Linear Conductors Research Articles

Finite element solution of 3-D eddy current flow in magnetically linear conductors at power frequencies

For eddy current flow problems in which the conductors have a constant permeability it has been found convenient to use scalar potentials outside the eddy region and vectors inside The vectors E and H have each been tried and a manner of coupling the different field quantities together in a way which is compatible with the finite element solution technique is discussed. The method has been tested in 2-D, quasi 3-D and 3-D.

Interchain coupling in linear conductors

The authors study the model of a quasi-one-dimensional metal in which the interaction of conduction electrons with intra-molecular modes and three-dimensional acoustic phonons generates two energy scales: the gap in the electron spectrum Delta and the temperature of the structural transition Tc. Tc proves to be the parameter determining the main properties of the system. An expansion in powers of the lattice deformation shows that the mean-field theory has no region of applicability in the system under study. Below the structural transition point there appears an optically active Frolich mode. In the case of compounds with two oppositely charged chains the frequency of this mode turns out to be of the order Tc. One further low-frequency optically active mode is found in the system under study. It corresponds to electron density excitations and has a gap approximately Tc. In the model considered, unlike the Peierls model, there is no adiabatic parameter and both modes result in the dielectric constant epsilon approximately omega 02/Tc2, where omega 0 is the plasma frequency.

Anomalous optical response with variation in band filling in linear chain conductors

We report the polarized infrared reflectance of ( N -methylphenazinium) x (phenazine) 1-x(tetracyanoquinodimethanide), (NMP) x(Phen) 1-x(TCNQ) for 0.5≤ x≤1.0. We demonstrate that the “Drude edge” in TCNQ salts is related to the conduction electron charge density. An anomalous rapid red shift of the plasma frequency, observed for x ∼ 2 3 , may signal the emptying of the conduction electrons from half of the chains and/or a crossover from small U/W (coulomb repulsion/bandwidth) to large U/W behavior.

The charge density wave and the impurity in a linear conductor

Two kinds of functions of the impurity are studied for the charge density wave in a linear conductor. It is pointed out that the impurity-induced Friedel oscillation of electron density as well as the symmetry breaking effect of impurity govern the process of the onset and the pinning of the charge density wave.

195Pt-NMR evidence of a low lying non-linear excitation in the linear conductor K 2Pt(CN) 4Br 0.33.2H 2O

195Pt-NMR line shift, linewidth and relaxational behavior in the temperature range 4–120 K indicate a solitary excitation with an activation energy of about E 0 k = 295 K .

Theory of the skin effect of an electrically conducting spherical shell

Since the periodic change of the polarity of the magnetic field of a considerable number of celestial bodies is well established, the need for a theoretical treatment of this problem becomes obvious. There exists a rather voluminous literature on the skin effect in configurations of linear conductors, but practically no literature on spheres or spherical shells. First steps were taken byFanselau andLucke [1]. Here in this paper the general theory of the problem is developed. In succeeding papers the theory will be applied to two limiting cases, namely small and large bodies.

Response behavior of the two-chain Fermi gas

We consider a model of TTF-TCNQ (tetrahiafulvalenium-tetracyanoquinodimethanide) and similar charge-transfer linear conductors in which there are two chains. The electrons on the acceptor (TCNQ) chains have a usual metallic band, but the electrons on the donor (TTF) chains have an inverted or hole band. The electrons on each chain interact via the forward and backward scattering ${g}_{2}$ and ${g}_{1}$ processes, respectively. Electrons on different chains interact via the analogous processes ${W}_{2}$ and ${W}_{1}$. The model is also applicable to two metallic chains, with the signs of ${W}_{1}$ and ${W}_{2}$ reversed. Using the techniques of Luther and Emery and of Chui and Lee we show that the problem may be mapped onto a similar problem of three coupled classical two-dimensional Coulomb gases. In addition to gaps in the spin degrees of freedom that were present in the single-chain problem, we find that the antisymmetric form of the resultant charge degrees of freedom may have a gap. We then investigate the predominant two-, four-, six-, and eight-particle response functions and calculate their temperature dependence. In addition to the four divergent two-particle response functions present in the single chain, there is a region for weak interaction strengths in which the $2{k}_{F}$ interchain Cooper pairing response is the most divergent as $T\ensuremath{\rightarrow}0$. The excitonic insulator response may also be important at high temperatures. For the single chain, either the $4{k}_{F}$ response or a four-particle $q=0$ response is the most divergent for strong coupling and repulsive ${g}_{1}$, depending upon the sign of ${g}_{2}\ensuremath{-}\frac{1}{2}{g}_{1}$. For the two-chain system, the most divergent response as $T\ensuremath{\rightarrow}0$ for strongly attractive interactions (${g}_{1}$ and ${g}_{2}$) is the response to the formation of excitonic molecules or exciton pairs. For strong coupling and repulsive ${g}_{1}$ either $8{k}_{F}$ or octet responses may be observable. We discuss these results in conjunction with our previous renormalization-group treatment, which indicates that for certain values of ${g}_{2}$, ${W}_{2}$, and ${W}_{1}$ the line ${g}_{1}=0$ may be crossed. We use these results to interpret the recent x-ray data on TTF-TCNQ showing a crossover from $4{k}_{F}$ to $2{k}_{F}$ behavior above the crossover from one-dimensional to three-dimensional behavior.

Dynamical aspects of fluctuations in linear conductors

A model is presented which describes the effect of a finite correlation length of the Peierls distortion on optical properties, width and position of the Raman line from the amplitude mode, and Knight shift in linear conductors. A canonical transformation to amplitude and phase variables is used which generalizes the linear transformation of Lee, Rice and Anderson. The non-linear effects are shown to be essential for the interpretation of experimental data in KCP.

Strain-Coupled Charge-Density Waves in a Linear Conductor

X-ray studies of tetrathiafulvalenium-thiocyanate [TTF${(\mathrm{SCN})}_{0.588}$] show a Peierls instability with one-dimensional charge-density waves near 300 K followed by three-dimensional order at ${T}_{c}=180$ K. Below ${T}_{c}$, an interchain competition between both elastic forces and Coulomb interactions drives a temperature-dependent monoclinic strain. A Landau theory including both charge-density and strain order parameters describes the relative TTF chain slip and the superlattice phase variation.

Infrared and Raman activities of organic linear conductors

Phonon spectra of organic linear conductors in the Peierls (semiconducting)phase are considered. It is shown that infrared absorption and Raman scattering can give information on the electron-phonon couplings of the various phonons. A rather sharp structure is predicted also above the electronic gap which is due to interference effects.

Correlation length of the Peierls distortion

A Peierls distortion incommensurate with the lattice constant is considered in the Frohlich model of a linear conductor. A prediction for the correlation length of the distortion is obtained using a Ginzburg-Landau expansion of the free energy for temperatures well belowT p , the mean field Peierls transition temperature. The correlation length is found to be strongly increasing at aboutT p /4.

Correlation length in incommensurate linear conductors

The free energy of an incommensurate Peierls system with the gap slightly off the Fermi surface is reinvestigated. In Ginzburg-Landau approximation we then obtain a correlation length for the Peierls distortion in KCP in accord with experimental limits.

Infrared absorption of incommensurate linear conductors

A quantitative theory is given for the dominant absorption maximum in the infrared observed in incommensurate one-dimensional conductors. This is achieved by reinvestigation and extension to finite temperatures of Sadovskii's (1974) highly renormalized theory of electrons interacting with the soft phonon of twice the Fermi wavevector. Numerical results for Re sigma ( omega ,T) are evaluated and compared with experimental results of KCP and TTF-TCNQ. Quantitative agreement is found for absolute magnitude and temperature shift of the infrared absorption peak. The asymptotic frequency behaviour of Re sigma ( omega ) is also investigated implying a free-particle relaxation time linearly increasing with frequency, again in accordance with measurements.

Role of interchain coupling in linear conductors

Renormalization-group methods are applied to a set of coupled linear chains in a model in which direct hopping between chains is excluded. Attention is focused on models in which intrachain interactions are repulsive. It is shown first for two chains and then for $N$ chains that a repulsive $\ensuremath{\delta}$-function intrachain interaction scales with decreasing temperature to the attractive fixed point. In the $N$-chain model this attractive fixed point is characterized by a charge-density wave whose phase is coherent between chains. A variety of response functions, spin and charge density wave at wave vector $2{k}_{F}$ (${k}_{F}$ is the Fermi wave vector), and excitonic response functions are calculated numerically. We also evaluate the uniform magnetic susceptibility and the charge-density-wave response at $4{k}_{F}$. A comparison is made to the behavior of TTF-TCNQ (tetrathiafulvalene-tetracyanoquinodimethane) at temperatures above 60 K. It is possible to qualitatively explain most of the behavior of this compound by assuming strong repulsion between electrons. A simple physical discussion of the strong-repulsion limit is given.

Diagrammatic calculation of infrared properties of linear conductors

The infrared properties of linear conductors are calculated using high order renormalization of electron properties by condensed and fluctuating phonons of around twice the Fermi wave vector. Results are given for the incommensurate and the half filled band case.

Dynamics of amplitude and phase mode and infrared absorption of linear conductors

The dynamics of the Amplitude and Phase mode in the incommensurate case is reduced to the dynamics of a diatomic molecule. Using this Hamiltonian, σ(ω) is given as a canonical average for a Penn model with fluctuating gap.

Ginzburg-Landau theory of phase transitions in pseudo-one-dimensional systems

Abstract The static and dynamic properties of weakly coupled chains undergoing a phase transition are reviewed. The discussion is based on the functional generalization of the Ginzburg-Landau theory, including systems with real and complex order parameter. Various predictions of the theory, such as static correlations, renormalized phonon frequencies and a central resonance in the dynamic form factor near structural instabilities are discussed and compared with recent experiments on linear conductors that undergo a Peierls transition. New results are obtained for the thermodynamic anomalies near the onset of 3-d ordering and for the dynamic form factor of systems with an incommensurate Peierls distortion.

Theory of infrared absorption of linear conductors

The infrared absorption is evaluated theoretically for a one-dimensional conductor with half-filled tight-binding band by incorporating the band symmetry into Sadovskii's highly renormalized theory (1974) of electrons interacting with the soft phonon of twice the Fermi wavevector. Closed analytic expressions are given for Re sigma ( omega ) for finite bandwidth and finite temperature. The final result is evaluated numerically. Re sigma ( omega ) is derived within a conserving approximation from a one-electron Green function qualitatively different from that found by Sadovskii. The spectral function, density of states and breakdown of the quasi-particle picture are also discussed.

Organic Linear Conductors as Systems for the Study of Electron-Phonon Interactions in the Organic Solid State

A model calculation shows that each phonon band which couples to the electron density in an organic linear-chain semiconductor effectively develops an infrared activity along the chain axis. The origin of the effect lies in phase oscillations of additional charge-density-wave distortions which inevitably arise in the presence of electron-phonon interactions. This suggests that organic linear conductors may constitute unique systems for the study of electron-phonon interactions in the organic solid state.

Organic Linear Conductors as Systems for the Study of Electron-Phonon Interactions in the Organic Solid State

A model calculation shows that each phonon band which couples to the electron density in an organic linear-chain semiconductor effectively develops an infrared activity along the chain axis. The origin of the effect lies in phase oscillations of additional charge-density-wave distortions which inevitably arise in the presence of electron-phonon interactions. This suggests that organic linear conductors may constitute unique systems for the study of electron-phonon interactions in the organic solid state.