Charge-density wave surface

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. 

Even if one assumes that the water near a surface has the same structure as it does in bulk, the oscillations of the short-range interactions between surfaces could be explained by a nonlocal dielectric constant for water.24 This model assumes that the dielectric displacement field (D = epE 4- P) at a position r not only depends on the local electric field [D(r) = r(r)E(r), but also depends on the electric field in the whole space D(r) = jr(r,r )E(r )dr. In this model, the oscillations of the interactions are due to charge overscreening25 and are analogous to the charge density waves in plasmas.24... 

It is also remarkable to point out that superconductivity has also been discovered in a family of charge-transfer compounds based on the molecule M(dmit)2, with M = Ni, Pd with Tc -1.6 K under 7 kbar [12] (Fig. 23). In this interesting series, structural and NMR studies support the picture of a one-dimensional Fermi surface, and the ground state competing with superconductivity is a charge density wave modulation driven by the Ni(dmit)2 stacks [85]. 

Different superlattices with -v/S X /3 periodicity have been imaged. This periodicity has been related to rotation of graphite lattice [17]. These superlattices can be produced by either a multiple tip effect [17b] or electronic perturbations caused by adsorbed molecules [17c]. A hexagonal superlattice with a 4.4 nm periodicity, rotated 30° with respect to the HOPG lattice, and 0.38 nm corrugation has also been reported [17a]. This superlattice was also attributed to rotation of the surface layer of graphite. As this type of superstructures is most frequendy observed for thin layers of material, they have been associated with charge density waves [14, 18]. 

The Au(lll) face, which is the closest packed fee structure, is known to have the lowest surface energy among all possible fee crystal faces. The clean Au( 111) face surface was first approximated to be a /3 X >/3.R30° unit cell. A model with a uniaxially contracted top hexagonal layer was proposed and a charge-density-wave (CDW) structure was also proposed as an explanation of the LEED observations. ... 

A fourth possibility was suggested by Tosatti and Anderson [140], the basis of which was that reconstructions derive from an electronic instability of the ideal surface, leading either to a charge density wave plus lattice distortions (a kind of Jahn—Teller effect) or possibly to a surface density wave. 

The modification of the electronic distribution through the charge density wave leads in turn to a softening of this phonon mode and thereby to the reconstruction of the surface. Thus, the forces which lead to the displacement of the atoms into the stable c 2 x 2) structure by the nominal transition temperature begin to be mobilized well above the transition temperature. 

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