Charge density wave state

Figure 14 Chemical structure of halogen-bridged mixed-valence complex [M(en)2][MX2(en)2) + (M = Pt, Pd, Ni X = Cl, Br, I) and electronic structures. Counter anions are omitted for clarity, (a) Spin density wave state (SDW) (b) charge density wave state (CDW).

Charge density wave, 54 Charge spreading, 127 Charge-resonant states, 13, 18 Charge-asymmetric dissociation, 9 Coherent control, 7... 

Many phenomena such as dislocations, electronic structures of polyacetylenes and other solids, Josephson junctions, spin dynamics and charge density waves in low-dimensional solids, fast ion conduction and phase transitions are being explained by invoking the concept of solitons. Solitons are exact analytical solutions of non-linear wave equations corresponding to bell-shaped or step-like changes in the variable (Ogurtani, 1983). They can move through a material with constant amplitude and velocity or remain stationary when two of them collide they are unmodified. The soliton concept has been employed in solid state chemistry to explain diverse phenomena. 

Figure 2.27 STM image of incommensurate charge density wave (CDW) state in Nbo.04Tao.96S2. Black lines highlight the insertion of extra rows of CDW maxima in the lattice (From Dai Lieber, 1993).

In conducting solids, the conduction electron density is spatially modulated, forming charge density waves (CDW) the periodic distortion accompanying the CDW (due to interaction between the conduction electron and the lattice) is responsible for the incommensurate phase (Overhauser, 1962 Di Salvo Rice, 1979 Riste, 1977). The occurrence of CDW and the periodic distortion can be understood in terms of the model proposed by Peierls and Frdhlich for one-dimensional metals. Let us consider a row of uniformly spaced chain of ions (spacing = a) associated with conduction electrons of energy E k) and a wave vector k. At 0 K, all the states are filled up to the Fermi energy, = E(kp). If the electron density is sinusoidally modulated as in Fig. 4.15 such that... 

Besides magnetic perturbations and electron-lattice interactions, there are other instabilities in solids which have to be considered. For example, one-dimensional solids cannot be metallic since a periodic lattice distortion (Peierls distortion) destroys the Fermi surface in such a system. The perturbation of the electron states results in charge-density waves (CDW), involving a periodicity in electron density in phase with the lattice distortion. Blue molybdenum bronzes, K0.3M0O3, show such features (see Section 4.9 for details). In two- or three-dimensional solids, however, one observes Fermi surface nesting due to the presence of parallel Fermi surface planes perturbed by periodic lattice distortions. Certain molybdenum bronzes exhibit this behaviour. 

Second, there is a line of charge-ordering in the T -p plane, where the charge-charge correlation function begins to oscillate. This line, as established from GDH theory, passes close to the critical point and may generate a virtual tricritical state. A charge-density wave scenario also arises from r-dependent cavity interactions. 

Last, it is well known that the ground state of the EPH model shows a Bond Order Wave if U > 2V and a Charge Density Wave in the other case [43]. In figure (10), we show the relative error of the RVA results compared to the DMRG ones for several choices of Coulombic parameters in function of the dimerization parameter A, in the two different regimes. Once again, the results show clearly that our ansatz is better when A increases. Moreover, its behaviour seems different in the two sides of the... 

The onset of electron-phonon interaction in the superconducting state is unusual in term of conventional electron-phonon interaction where one would expect that the phonon contribution is weakly dependent on the temperature [19], and increase at high T. Indeed, based on this naive expectation, this type of unconventional T dependence has been often used to rule out phonons. Here, however, we see clearly that this reasoning is not justified. Moreover, this type of unconventional enhancement of the electron phonon interaction below a characteristic temperature scale is actually expected for other systems such as spin-Peierls systems or charge density wave (CDW) systems. Thus, our results put an important constraint on the nature of the electron phonon interaction in these systems. 

As far as the continuous symmetry breaking is concerned, the Goldstone theorem states [4] that this will generate hydrodynamic modes, that is, gapless excitations. The order parameter is multicomponent (n > 1) a vector i for magnetism breaking the rotational symmetry, a complex variable i j = ip e/e for charge-density waves and for superconductivity which... 

---