Charge-density wave systems

M. Naito, H. Nishihara and T. Butz, in Nuclear Spectroscopy on Charge Density Wave Systems , ed. T. Butz, Kluwer Academic Publishers, 1992, p. 35. 

In what follows we will discuss systems with internal surfaces, ordered surfaces, topological transformations, and dynamical scaling. In Section II we shall show specific examples of mesoscopic systems with special attention devoted to the surfaces in the system—that is, periodic surfaces in surfactant systems, periodic surfaces in diblock copolymers, bicontinuous disordered interfaces in spinodally decomposing blends, ordered charge density wave patterns in electron liquids, and dissipative structures in reaction-diffusion systems. In Section III we will present the detailed theory of morphological measures the Euler characteristic, the Gaussian and mean curvatures, and so on. In fact, Sections II and III can be read independently because Section II shows specific models while Section III is devoted to the numerical and analytical computations of the surface characteristics. In a sense, Section III is robust that is, the methods presented in Section III apply to a variety of systems, not only the systems shown as examples in Section II. Brief conclusions are presented in Section IV. 

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. 

While there is thus much spirited theoretical discussion, there is no direct experimental evidence for such effects, except that this scenario might be a rationale for the observed [108, 109] sharp crossover. Balevicius and Fuess [306] have recently attributed some puzzling visual observations of salt precipitation and turbidity phenomena in ternary aqueous systems to the presence of charge-density waves, but this seems to be pure speculation. 

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. 

One can describe this as the presence of a charge-density wave in the electronic system. In this case the charge-density wave follows from displacement of the atoms. One can ask the question whether in a rigid lattice the electron system itself can distort spontaneously to lower its symmetry, producing an effect that would then attempt to force the nuclei to follow suit. The driving force in this case would not be the movement of the atoms as in the Peierls instability but rather the inherent instability of the electron system itself. The answer to this question is yes. The study of these types of instabilities and associated instabilities in the spin system of the electrons has become an important part of the physics of limited dimensionality. 

To emphasize the importance of structural studies at LT or HP, let us take the example of TTF-TCNQ. This prototype charge density wave (CDW) system undergoes at ambient pressure a succession of three structural and electronic phase transitions, from a high-temperature metallic phase down to a low-temperature insulator phase. There has been a considerable debate about the mechanism of these transitions, and many distortional modes have been proposed to account for the physical properties of this material (e.g., rigid molecule displacement as translations [73,74] or librations [75,76] or even internal deformations of the molecules [77,78]. Indeed, an experi-... 

One may be tempted to discuss the system in terms of the interface a plane separating the two phases. This is, however, an ill-defined quantity, since it is not possible to define exactly the boundary of a phase, even a metal, on the subatomic level. In other words, one does not know exactly "where the metal ends". Is it the plane going through the center of the outermost layer of atoms, is it one atomic radius farther out, or is it even farther, where the charge density wave of the free electrons has decayed to essentially zero Fortunately, we do not need to know the position of this plane for most purposes when we discuss the properties of the interphase, as defined earlier. 

Peierls showed that a different, energetic instability of a ID system, driven by electron-phonon interactions, creates a non-uniform electron distribution, and leads to a stractural distortion and a (normally second-order) phase transition, at the Peierls temperature Tp [158]. Below Tp either a dimerization into two sets of unequal interparticle distances d and d" (such that d -i- d" = 2d), or some other structural distortion must occur. The electronic energy of the metallic chain is lowered by the formation of a charge-density wave (CDW) of amplitude p(x) ... 

---