Low-Dimensional Electronic Properties of Molybdenum Bronzes and Oxides

Transition Metal Oxide Bronzes with Quasi Low-Dimensional Properties.- 1. Introduction.- 2. Band Structure and Electronic Properties of Oxide Bronzes.- 3. Molybdenum Bronzes.- 3.1. Introduction.- 3.2. Preparation.- 3.3. The Blue Bronzes.- 3.3.1. Crystal Structures.- 3.3.2. Physical Properties — The Peierls Transition.- 3.4. The Purple Bronzes.- 3.4.1. Crystal Structure.- 3.4.2. Charge Density Wave Instabilities.- 3.5. The Red Bronzes, A0.33MoO3.- 3.6. La2Mo2O7 — A Rare-Earth Molybdenum Bronze-Like Phase.- 4. Vanadium Bronzes with Quasi Low-Dimensional Properties — ?-AxV2O5.- 4.1. Introduction.- 4.2. Preparation.- 4.3. Crystal Structure.- 4.4. Is There CDW Instability or Bipolaron Ordering in ?-Vanadium Bronzes?.- 5. Tungsten Bronzes with Quasi Low-Dimensional Properties.- 5.1. Hexagonal Tungsten Bronzes (HTB).- 5.2. Phosphate Tungsten Bronzes.- Acknowledgements.- References.- On Structural Aspects of Molybdenum Bronzes and Molybdenum Oxides in Relation to Their Low-Dimensional Transport Properties.- 1. Introduction.- 2. Molybdenum Bronzes.- 2.1. Molybdenum Bronzes Containing Infinite Single ReO3 Octahedral Chains.- 2.1.1. The Red Na0.9MoO3 and K0.9MoO3 Bronzes.- 2.1.2. The Blue Bronze K0.5MoO3.- 2.1.3. The Violet Rb0.27MoO3 and Blue-Black Rb0.44MoO3 Bronzes.- 2.2. Molybdenum Bronzes Containing Infinite Two-Dimensional Slabs Comprised of Corner-Sharing Octahedra.- 2.2.1. The Violet Bronzes A0.9Mo6O17 with A = Li, Na, K, Tl.- 2.2.2. The Blue-Black Cs0.25Mo0.97O3 Bronze.- 2.3. Molybdenum Bronzes Containing Infinite Double ReO3 Chains.- 2.3.1. Hydrogen Molybdenum Bronzes, HxMoO3.- 2.3.2. Sodium Hydrated Molybdenum Bronzes.- 2.4. Molybdenum Bronzes Containing Infinite Single Octahedral Ribbons.- 2.4.1. The Triclinic Lithium Bronze, Li0.33MoO3.- 2.5. Molybdenum Tc).- 3.5. The Modulated Structure (T < Tc).- 3.5.1. The CDW Order.- 3.5.2. Atomic Displacements.- 3.6. CDW Disorder.- 3.6.1. Substitutional Disorder.- 3.6.2. Electric Field Induced Tc).- 3.7.2. Phase and Amplitude Excitations of the Incommensurate Structure (T < Tc).- 3.8. Microscopic Parameters.- 3.8.1. In-Chain Parameters.- 3.8.2. Transverse Coupling.- 4. Other Oxides.- 4.1. The Titanium Bronze Na0.25TiO2.- 4.2. The Layer Type Mo Oxides and Bronzes.- 4.2.1. Phase Diagrams.- 4.2.2. Mo4O11.- 4.2.3. Purple Bronzes and Magneli Phases.- 5. Conclusion.- Appendix A.- Appendix B.- Notes.- References.- Charge Density Wave Instabilities and Transport Properties of the Low Dimensional Molybdenum Bronzes and Oxides.- 1. Introduction.- 2. Theoretical Background.- 2.1. The Peierls Transition and the CDW State.- 2.2. Charge Density Wave Transport.- 2.2.1. The Fröhlich Mechanism.- 2.2.2. Rigid CDW: Phenomenological Description of the Motion.- 2.2.3. Deformable CDW: Microscopic Models of Pinning by Impurities.- 2.2.4. Model Based on the Coupling of CDW with Lattice Phonons.- 2.2.5. Models Involving CDW Structural Defects: Discommen-surations and Phase Dislocations.- 2.2.6. Quantum Models.- 3. Quasi One-Dimensional Compounds: The Blue Bronzes A0.30MoO3.- 3.1. Introduction.- 3.2. The Peierls Transition.- 3.2.1. Ohmic Transport.- 3.2.2. Magnetic Susceptibility.- 3.2.3. Thermal and Elastic Properties.- 3.2.4. Effect of Impurities and Point Defects.- 3.3. Band Structure: Experiment and Theory.- 3.4. Nonlinear Transport.- 3.4.1. Introduction.- 3.4.2. Threshold Electric Field.- 3.4.3. Broad Band Noise.- 3.4.4. Periodic Voltage Oscillations.- 3.4.5. Very Low Frequency Phenomena.- 3.4.6. High Velocity Sliding of the CDW at Low Temperature.- 3.5. Hysteresis and Metastability Phenomena.- 3.5.1. Introduction.- 3.5.2. Low Field Regime.- 3.5.3. Nonlinear Regime.- 3.5.4. Pulse Memory Effects.- 3.5.5. Remanent CDW Polarization.- 3.5.6. Field Induced Deformation of the CDW.- 3.6. Local Properties.- 3.6.1. Ion Channeling Technique.- 3.6.2. Mössbauer Effect.- 3.6.3. Electron Paramagnetic Resonance Studies.- 3.6.4. Nuclear Magnetic Resonance Studies.- 3.7. Summary.- 4. Quasi Two-Dimensional Compounds: The Molybdenum Purple Bronzes and the Molybdenum Oxides.- 4.1. Introduction.- 4.2. Charge Density Wave Instabilities and Transport Properties.- 4.2.1. Electrical Resistivity.- 4.2.2. Thermopower.- 4.2.3. Galvanomagnetic Properties.- 4.3. Magnetic Susceptibility.- 4.3.1. Experimental Results.- 4.3.2. Discussion.- 4.4. Specific Heat.- 4.5. Band Structure.- 4.6. Quantum Transport.- 4.6.1. Experimental Results.- 4.6.2. Discussion.- 4.7. Superconductivity in Li0.9Mo6O17.- 5. Conclusion.- Acknowledgements.- References.- Frequency-Dependent Conductivity in K0.30MoO3.- 1. Introduction.- 1.1. Conceptual Models.- 1.2. Uniform Pinning Model.- 1.3. Random Pinning Model.- 2. Dielectric Relaxation Regime.- 2.1. Phenomenological Description.- 2.2. Dielectric Relaxation: Zero dc Bias.- 2.3. Chemical Doping: Zero Bias.- 2.4. Dielectric Relaxation: Finite dc Bias.- 2.5. Dielectric Relaxation Temperature Dependence: Finite dc Bias.- 3. Phase Mode Regime.- 4. Far Infrared Regime.- 5. Normal-Electron Screening.- 6. Summary.- Acknowledgements.- References.- Breaking of Analyticity in Charge Density Wave Systems: Physical Interpretation and Consequences.- 1. Introduction: The Peierls Instability in 1D Conductors.- 2. The Transition by Breaking of Analyticity (TBA) in the Discrete Frenkel—Kontorova (FK) Model.- 2.1. Commensurate Ground States.- 2.2. Incommensurate Ground States.- 2.3. Critical Behavior at the TBA.- 2.4. Incommensurate Structure as an Array of Equidistant Discommensurations.- 2.5. Ising Representation of a Nonanalytic Incommensurate Structure.- 2.6. Extended FK Models and Thermal Fluctuations.- 3. Another Transition by Breaking of Analyticity: The Localization Transition of Electrons in an Incommensurate Potential.- 3.1. Description of the Breaking of Analyticity of the Eigenwaves of a Quasi-Periodic Schroedinger Equation.- 3.2. Exact Results for a Self-Dual Model.- 3.3. Some Numerical Investigations of the Self-Dual Model and Other Non-Self-Dual Models in One Dimension.- 3.4. Other Self-Dual Models in One and Several Dimensions.- 3.5. Questions and Remarks Concerning Discontinuous Quasi-Periodic Potentials.- 3.6. Comparison Between Extended States in Quasi-Periodic and Random Potentials.- 3.6.1. The Kubo—Greenwood Formula.- 3.6.2. The Numerical Technique.- 3.6.3. Results for a Quasi-Periodic Potential in One and Two Dimensions.- 3.6.4. Results for a Random Potential in One and Three Dimensions.- 4. The Transition by Breaking of Analyticity in One-Dimensional Peierls Chains.- 4.1. The Holstein Model.- 4.2. The Fröhlich-SSH Model.- 4.3. Numerical Observation of the Transition by Breaking of Analyticity in Peierls Chains.- 4.4. Critical Behavior at the TBA of Peierls Chains.- 4.4.1. Coherence Length.- 4.4.2. Peierls—Nabarro Energy Barrier.- 4.4.3. Phason Gap and Phonon Spectrum.- 4.5. Electronic Behavior at the TBA.- 4.6. A Classical Lattice Gas Model for the Holstein Model in the Large Electron—Phonon Coupling Limit.- 5. Future Prospects: Quantum Lattice Effects and Thermal Effects.- 5.1. Quantum Lattice Effects.- 5.1.1. A Quantum Lattice Gas Model for the Holstein Model in the Large Electron—Phonon Coupling Limit.- 5.1.2. Effects of the Quantum Lattice Fluctuations on an Incommensurate CDW.- 5.2. Thermal Effects on a Nonanalytic Incommensurate CDW Ground State.- 5.2.1. Order-Disorder CDW.- 5.2.2. Displacive CDW.- 5.2.3. Ohmic Conductivity of a Nonanalytic CDW.- 5.2.4. Nonlinear Electric Conductivity of a Nonanalytic CDW.- Acknowledgements.- References.- Imperfections of Charge Density Waves in Blue Bronzes.- 1. Introduction.- 2. Properties of Static Imperfections of CDWs.- 2.1. Incommensurate CDW.- 2.1.1. Long Wavelength Distortions; the 3D Elastic Limit.- 2.1.2. Short Wavelength Distortions. 2D Ridges and Walls.- 2.1.3. 1D Perfect Dislocations of the CDW.- 2.1.4. Disclinations and Point Singularities of CDWs.- 2.2. Nearly Commensurate CDW.- 2.3. Commensurate CDW.- 3. Interaction of CDW with Lattice Defects.- 3.1. Surfaces and Interfaces.- 3.1.1. Brute Force Processes.- 3.1.2. Dislocation Multiplication.- 3.2. Lattice Dislocations.- 3.3. Point Defects.- 3.3.1. Interactions with CDW.- 3.3.2. Interaction with Dislocations of the CDW.- 4. Elastic and Anelastic Responses of CDW.- 4.1. Elastic Equilibrium of a CDW under an Electric Field.- 4.2. Anelastic Response.- 5. Plastic Properties of CDW.- 5.1. Amplitude-Dependent Internal Friction. Approach to Critical Current.- 5.2. Critical Field for Fröhlich Current.- 5.3. Remanent Polarisation.- 6. Conclusions.- Acknowledgements.- References.