Charge density wave condensations

Maki, K. 1977. Creation of soliton pairs by electric fields in charge-density— wave condensates. Phys Rev Lett 39 46. 

Some needle-shaped crystals of a -TTF[Pd(dmit)2]2 [lc,ld,27] are also isostructural with TTF[Ni(dmit)2]2-This phase also undergoes a metal-to-insulator transition at around 220 K. However, this transition is completely reversible and shows no hysteresis [27]. The effect of high pressure is the suppression of this metal-to-insulator transition. The superconducting transition is observed at 5.93 K and 24 kbar [Id]. A gradual localization of the carriers is observed at low pressure, which can be related to a charge density wave condensation evidenced by X-ray diffuse scattering experiments [23]. a -TTF[Pd(dmit)2]2 is the first example in which competition between CDW and superconductivity is observed. 

In the following we use a minimal model for the low energy, long wave length excitations of the condensed charge density wave. Since fluctuations in the amplitude Z are suppressed, because they are massive, we take only fluctuations of the phase cp (cf. eq. 2) into account. Clearly, such an approach breaks down sufficiently close to the mean-field transition temperature TCMF. Neglecting fluctuations in Z, the Hamiltonian for our model is given by... 

Condensed-matter physics (Josephson junction, charge-density waves) Mechanics (Overdamped pendulum driven by a constant torque)... 

The collective behavior of condensed modulated structures like charge or spin density waves (CDWs/SDWs) [23, 22, 4], flux line lattices [2, 36] and Wigner crystals [4] in random environments has been the subject of detailed investigations since the early 1970s. These were motivated by the drastic influence... 

Although the existence of charged particles in the deton waves of solid expls has been known for some time, it was Lewis and then Bone et al who indirectly demonstrated the existance of electrons as well as positive ions in condensed and gaseous deton flames. However, it was not until 1956 that measurements of electron densities in the detonation waves of solids were carried out by Cook et al (Ref 6). They found free-electron densities in excess of 10 7/cc in the de ton reaction zone dropping slharply outside the reaction zone (Ref pl44)... 

There are many other types of solution data that support the half-wave reduction potential and charge transfer complex data. These include the measurement of cell potentials or equilibrium constants for electron transfer reactions. Another important condensed phase measurement involving a negative ion is the determination of electron spin resonance spectra. In these studies the existence of a stable molecular anion is established and the spin densities can be measured [79]. The condensed phase measurements support the electron affinities in the gas phase and extend the measurements to lower valence-state electron affinities. 

The quantity/ is called the condensed Fukui function.It has a single value for each atom, k, in the molecule, and is not otherwise a function of position. The qkS are net charges on the atoms. In the last equation 4 is simply the square of the atom coefficient in the HOMO. It is also the frontier orbital density in FMO theory. It is the easiest to calculate, since we only need the wave function for the HOMO, which can often be found, at least roughly, from HMO theory. 

From a conceptual point of view, it appears that polymer quantum chemistry is an ideal field for cooperation between condensed matter physicists and molecular quantum chemists. There exists a common interpretation in the discussions concerning orbital energies, orbital symmetry, and gross charges by chemists and solid-state physicists. These physicists use terms less familiar to the chemist, such as first Brillouin zone, dependence of wave function with respect to wave vector k (the one-electron wave function is called an orbital by the chemist), Fermi surfaces, Fermi contours, and density of states (DOS). 

When the partial charges included in a force field that does not include the polarizabihty are adjusted in order to reproduce the condensed phase properties, they are usually not efficient for modelling properties of the dimer or small clusters. To build accurate electrostatic models, several groups have proposed methods to obtain distributed multipoles from knowledge of the electronic wave fimction, the electron density or the electrostatic potential around a molecule [1-8]. These distributed multipole models should then be used in a force field with a polarizability model. 

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