Electron-Phonon Interactions and Phase Transitions

This NATO Advanced Study Institute was the fourth in a series devoted to the subject of phase transitions and instabilities with particular attention to structural phase transforma~ions. Beginning wi th the first Geilo institute in 19'(1 we have seen the emphasis evolve from the simple quasiharmonic soft mode description within the Landau theory, through the unexpected spectral structure re­ presented by the "central peak" (1973), to such subjects as melting, turbulence and hydrodynamic instabilities (1975). Sophisticated theoretical techniques such as scaling laws and renormalization group theory developed over the same period have brought to this wide range of subjects a pleasing unity. These institutes have been instrumental in placing structural transformations clearly in the mainstream of statistical physics and critical phenomena. The present Geilo institute retains some of the counter cul­ tural flavour of the first one by insisting whenever possible upon peeking under the skirts of even the most successful phenomenology to catch a glimpse of the underlying microscopic processes. Of course the soft mode remains a useful concept, but the major em­ phasis of this institute is the microscopic cause of the mode softening. The discussions given here illustrate that for certain important classes of solids the cause lies in the electron phonon interaction. Three major types of structural transitions are considered. In the case of metals and semimetals, the electron phonon interaction relie6 heavily on the topology of the Fermi surface.

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.