Structural Phase in Transitions in Layered Transition Metal Compounds

Microscopic Theory of Structural Phase Transitions in Layered Transition-metal Compounds.- 1. Introduction.- 2. General theory of electron-lattice interaction and lattice dynamics based on the nonorthogonal tight-binding approximation.- 2.1. Electron-lattice interaction.- 2.2. Generalized electronic susceptibility.- 2.3. Interatomic force, phonon dispersion, and lattice instability.- 2.4. Electronic structure of the CDW state.- 2.5. Other methods of lattice dynamical calculation.- 3. 1T-type transition-metal dichalcogenides.- 3.1. TiSe2.- 3.1.1. Formation of superlattice.- 3.1.2. Electronic structure.- 3.1.3. Electron-lattice interaction and generalized electronic susceptibility.- 3.1.4. Lattice dynamics.- 3.1.5. The CDW state.- 3.2. TiS2.- 3.3. Mixed compounds.- 3.4. VSe2 and CrSe2.- 3.4.1. Summary of experimental evidence regarding structural transformation.- 3.4.2. Electronic structure.- 3.4.3. Electron-lattice interaction and lattice instability.- 3.5. TaS2 and TaSe2.- 3.5.1. Summary of successive phase transitions.- 3.5.2. Electronic structure.- 3.5.3. Lattice instability.- 4. 2H-type transition-metal dichalcogenides.- 4.1. Formation of superlattice.- 4.2. Electronic structure.- 4.3. Electron-lattice interaction and generalized electronic susceptibility.- 4.4. Lattice dynamics and phonon anomaly.- 4.5. Discussion.- 5. Transition-metal trichlorides MCl3 (M = Ti, V, Cr).- 5.1. Summary of experimental results.- 5.2. Electronic structure.- 5.2.1. Tight-binding calculation.- 5.2.2 The Wannier function.- 5.2.3 Estimation of band parameters.- 5.3. Electron-lattice interaction and lattice instability in TiC13.- 5.3.1. Generalized electronic susceptibility.- 5.3.2. Effective d-electron-lattice interaction and lattice instability.- 5.3.3. The transition temperature.- 5.3.4. Some remarks regarding VCl3 and CrCl3.- 5.4. Phase transition.- 5.4.1. Calculation of free energy.- 5.4.2. Magnetic susceptibility.- Appendix A. Perturbation theory in nonorthogonal representation.- Appendix B. Electronic free energy expansion in the adiabatic approximation and derivation of generalized electronic susceptibility.- Appendix C. Frohlich model and Bloch model.- Appendix D. Expressions for the overlap and transfer integrals and their derivatives in terms of Slater-Koster integrals.- Microscopic Theory of Effects of Lattice Fluctuation on Structural Phase Transitions.- 1. Introduction.- 2. Formulation.- 2.1. Hamiltonian and Green's functions for electron and phonon systems.- 2.1.1. Hamiltonian.- 2.1.2. Thermal Green's functions for electrons.- 2.1.3. Thermal Green's functions for phonons.- 2.1.4. Self-energy ? and polarization function ?.- 2.2. Random phase approximation.- 2.3. Mode-mode coupling.- 2.3.1. Lattice fluctuation.- 2.3.2. Transition temperature.- 2.3.3. Coherence length.- 2.3.4. Electron self-energy.- 2.4. Spin susceptibility and electrical resistivity.- 3. Effects of lattice fluctuation on CDW transition.- 3.1. Model.- 3.2. Calculated results for the 1D system.- 3.3. Calculated results for the 3D system.- 4. Effects of lattice fluctuations on the electronic density of states, spin susceptibility, and electrical resistivity.- 4.1. The 1D system.- 4.2. The 3D system.- 5. Supplementary remarks.- Appendix A. Feynman rules for ? and ?.- Appendix B. Evaluation of frequency sum with the use of contour integral in the complex plane.- Phenomenological Landau Theory of Charge Density Wave Phase Transitions in Layered Compounds.- 1. Introduction.- 2. Construction of Landau free energy.- 2.1. 2H-TaSe2.- 2.2. 1T-TaS2 and TaSe2.- 3. A simple example: single-q CDW.- 3.1. Successive phase transitions and discommensurate state.- 3.2. Fluctuation modes.- 4. 2H-TaSe2.- 4.1. Basic features of phase transitions.- 4.2. Single-layer properties.- 4.3. Commensurate phases with various symmetries.- 4.4. Discommensuration structures of two-layer stacking.- 4.5. Reentrant lock-in transition caused by pressure.- 4.6. Discommensuration diagram and dislocations.- 4.7. Fluctuation modes.- 4.8. 2H-NbSe2.- 5. 1T-TaS2 and TaSe2.- 5.1. Brief summary of observed phase transitions.- 5.1.1. 1T-TaS2.- 5.1.2. 1T-TaSe2.- 5.2. Single-layer properties.- 5.2.1. Commensurate state.- 5.2.2. Incommensurate states and discommensuration structures.- 5.3. Three-dimensional orderings of charge density waves.- 5.3.1. Commensurate states.- 5.3.2. Incommensurate and discommensurate states.- 5.4. New phase of 1T-TaS2.- 6. Concluding remarks.- Charge Density Waves in the Transition-metal Dichalcogenides: Recent Experimental Advances.- 1. Introduction.- 2. Charge density wave transformations observed in the Group Vb compounds.- 2.1. 2H structures.- 2.2. 1T structures.- 3. The 2a0 superlattice in the Group IVb compound 1T-TiSe2.- 3.1. General features.- 3.2. Infrared reflectivity-free carrier and phonon effects.- 3.3. Phonon dispersion at low temperature.- 3.4. Angle-resolved photoemission and the electronic structure of TiSe2.- 3.5. The transformed band structure of TiSe2.- 4. Recent developments.- Index of Names.- Index of Subjects.