Collective Excitations in Solids

This book presents an ac count of the NATO Advanced Study Institute on "Collective Excitations in Solids," held in Erice, Italy, from June 15 to June 29, 1981. This meeting was organized by the International School of Atomic and Molecular Spectroscopy of the "Ettore Majorana" Centre for Scientific Culture. The objective of the Institute was to formulate a unified and coherent treatment of various collective excitation processes by drawing on the current advances in various branches of the physics of the solid state. A total of 74 participants came from 54 laboratories and 20 nations (Australia, Belgium, Burma, Canada, China, France, F. R. Germany, Greece, Israel, Italy, Mexico, The Netherlands, Pakistan, Poland, Portugal, Romania, Switzerland, Turkey, The Uni ted Kingdom, and The United States). The secretaries of the course were: Joseph Danko for the scientific aspects and Nino La Francesca for the administrative aspects of the meeting. Fourty-four lectures divided in eleven series were given. Nine "long" seminars and eight "short" seminars were also presented. In addition, two round-table discussions were held.

Quantum Mechanical Description of Solids.- Abstract.- I. Introduction.- II. Adiabatic Approximation.- III. HartreeFock Approximation.- IV. Electronic Bands in Crystals.- V. Lattice Dynamics as Collective Excitations: Phonons.- VI. Collective Excitations of Electrons: Plasmons.- VII. Extrinsic States.- VIII. Some Effects of Applied Stress.- IX. Conclusions.- References.- to Collective Excitations in Solids.- Abstract.- I. Interactions in a TwoLevel System.- I.A. QuantumMechanical Resonance.- I.B. Static Effects of Perturbation.- II. Collective Excitations.- II.A. Setting of the Problem.- II.B. Eigenfunctions.- II.C. Dispersion Relations.- II.D. Effective Mass.- II.E. Generalization to Three Dimension.- II.F. Periodic Boundary Conditions and Density of States.- III. Interaction of Radiation with Collective Excitations.- III.A. The Radiation Field.- 1. The Classical Radiation Field.- 2. The Quantum Radiation Field.- III.B. The Form of the Interaction.- III.C. Absorption and Emission Processes.- III.D. Interaction of Photons with Collective Excitations.- IV. Propagation of Radiation in a Dispersive Medium.- IV.A. Introduction.- IV.B. Dielectric Constant.- IV.C. Propagation of Electromagnetic Waves in a Dispersive Medium.- V. Examples of Collective Excitations.- V.A. Phonons.- 1. Summary of Properties.- 2. Infrared Absorption by Ionic Solids.- V.B. Excitons.- 1. General Theory.- 2. The Frenkel Exciton.- 3. The Wannier Exciton.- 4. The Intermediate Case.- 5. The PhotonExciton System.- 6. The PhotonExcitonPhonon System.- 7. Indirect Transitions.- V.C. Magnons.- 1. Setting of the Problem.- 2. Hamiltonian and Eigenstates.- 3. Semiclassical Treatment.- 4. Thermodynamics of Magnons.- V.C. Plasmons.- 1. Dielectric Response of an Ensemble of Oscillators.- 2. Dielectric Response of a Free Electron Gas.- 3. Transversal Optical Modes in a Plasma.- 4. Longitudinal Optical Modes in a Plasma.- References.- Quasi-Particles and Excitons: Models of Structure and Correlation.- Abstract.- I. Introduction.- II. Basic Concepts of Quantum Field Theory.- II.A. Quantization of Classical Fields.- II.B. Schrödinger Field.- II.C. Occupation Number Representation.- II.D. SelfInteraction.- II.E. Sources.- II.F. Effective Vacuum.- III. Models.- III.A. Empty Band Model.- III.B. Fermi Gas Model.- III.C. Tight Binding Model (TBM).- III.D. Models with Particle Interactions.- III.E. Random Cell Model (RCM).- III.F. Driven Systems.- IV. Conclusions.- References.- Coherent Wavepackets of Phonons.- Abstract.- I. OneDimensional Elastic Line.- I.A. Monatomic Array of Rigid Atoms.- I.B. Forces.- I.C. Energy 15.- 1. Potential Energy.- 2. Kinetic Energy.- 3. Total Energy.- I.D. Continuous Vibrating Line.- II. Beyond the Model of a Chain of Masses and Springs.- III. Motion of a Pulse in the Classical Limit.- III.A. General Features.- III.B. Pulse Shape and Dispersion.- IV. Motion of a Pulse in Quantum Mechanics.- IV.A. Variables.- IV.B. Phonons and Phonon Wavepackets.- IV.C. Propagation of a Pulse: Moment and Energy.- 1. Moment.- 2. Energy.- V. Birth and Death of a Pulse.- References.- Appendix A: The Coherent States.- 1. Definition of the Coherent State |?>.- 2. Some Properties.- 3. Significant Averages.- 4. Time Evolution.- 5. Coordinate Representation.- 6. Why Coherent.- 7. Why Minimum Uncertainty.- 8. Why Semiclassical.- 9. Why Displaced.- 10. Multimode Coherent State.- Appendix B: The Poisson Distribution.- 1. Poisson Distribution.- 2. Perfect Gas in a Container.- 3. Harmonic Oscillator in a Coherent State.- References.- to Exciton Physics.- Abstract.- I. Introduction.- II. Electronic Structure.- II.A. Excitons in a Static Crystal.- 1. Atomic and Molecular Approach.- 2. Effective Mass Approach.- 3. Unified Approach.- 4. Excitons in Disordered Materials.- 5. Effects of External Fields.- 6. Excitons as Quasiparticles.- 7. Manybody Considerations.- II.B. Excitons in Real Materials.- 1. Observation.- 2. Spectral Characteristics.- 3. Surface Excitons.- 4. Trapped and Localized Excitons.- III. Interactions with Phonons.- III.A. Formalism.- 1. Phonons.- 2. Linear ExcitonPhonon Coupling.- 3. Clothing of Excitons.- 4. Effects of HigherOrder Coupling.- III.B. Applications.- 1. Coupling Strengths.- 2. Scattering.- 3. SelfTrapping.- IV. Interactions with Photons.- IV.A. Semiclassical Radiation Theory.- 1. Transition Rates.- 2. Direct Transitions.- 3. Indirect Transitions.- 4. Giant TwoPhoton Effects.- IV.B. The Polariton.- 1. Background.- 2. Polariton Picture and Optical Properties.- 3. Direct Observation of Polariton Dispersion.- 4. Surface Polaritons.- IV.C. Special Topics.- 1. Davydov Splitting.- 2. Excitons in Mixed Crystals.- 3. Line Shapes and Widths.- 4. Urbach’s Rule.- V. Kinetics and Dynamics at Low and Intermediate Densities.- V.A. Introduction.- V.B. Exciton Diffusion.- 1. Historical.- 2. Förster’s Theories.- 3. TimeResolved Studies of Singlets Assumed to Diffuse.- 4. Triplet Exciton Diffusion.- V.C. Coherence.- 1. General Remarks.- 2. Coherence as Described by a Memory Function.- 3. Observation of Coherence.- V.D. Phenomena at Intermediate Densities.- 1. General Remarks.- 2. Annihilation.- 3. Biexciton Formation.- Acknowledgements.- References.- Excitons in Semiconductors.- Abstract.- I. Basic Properties of the Free Exciton.- I.A. Concept of the Free Exciton.- I.B. Energy States of the Free Exciton.- I.C. Frenkel and WannierMott Free Excitons.- I.D. Direct and Indirect Gap Semiconductors.- I.E. Phonon Assisted Free Exciton Absorption in Direct Transition.- I.F. Higher Energy Free Exciton States.- I.G. Zeeman Splittings and Diamagnetic Shifts.- II. Introduction to Bound Excitons.- II.A. History of Bound Excitons.- II.B. Typical Near Gap Bound Exciton Luminescence.- II.C. Trends of EBXHaynes’ Rule.- II.D. Additional Aspects of jj Coupling and Other ZeroField Bound Exciton States.- II.E. MagnetoOptical Effects.- II.F. Auger Recombinations.- II.G. Giant Oscillator Strength.- III. Bound Exciton Satellite Structure.- III.A. Phonon Replicas.- III.B. Electronic Satellites.- III.C. The Use of Luminescence Excitation Spectra.- IV. High Excitation Intensity Effects.- IV.A. Stimulated Emission.- IV.B. Excitonic Molecules and BoseEinstein Condensation.- IV.C. Multiple Bound Excitons.- References.- Excitons in Insulators.- Abstract.- I. Introduction.- II. Theoretical and Experimental Background.- III. Excitons in Alkali Halides.- III.A. Absorption and Reflectivity Measurements.- III.B. Intrinsic Luminescence Measurements.- IV. Excitons in Rare Gas Solids.- V. Concluding Remarks.- References.- Inelastic Scattering of Fast Particles by Plasmons.- Abstract.- I. Introduction.- II. Bulk and Surface Plasmon Hamiltonian.- II.A. Classical Concepts.- 1. Bulk Modes.- 2. Planar Interface Modes.- 3. Thin Film Modes.- 4. Sphere and Void Modes.- II.B. Model Hamiltonians.- 1. Bulk Plasmon Hamiltonian.- 2. Surface Plasmon Hamiltonian.- 3. Multipole Hamiltonian.- III. Charge Particle Spectroscopies of Plasmons.- III.A. High Energy Approximation.- III.B. Bulk, Transmission Spectrum.- III.C. Surface, Reflection Spectrum.- III.D. Fluorescence.- References.- From Magnons to Solitons.- Abstract.- I. Introduction.- II. Magnons.- III. MagnonMagnon Forces.- IV. TwoMagnon Bound States.- V. ManyBody Scattering Theory.- VI. XY Model: A Model Antiferromagnet.- VII. Heisenberg Antiferromagnet: Ground State.- VIII. Some Consequences.- IX. Effects of Surfaces on Magnons.- X. Magnons vs. Solitons.- XI. Soliton Solutions.- References.- Quasiparticles in Magnetic Metals.- Abstract.- I. Introduction.- II. Low Density Electron Gas.- III. Criterion for Magnetic Ground State.- IV. Quasiparticles.- V. Nearly HalfFilled Band: Nagaoka’s Theory.- VI. Two or More Magnetic SubBands.- VII. Magnons in Metals.- VIII. Antiferromagnetism in Metals.- Polaritons.- Abstract.- I. Introduction.- II. Bulk Polariton Linear Response.- III. Experiments on Bulk Polaritons.- IV. Surface Polariton Linear Response.- V. Experiments on Surface Polaritons.- VI. Conclusion.- References 49.- Polarons.- Abstract.- I. Introduction.- II. The LandauPekar StrongCoupling Theory.- III. FieldTheory Formalism, Fröhlich’s Hamiltonian and WeakCoupling Theory.- IV. Other Methods for Large (Fröhlich) Polarons.- V. Small Polarons and SelfTrapping.- References.- Long Seminars.- Surface Collective Excitations.- Abstract.- I. Introduction.- I.A. The Surface as a Perturbation.- I.B. Macroscopic and Microscopic Surface Excitations.- II. Surface Elastic Waves.- II.A. Theory.- II.B. Isotropic Crystals.- II.C. Anisotropic Cubic Crystals.- III. Surface Polaritons.- III.A. Introduction.- III.B. Surface Dielectric Polaritons.- III.C. Surface Plasmon Polaritons.- III.D. Polaritons Associated with Surface Phonons and Excitons.- III.E. Surface Magnon Polaritons.- IV. Surface Lattice Dynamics.- IV.A. Introduction.- IV.B. Dynamics of a Thin Slab.- IV.C. The Green’s Function Method.- 1. The Free Surface as a Perturbation.- 2. The SemiInfinite Lattice.- 3. Example and Comparison with Experimental Data.- Acknowledgement.- References.- Collective Excitations in Concentrated Mn2+ Systems: Spectral Properties.- Abstract.- I. Introduction.- II. The Mn2+ Ion in a Crystal.- II.A. Basic Properties.- II.B. Collective Excitations in Mn2+ Systems.- II.C. Antiferromagnetism in Mn2+ Systems.- III. Excitons in Concentrated Mn2+ Systems.- III.A. Exciton Dispersion and Energy Transport.- III.B. Validity of the Wavevector Description.- IV. Magnons in Concentrated Mn2+ Systems.- IV.A. Basic Theory.- IV.B. Improvement to the Theory.- V. Spectral Features of Mn2+ Systems.- V.A. Appearance of Magnon Sidebands.- V.B. Sideband Profiles.- VI. Phonon Sidebands.- VII. Concluding Remarks.- References.- Optical Dynamics in Concentrated Mn2+ Systems.- Abstract.- I. Introduction.- II. General Aspects of the Optical Properties of Manganese Fluoride Systems.- II.A. Crystal Structure.- II.B. Spectroscopic Properties.- 1. OneParticle Optical Transitions.- 2. TwoParticle Transitions.- 3. Experimental Aspects.- III. Optical Collective Excitations in Concentrated Manganese Fluorides.- III.A. Thermal Studies.- III.B. Uniaxial Stress Effects.- III.C. Magnetic Field Effects.- IV. Validity of the Exciton Model in Fluorescence.- IV.A. Exciton Dispersion and Phase Memory.- IV.B. Exciton Lineshape and Impurity Effects.- 1. Inhomogeneous Broadening.- 2. Diffusion — Limited Energy Transfer.- IV.C. Fluorescence Decay Modes and Deexcitation Models.- 1. Exciton Dynamics at Very Low Temperature.- 2. BoilBack Processes and Magnon Assisted Fluorescence at High Temperature.- IV.D. Effect of External Perturbation.- 1. Effect of Magnetic Field on Exciton Derealization.- 2. Increase of Exciton Density under Uniaxial Stress and Intersublattice Relaxation.- 3. Effect of Intense Light Excitation.- Acknowledgements.- References.- Spectroscopy of Stoichiometric Laser Materials: Excitons or Incoherent Transfers?.- Abstract.- I. Introduction.- II. Experimental Results.- III. Interpretation of Results.- III.A. The Exciton Concept.- III.B. The Energy Transfer Approach.- IV. Conclusion.- References.- Exciton-Hole Droplets in Semiconductors.- Abstract.- I. Introduction.- II. EHL Stability.- III. ManyBody Corrections to OneElectron Properties in EHL.- III.A. Fluorescence Lineshape and Radiative Lifetime.- III.B. Mass Renormalization.- IV. Optical Properties of EHL.- V. Inhomogeneous Electron Hole Liquid.- V.A. Surface Energy.- V.B. Effect of Shallow Impurities on EHL.- V.C. Effect of Isoelectronic Impurities on EHL.- References.- Excitons and Plasmons: Collective Excitations in Semiconductors.- Abstract.- I. Introduction.- II. Eigenvalue Equation.- III. Excitons and Plasmons.- IV. The ExcitonPolariton.- V. Summary.- References.- Picosecond Exciton Phenomena in Chlorophyll Complexes (Abstract only).- Bose-Einstein Statics in Exciton Systems.- Abstract.- I. Introduction.- II. The Ideal (or Nearly Ideal) Bose Gas.- III. The Case of Excitons.- IV. Methods of Detection.- V. Experimental Results in Cu2O.- VI. Experimental Results in CuC1.- VII. Conclusion.- References.- Small Polarons in Biological Systems (Abstract only).- Short Seminars (Abstracts).- Perspectives of Free Electron Lasers in Solids.- The Dispersion Curves of Excitonic Polaritons and Their Distortion with Increasing Density.- Motion of a Magnon Soliton About a Phonon Soliton in a Onedimensional Ferromagnet.- Interconfiguration Fluctuations.- Luminescence of Mn2+ IN RbMnxMg1xF3.- Effect of Hydrostatic Pressure on the Luminescence Spectra of the S2 Centre and the EPR of This S2 Centre for the Crystal Scapolite.- On the Calculation of Polaron Wavefunction in the Static Electronlattice Coupling.- Semiconductor Surface Inversion Layers and Their Collective Modes.- Concluding Article.- Present Trends in Collective Excitations in Solids.- Abstract.- I. Introduction.- II. The Solid State as a ManyBody Problem.- III. Complete Description Including Probes, Sources and Stresses.- IV. General Trends.- V. Trends Specific to Particular Classes of Collective Excitations.- VI. Conclusions.- Acknowledgements.- Contributors.