Low-Dimensional Electronic Properties of Molybdenum Bronzes and Oxides, 1989 Physics and Chemistry of Materials with Low-Dimensional Structures Series, Vol. 11

The history of low dimensional conductors goes back to the prediction, more than forty years ago, by Peierls, of the instability of a one dimensional metallic chain, leading to what is known now as the charge density wave state. At the same time, Frohlich suggested that an "ideal" conductivity could be associated to the sliding of this charge density wave. Since then, several classes of compounds, including layered transition metal dichalcogenides, quasi one-dimensional organic conduc­ tors and transition metal tri- and tretrachalcogenides have been extensively studied. The molybdenum bronzes or oxides have been discovered or rediscovered as low dimensional conductors in this last decade. A considerable amount of work has now been performed on this subject and it was time to collect some review papers in a single book. Although this book is focused on the molybdenum bronzes and oxides, it has a far more general interest in the field of low dimensional conductors, since several of the molybdenum compounds provide, from our point of view, model systems. This is the case for the quasi one-dimensional blue bronze, especially due to the availability of good quality large single crystals. This book is intended for scientists belonging to the fields of solid state physics and chemistry as well as materials science. It should especially be useful to many graduate students involved in low dimensional oxides. It has been written by recognized specialists of low dimensional systems.

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.