Electron-Phonon Interactions and Phase Transitions

Phase Transitions and Electron-Phonon Couplings in Perfect Crystals. Modulated Structures. An Introduction.- I. The Framework.- A. Phase changes in perfect crystals.- B. Interatomic forces.- II. Electron-Phonon Couplings (for Delocalized Electrons).- A. Soft modes at OK. Adiabatic and kinematic approximations.- 1. General (crystals).- 2. Energy change for the phonon.- 3. Classical examples.- B. Discussion of the approximations.- 1. The meaning of v.- 2. Self consistency (to first order).- 3. Other correlation effects.- 4. Degeneracy of electronic states.- 5. Anharmonic terms.- 6. Adiabatic approximation.- 7. Entropy at finite temperature.- Appendix A. Short Range Order due to Dispersion Forces.- Appendix B. LCAO Studies of the Band Structures of Metals and Covalents.- Appendix C. Phase Stability for Nearly Free Electrons.- Appendix D. Cohesion in Transitional Metals.- Neutron Scattering Studies of Electron-Phonon Interactions.- I. Phonon Dispersion in Metals.- II. Kohn Singularities.- III. Neutron Spectroscopy of Superconductors.- IV. Magnetic Field Effects.- V. Charge Density Wave Instabilities.- Phase Transitions in Quasi One-Dimensional Metals (TTF-TCNQ and KCP).- 1. Introduction.- 2. Interchain Coupling.- 3. Landau-Ginzburg Theory of Structural Phase Transformations and Charge Density Waves in TTF-TCNQ.- 3.1 The 54K transition.- 3.2 The 47K transition.- 3.3 The 38K transition.- 3.4 The 4kF anomaly.- 3.5 Critical behaviour.- 4. Impurities.- 4.1 One-dimensional random systems.- 4.2 Combined effects of random impurities and interchain coupling.- Solitons and Charge Density Waves.- 1. Abstract.- 2. Introduction.- 3. Change Density Waves and the Sine-Gordon Equation.- 4. Solitons and Charge Density Waves.- 5. Solitons in Disordered Systems.- 6. Classical Solitons in Two Dimension.- 7. Three Dimensional Ordering.- Charge Density Waves in Layered Compounds.- Landau Theory of the Charge Density Waves.- A. The Landau Free Energy.- B. Phase Transitions.- C. Fluctuation Modes.- D. Impurity Effects l.- E. CDW Dislocations l.- F. Discommensurations.- Microscopic Model of CDW in 2H-TaSe2.- Light Scattering by Charge Density Wave Modes in KCP and 2H-TaSe2.- Symmetry Classification of Modulated Structures.- 1. Definition of Modulated Structures.- 2. Symmetry Operations and -Translations.- 3. Properties of MS-Space Group Operations.- 4. Reduced Form of Point Group Operations.- 5. Equivalence and Invariance of k-vectors.- 6. Point Groups.- 7. Rational and Irrational Non-Zero Components of k l.- 8. Necessity of Introduction of Bravais Lattice Types with Improper Translations.- 9. Two-Dimensional Example of Improper Translations.- 10. Enumeration of Lattice Types.- Superspace Groups for the Classification of Modulated Crystals.- I. Introduction.- II. Superspace Groups.- III. Equivalence Classes.- IV. Examples.- V. Conclusions.- Structural Phase Transitions and Superconductivity in A-15 Compounds.- I. Introduction.- II. Instabilities and Transformation Effects on the Physical Behaviour.- III. More on the Relation of Structural Instability and High Temperature Superconductivity.- IV. Instabilities, Unstable Phases, and Superconductivity.- V. Defects, Instabilities, and Superconductivity.- Superconductivity and Martensitic Transformations in A-15 Compounds.- p-d Hybridization, Incipient Lattice Instabilities and Superconductivity in Transition METAL Compounds.- Pseudo-Spin Approach to Structural Phase Transitions.- Abstract.- 1. Introduction.- 2. Models.- (i) Spin-phonon systems.- (ii) Jahn-Teller systems.- (iii) Order-disorder and tunnelling ferroelectrics.- (iv) Displacive ferroelectrics 2l.- (v) Hamiltonians.- 3. Properties of Models.- (i) Statics.- (ii) Formalism for dynamics.- (iii) Dynamic properties.- (iv) Damping.- 4. Mixed and Dilute Systems.- (i) Statics.- (ii) Dynamics.- (iii) Generalisations.- 5. The Central Peak; Critical Behaviour.- (i) The central peak.- (ii) Critical behaviour.- Theory of Jahn-Teller Transitions.- 1. Introduction.- 2. Dynamics of JT-Systems.- 2.1 Electronic configuration.- 2.2 Vibronic coupling.- 2.3 Collective behaviour, mean-field approximation (MFA).- 2.4 Coupling to eleastic strain.- 3. Specific Cases.- 3.1 E x ? coupling.- 3.2 E x ? coupling.- 3.3 T ? ? coupling.- 3.4 T ? t2 coupling.- 3.5 (A+B) ? ? pseudo-JT coupling.- Local Jahn-Teller Effect at a Structural Phase Transition.- Abstract.- 1. Introduction.- 2. Multimode JT-Effect.- 3. Critical Enhancement.- Optical Studies of Jahn-Teller Transitions.- 1. Introduction.- 2. 3d-Transition Metal Ions.- Cu2+:CaO.- Ti3+:A12O3.- 3. Cooperative Jahn-Teller Effects in Rare-Earth Crystals.- 4. Optical Studies of Complicated Jahn-Teller Transitions.- 5. Conclusion.- Electric Susceptibility Studies of Cooperative Jahn-Teller Ordering in Rare-Earth CRYSTALS.- Neutron Scattering Studies of the Cooperative Jahn-Teller Effect.- Abstract.- 1. Introduction.- 2. The Neutron Probe.- 3. Symmetries and Crystal Fields.- 4. Theory.- 5. Static and Critical Properties.- 6. Normal and Mixed Modes.- 7. Discussion 3l.- Gamma-Ray Diffraction Studies of the Mosaic Distribution in TmAsO4 Near the Cooperative Jahn-Teller Transition at 6 K.- The Central Peak in TbVO4.- The Nature of the Eigenfunctions in a Strongly Coupled Jahn-Teller Problem.- I. Introduction.- II. The Physical Setting.- III. The Hamiltonian.- IV. Absorption Spectrum.- V. Summary and Conclusions.- Cooperative Pseudo Jahn-Teller Model of the Sequence of Ferroelastic Transitions in Barium Sodium Niobate.- Single Ion and Cooperative Jahn-Teller Effect for a Nearly Degenerate E Doublet.- Abstract.- 1. Physical System and Model.- 2. Calculations, Results and Discussion.- 3. Conclusions.- Study of the Mott Transition in n.Type CdS by Spin Flip Raman Scattering and Faraday Rotation.- I. Introduction.- II. Basic Properties of Cadmium Sulfide.- Band structure.- Impurity levels.- Free exciton.- Bound exciton.- III. Spin Flip Scattering.- IV. Study of the SFRS Linewidth.- Mott transition in CdS.- Analysis of experimental results.- V. Measurement of X0 Rotation.- VI. Discussion of Results.- Electron Phonon Interactions and Charge Ordering in Insulators.- I. Charge Ordering in Insulators.- II. Second Grade Ordering: Jahn-Teller Ordering in K2PbCu(NO2)6..- II.1 Introduction.- II. 2 Successive Phase Transitions.- II.3 Phase III: Canted pseudospin structure, antiferrodistortive phase.- II.4 Phase III: ‘Fan’ spin structure, incommensurate phase.- II.5 Summary and discussions.- III. Zeroth Grade Ordering in Fe3O4.- III.1 Introduction.- III.2 Symmetry property of the phonon field and the charge density field.- III.3 Pseudospin-phonon formalism and neutron scattering cross sections.- III.4 Summary.- The Verwey Transition in Magnetite.- I. Introduction.- II. Crystal and Symmetry.- III. Critical Scattering.- IV. Structure below TV.- Participants.