Quasi-one-dimensional systems

In this contribution, we discussed effects of disorder on the electronic properties of quasi-one-dimensional Peierls systems, like the conjugated polymer fraus-poly-acetylene. Since polymer materials generally are rather disordered and the effect of disorder on any quasi-one-dimensional system is strong, a proper description of these materials requires consideration of such effects. 

This model, which is sometimes referred to as the Fluctuating Gap Model (FGM) [42], has been used to study various aspects of quasi-one-dimensional systems. Examples arc the thermodynamic properties of quasi-one-dimensional organic compounds (NMP-TCNQ, TTF-TCNQ) [271, the effect of disorder on the Peierls transition [43, 44, and the effect of quantum lattice fluctuations on the optical spectrum of Peierls materials [41, 45, 46]. 

S.L. Dexheimer, in Coherent Vibrational Dynamics of Exciton Self-Trapping in Quasi-One-Dimensional Systems, ed. by S. De Silvestri, G. Cerullo, G. Lanzani. Coherent Vibrational Dynamics (CRC, Boca Raton, 2007), p. 223... 

In (quasi-)one-dimensional systems [22] also SDWs can be found, but in contrast to CDWs they arise due to electron-electron and not to electron-phonon interaction. A SDW can be considered to consist of two CDWs, one for spin-up and another for spin-down electrons (see, e.g., Fig. 5 in [22]). Therefore the spatial modulation of SDWs is characterized by a wave vector Q = 2kp, as for CDWs. 

From this expression one finds that f(T) approaches 1 for T —> 0 (by integration) and /(T) 2(1 - T/TCMF) - Z 2 for T -> TCMF. TCMF denotes the mean-field transition temperature. For quasi one-dimensional systems p1 has an additional factor C-2 (the inverse area perpendicular to the chain). 

In the other case - with weak screening - Vc(k) pc Vr°(fc) shows the dispersion given in (12) and in general, the details of the fc-dependence are not only up to the transverse extension ( of the quasi one-dimensional system under consideration but also to the screening length [3, 11, 46, 34]. 

Most organic conductors behave as quasi-one-dimensional systems, at least at high temperatures. It is generally accepted that due to the narrow band-widths, the strongest interactions are the electron-electron Coulomb interaction, U for two electrons on the same site, and V for electrons in nearest-neighbor sites, in agreement with the extended Hubbard Hamiltonian, which is usually taken as a good approximation. 

Using a scaling theory of localization, adapted for anisotropic materials, Apel and Rice [76] find that the condition Le, c does correspond to the Anderson metal-insulator transition of a quasi-one-dimensional system. 

At birth, the molecular metal was the one-dimensional metal. KCP and TTF-TCNQ are typical examples. The one-dimensional metal, however, is not a metal in the low temperature region due to the instability of the planar Fermi surface. Of course, this instability has provided rich physics [3], but is not favorable to the superconductivity. Therefore, chemists made efforts to increase the dimensionality of the electronic structure by the chemical modification with great success. The first organic superconducting system, the Bechgaard salt, is a quasi-one-dimensional system [4]. BEDT-TTF salts, the second-generation organic superconductors, have typical two-dimensional Fermi surfaces [5]. Three-dimensional Fermi surface has been found in the DCNQI-Cu salt [6]. 

The Hamiltonian of intramolecular collective vibrations of the quasi-one-dimensional system of coupled C=C bonds can be written as... 

Hodak, M. and Girifalco, L.A. (2001). Quasi-one-dimensional system of molecules inside carbon nanotubes exact solution for the lattice gas model and its application to fuUerene-fiUed nanotubes. Phys. Rev. B, 64, 035407 1—9. 

One factor affecting the dielectric strength is the electronic structure of the polymer, and in particular its band gap. In quantum mechanics [29], each electron in a molecule can only occupy one of a discrete set of allowed energy levels. In solids, the overlaps between different repeating units of the material (for example, the repeat units in quasi-one-dimensional systems such as polymer chains [29-31]) cause these discrete energy levels to broaden into bands. The band gap is the energy difference between the top of the valence band and the bottom of the conduction band. (In terms which are equivalent but more familiar to chemists, the band gap is... 

ON THE CHARGE DISTRIBUTION AND THE LATTICE DISTORTION OF QUASI ONE-DIMENSIONAL SYSTEMS... 

In the quasi one-dimensional systems these fluctuations are suppressed to some extent by the interchain hopping of electrons (see e.g. and this makes the transitions possible. However... 

Therefore, with respect to the lattice dynamics (SN)x can be regarded either as a quasi one-dimensional system or as a layer-type crystal. 

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