginzburg-Landau Theory I. Introduction II. Order Parameter III. Ginzburg-Landau Equations IV. Zero-Field Case Deep inside Superconductor V. Zero-Field Case near Superconductor Boundary VI. Fluxoid Quantization VII. Penetration Depth VIII. Critical Current Density IX. London Equations X. Exponential Penetration XI. Normalized Ginzburg-Landau Equations XII. Type I and Type II Superconductivity XIII. Upper Critical Field Bc2 XIV. Quantum Vortex A. Differential Equations B. Solutions for Small Distances C. Solutions for Large Distances Further Reading Problems 6 BCS Theory I. Introduction II. Cooper Pairs III. BCS Order Parameter IV. Generalized BCS Theory V. Singlet Pairing in a Homogeneous Superconductor VI. Self-Consistent Equation for the Energy Gap VII. Response of a Superconductor to a Magnetic Field Further Reading 7 Perovskite and Cuprate Crystallographic Structures I. Introduction II. Perovskites A. Cubic Form B. Tetragonal Form C. Orthorhombic Form D. Planar Representation III. Cubic Barium Potassium Bismuth Oxide IV. Barium Lead Bismuth Oxide V. Perovskite-Type Superconducting Structures VI. Aligned YBa2Cu307 A. Copper Oxide Planes B. Copper Coordination C. Stacking Rules D. Crystallographic Phases E. Charge Distribution F. YBaCuO Formula G. YBa2Cu408 and Y2Ba4Cu7015 VII. Body Centering VIII. Body-Centered La2Cu04 and Nd2Cu04 A. Unit Cell Generation of La2Cu04 (T Phase) B. Layering Scheme C. Charge Distribution D. Superconducting Structures E. Nd2Cu04 Compound (T' Phase) F. La2_x_yRxSryCu04 Compounds (T* Phase) IX. Body-Centered BiSrCaCuO and TIBaCaCuO A. Layering Scheme B. Nomenclature C. Bi-Sr Compounds D. Tl-Ba Compounds E. Modulated Structures F. Aligned Tl-Ba Compounds G. Lead Doping X. Aligned HgBaCaCuO XI. Buckminsterfullerenes XII. Symmetries XIII. Crystal Chemistry XIV. Comparison with Classical Superconductor Structures XV. Conclusions Further Reading Problems 8 Hubbard Models and Band Structure I. Introduction II. Reciprocal Space and Brillouin Zone III. Free Electron Bands in Two Dimensions IV. Nearly Free Electron Bands V. Fermi Surface in Two Dimensions A. Fermi Surface B. Closed Fermi Surface C. Open Fermi Surface VI. Electron Configurations A. Electronic Configurations and Orbitals B. Tight-Binding Approximation VII. Hubbard Models A. Wannier Functions and Electron Operators B. One-State Model C. Electron-Hole Symmetry D. Half-Filling and Antiferromagnetic Correlations E. t-J Model F. Resonant-Valence Bonds G. Spinons, Holons, Slave Bosons, Anyons, and Semions H. Three-State Model I. Energy Bands J. Metal-Insulator Transition VIII. Transition Metal Elements IX. A-15 Compounds X. Buckminsterfullerenes XI. BaPb1_xBix03 System XII. Ba1_xKxBi03 System XIII. Band Structure of YBa2Cu307 A. Energy Bands and Density of States B. Fermi Surface: Plane and Chain Bands C. Charge Distribution XIV. Band Structure of (La1_xSrx)2Cu04 A. Orbital States B. Energy Bands and Density of States C. Brillouin Zone D. Fermi Surface E. Orthorhombic Structure XV. Bismuth and Thallium Compounds XVI. Mercury Compounds XVII. Fermi Liquids XVIII. Fermi Surface Nesting XIX. Charge-Density Waves, Spin-Density Waves, and Spin Bags XX. Mott-Insulator Transition XXI. Anderson Interlayer Tunneling Scheme XXII. Comparison with Experiment XXIII. Discussion Further Reading Problems 9 Type II Superconductivity I. Introduction II. Internal and Critical Fields A. Magnetic Field Penetration B. Ginzburg-Landau Parameter C. Critical Fields III. Vortices A. Magnetic Fields B. High-Kappa Approximation C. Average Internal Field and Vortex Separation D. Vortices near Lower Critical Field E. Vortices near Upper Critical Field F. Contour Plots of Field and Current Density G. Closed Vortices IV. Vortex Anisotropies A. Critical Fields and Characteristic Lengths B. Core Region and Current Flow C. Critical Fields D. High-Kappa Approximation E. Pancake Vortices F. Flux Trapping V. Individual Vortex Motion A. Vortex Repulsion B. Pinning C. Equation of Motion D. Onset of Motion E. Magnus Force F. Steady-State Vortex Motion G. Intrinsic Pinning H. Vortex Entanglement VI. Flux Motion A. Flux Continuum B. Entry and Exit C. Two-Dimensional Fluid D. Dimensionality E. Solid and Glass Phases F. Moving Flux G. Transport Current in a Magnetic Field H. Dissipation I. Magnetic Phase Diagram VII. Fluctuations A. Thermal Fluctuations B. Characteristic Length C. Entanglement of Flux Lines D. Irreversibility Line E. Kosterlitz-Thouless Transition VIII. Quantized Flux Further Reading Problems 10 Magnetic Properties I. Introduction II. Susceptibility III. Magnetization and Magnetic Moment IV. Magnetization Hysteresis V. Zero Field Cooling and Field Cooling VI. Granular Samples and Porosity VII. Magnetization Anisotropy VIII. Measurement Techniques IX. Comparing Susceptibility and Resistivity Results X. Ellipsoids in Magnetic Fields XI. Demagnetization Factors XII. Measured Susceptibilities XIII. Sphere in a Magnetic Field XIV. Cylinder in a Magnetic Field XV. ac Susceptibility XVI. Temperature-Dependent Magnetism A. Pauli Paramagnetism B. Paramagnetism C. Antiferromagnetism XVII. Pauli Limit and Upper Critical Fields XVIII. Ideal Type II Superconductor XIX. Magnets Further Reading Problems 11 Intermediate and Mixed States I. Introduction II. Intermediate State III. Surface Fields and Intermediate-State Configuration IV. Type I Ellipsoid V. Susceptibility VI. Gibbs Free Energy for the Intermediate State VII. Boundary-Wall Energy and Domains VIII. Thin Film in Applied Field IX. Domains in Thin Films X. Current-Induced Intermediate State XI. Mixed State in Type II Superconductors Further Reading Problems 12 Critical States I. Introduction II. Current-Field Relations A. Transport and Shielding Current B. Maxwell Curl Equation and Pinning Force C. Determination of Current-Field Relationships III. Critical-State Models A. Requirements of Critical-State Model B. Examples of Models C. Model Characteristics IV. Fixed Pinning Model V. Bean Model A. Low-Field Case B. High-Field Case C. Transport Current D. Circular Cross Section E. Combining Screening and Transport Current F. Pinning Strength VI. Reversed Critical States and Hysteresis A. Reversing Field B. Average Internal Field C. Magnetization D. Hysteresis Loops E. Magnetization Current F. Critical Currents G. Reversing Fields with Transport Currents VII. Kim Model VIII. Comparison of Critical-State Models with Experiment IX. Concluding Remarks Further Reading Problems 13 Tunneling I. Introduction II. The Phenomenon of Tunneling A. Conduction-Electron Energies B. Types of Tunneling III. Energy Level Schemes A. Semiconductor Representation B. Boson Condensation Representation IV. Tunneling Processes A. Conditions for Tunneling B. Normal Metal Tunneling C. Normal Metal-to-Superconductor Tunneling D. Superconductor-to-Superconductor Tunneling V. Quantitative Treatment of Tunneling A. Distribution Function B. Density of States C. Tunneling Current D. N - I -N Tunneling Current E. N-I-S Tunneling Current F. S-I-S Tunneling Current G. Nonequilibrium Quasiparticle Tunneling VI. Tunneling Measurements A. Weak Links B. Experimental Arrangements for Measuring Tunneling C. N-I-S Tunneling Measurements D. S-I-S Tunneling Measurements E. Energy Gap F. Proximity Effect G. Even-Odd Electron Number Effect VII. Josephson Effect A. Cooper Pair Tunneling B. dc Josephson Effect C. ac Josephson Effect D. Driven Junctions E. Inverse ac Josephson Effect F. Analogues of Josephson Junctions VIII. Magnetic Field and Size Effects A. Short Josephson Junction B. Long Josephson Junction C. Josephson Penetration Depth D. Two-Junction Loop E. Self-Induced Flux F. Junction Loop of Finite Size G. Ultrasmall Josephson Junction H. Arrays and Models for Granular Superconductors I. Superconducting Quantum Interference Device Further Reading Problems 14 Transport Properties I. Introduction II. Inductive Superconducting Circuits A. Parallel Inductances B. Inductors C. Alternating Current Impedance III. Current Density Equilibration IV. Critical Current A. Anisotropy B. Magnetic Field Dependence V. Magnetoresistance A. Applied Fields above Tc B. Applied Fields below Tc C. Fluctuation Conductivity D. Flux Flow Effects VI. Hall Effect A. Hall Effect above Tc B. Hall Effect below Tc VII. Thermal Conductivity A. Heat and Entropy Transport B. Thermal Conductivity in the Normal State C. Thermal Conductivity below Tc D. Magnetic Field Effects E. Anisotropy VIII. Thermoelectric and Thermomagnetic Effects A. Thermal Flux of Vortices B. Seebeck Effect C. Nernst Effect D. Peltier Effect E. Ettinghausen Effect F. Righi-Leduc Effect IX. Photoconductivity X. Transport Entropy Further Reading Problems 15 Spectroscopic Properties I. Introduction II. Vibrational Spectroscopy A. Vibrational Transitions B. Normal Modes C. Soft Modes D. Infrared and Raman Active Modes E. Kramers-Kronig Analysis F. Infrared Spectra Results G. Light-Beam Polarization H. Raman Spectra Results I. Energy Gap III. Optical Spectroscopy IV. Photoemission A. Measurement Technique B. Energy Levels C. Core-Level Spectra D. Valence Band Spectra E. Energy Bands and Density of States V. X-ray Absorption Edges A. X-ray Absorption B. Electron-Energy Loss VI. Inelastic Neutron Scattering VII. Positron Annihilation VIII. Magnetic Resonance A. Nuclear Magnetic Resonance B. Quadropole Resonance C. Electron-Spin Resonance D. Nonresonant Microwave Absorption E. Microwave Energy Gap F. Muon Spin Relaxation G. Mössbauer Resonance Further Reading Problems References Appendix Index

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Horacio A. Farach

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