Theoretical Aspects of Band Structures and Electronic Properties of Pseudo-One-Dimensional Solids

This volume presents a sequence of articles which describe the theoretical treat­ ments of investigating the fundamental features in the electronic structures and properties of typical quasi-one-dimensional solids; organic conductor TTF-TCNQ, polyacetylene, metallic and superconducting polymer (SN)n and linear chain chal­ cogenides and halides of transition elements including NbSe3' The aim of this volume is not to present an exhaustive review but rather to touch on a selective class of problems which appear to be fundamental for typical quasi-one-dimensional solids. Thus the topics in this volume are rather confined to the key basic properties of quasi-one-dimensional systems. The quasi-one-dimensional solids are one of the most extensively investigated subjects in current physics, chemistry and materials science. These materials are unique in attracting a broad range of scientists, chemists, experimental and theore­ tical physicists, materials scientists and engineers. In 1954 Frohlich constructed a theory of superconductivity based on a one-dimensional model of moving charge density waves. In 1955 Peierls predicted that anyone-dimensional metal is unstable against the distortion of a periodic lattice so that a metal-nonmetal transition occurs at a certain temperature for a one-dimensional metal. According to these theories a gap is opened at the Fermi surfaces of one-dimensional conductors at low tempera­ tures and the charge density wave is created in connection with the occurrence of the gap.

Theoretical Aspects of Conducting Polymers: Electronic Structure and Defect States.- 1. Introduction.- 2. Ground State Configuration (Hückel Theory).- 2.1. Model and Basic Assumptions.- 2.2. Bond Order.- 2.3. Equilibrium Configuration and Bond—Bond Polarizability.- 2.4. Parametrization.- 2.5. Peierls Instability and Bond Alternation in Polyacetylene.- 2.6. Phonons.- 3. The Continuum Limit.- 3.1. Definition of the Fields and Appropriate Boundary Conditions.- 3.2. Bogoliubov—de Gennes Equations and Self-Consistency Condition.- 3.3. Ground State and Small Amplitude Fluctuations.- 4. Intrinsic Defects.- 4.1. The Kink Solution.- 4.2. Polarons, Bipolarons, and Excitons.- 4.3. Solitons?.- 5. Towards a More Realistic Theory of Conducting Polymers.- 5.1. Electron—Electron Interaction.- 5.2. Disorder.- 5.3. Interchain Coupling.- 6. Concluding Remarks.- Appendix A: Local Bond Order and Local Density in the Peierls Distorted State.- Appendix B: Polaron—Type Solutions.- Appendix C: Acoustic Phonons.- References.- Equilibrium Properties of TTF-TCNQ.- 1. Introduction.- 2. Interaction Scheme.- 2.1. Electron Bands.- 2.2. Coulomb Interactions.- 2.3. Phonons and Electron7—Phonon Interactions.- 2.4. Instabilities.- 3. Coulomb Correlated Electron Gas.- 3.1. Cohesion of TTF-TCNQ.- 3.2. Parquet Approximation — Coupling Constants.- 3.3. Parquet Sums.- 3.4. Exact Theory.- 3.5. Coulomb Interchain Coupling.- 3.6. 4kF Correlations.- 4. CDW Coupling to the Lattice.- 4.1. Harmonic Theory.- 4.2. Quartic Interaction of Phonons.- 4.3. Microscopic Picture — Summary.- 5. Three-Dimensional Ordering.- 5.1. Phase Transitions at 54, 49, and 38 K.- 5.1(a) 2kF Ordering.- 5.1(b) Landau Model for the Sliding Regime (T > 38 K).- 5.1(c) The Commensurate Lock-in at a*/4.- 5.2. Hysteresis in the Temperature Range 38 K < T < 49 K.- 5.3. 4kF Ordering.- 5.4. (p, T) Phase Diagram.- 5.4(a) Experimental Situation.- 5.4(b) Symmetry Analysis.- 5.4(c) The Commensurate Lock-in of 2kF at b*/3.- 5.4(d) The Pressure Dependence of TF and Tx.- 5.5. Conclusion.- References.- Band Structures and Electronic Properties of Metallic Polymer (SN)x and Its Intercalates (SNBry)x.- 1. Introduction.- 1.1. Brief Survey of Band Structure Calculations up to Self-Consistent Calculation.- 1.2. Crystal Structure of (SN)x.- 2. Self-Consistent Numerical Basis Set LCAO Method.- 2.1. Local Density Functional Formalism.- 2.2. Effects of Charge Transfer.- 3. Band Structure and Fermi Surface of (SN)x.- 4. Optical Absorption Spectra of (SN)x.- 5. Fermi Surfaces and Optical Absorption Spectra of (SNBry)x.- 6. Electrical Resistivity in an Interacting Two-Carrier System.- 7. Electrical Resistivity of (SN)x and (SNBry)x.- 7.1. Model.- 7.2. Temperature Dependence and Magnitude of Resistivity.- 7.2.1. Electron—Hole Scattering.- 7.2.2. Carrier—Phonon Scattering.- 7.2.3. Resistivity of (SN)x and (SNBry)x.- 8. Summary.- References.- The Quasi-One-Dimensional Chalcogenides and Halides of Transition Elements.- 1. Introduction.- 1.1. One-Dimensional Compounds and Metal—Metal Bonding.- 1.2. Electron Band Structure Methods.- 2. Metal—Metal Pairing in NbI4.- 2.1. The NBI4 Crystal Structure.- 2.2. Metal—Metal Bonding and the Electronic Structure of NbI4.- 3. Transition Metal Trichalcogenides.- 3.1. Trichalcogenides of Group IV.- 3.1.1. MX3 Structure for Group IV Transition Metals.- 3.1.2. Optical Properties.- 3.1.3. Electronic Structure Calculations.- 3.1.4. Transport Properties.- 3.1.5. Raman and Infrared Spectra of the Group IV Trichalcogenides.- 3.1.6. Intercalation Properties.- 3.2. Trichalcogenides of Group V.- 3.2.1. NbS3.- 3.2.2. TaSe3.- 3.2.3. NbSe3.- 3.2.4. TaS3.- 3.2.5. FeNb3Sel0.- 4. Zirconium and Hafnium Pentatellurides.- 5. Other One-Dimensional Compounds.- 5.1 NbTe4 and TaTe4.- 5.2 Nb3X4.- 5.3 Other Nb Chalcogenides, Halides, and Chalcogenide Halides.- 5.4 K0.30MoO3.- 5.5 TlMo3Se3.- References.- Electronic Structure of NbSe3.- 1. Low-Dimensional Material NbSe3.- 1.1. Introduction.- 1.2. General Characters of MX3 Compounds.- 1.2.1. Structures and Electronic Properties of MX3 Compounds.- 1.2.2. Relation between Crystal Structures and Electronic Properties of MX3.- 1.2.3. Electronic Structure and CDW Transition.- 1.2.4. Important Factors Determining the Electronic Properties of MX3 Compounds.- 1.3. Electronic Properties of NbSe3.- 1.3.1. Structure of NbSe3.- 1.3.2. Experimental Results of NbSe3.- 1.3.3. CDW Transitions and Band Calculation.- 2. Methodology of a Band Calculation.- 2.1. Formalism of a Calculation.- 2.2. Hamiltonian of a System.- 2.3. Basis Functions and Matrix Element.- 2.4. Charge Distribution.- 2.5. Density of States and Brillouin Zone Integral.- 2.6. Summary.- 3. Results of the Band Calculation.- 3.1. Charge Distribution in a Unit Cell.- 3.2. Energy Dispersion.- 3.3. Density of States.- 3.4. Fermi Surfaces.- 4. Discussion.- 4.1. Fermi Surfaces and CDW Transitions.- 4.2. CDW Transitions and Transport Properties.- 4.2.1. Hall Constant.- 4.2.2. Resistivity.- 4.3. Concluding Remarks.- References.- Index of Names.- Index of Subjects.