Structural Phase Transitions in Layered Transition Metal Compounds

The structural phase transition is one of the most fundamental problems in solid state physics. Layered transition-metal dichalcogenides provide us with a most exciting area for the study of structural phase transitions that are associated with the charge density wave (CDW). A large variety of structural phase transitions, such as commensurate and incommensurate transitions, and the physical proper­ ties related to the formation of a CDW, have been an object of intense study made for many years by methods employing modem microscopic techniques. Rather recently, efforts have been devoted to the theoretical understanding of these experimental results. Thus, McMillan, for example, has developed an elegant phenomenological theory on the basis of the Landau free energy expansion. An extension of McMillan's theory has provided a successful understanding of the successive phase transitions observed in the IT- and 2H-compounds. In addition, a microscopic theory of lattice instability, lattice dynamics, and lattice distortion in the CDW state of the transition-metal dichalcogenides has been developed based on their electronic structures. As a result, the driving force of the CDW formation in the IT- and 2H-compounds has become clear. Furthermore, the effect of lattice fluctuations on the CDW transition and on the anomalous behavior of various physical properties has been made clear microscopically.

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. Fröhlich 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.