Model Of Polyacetylene Research Articles

Charge fractionalization and relics of supersymmetry

A connection between fermion zero modes and supersymmetry is discussed for the N = 2, ( ψψ ) 2 theory which is regarded as a continuum model of polyacetylene. It is shown that fermion zero modes in the ( ψψ ) 2 theory can be constructed by solving the first-order differential equations of the supersymmetric sine-Gordon theory. Supersymmetry generators are also constructed in this model.

Time-domain analysis of EPR measurements of polyacetylene and soliton diffusion

A novel analysis of EPR measurements on polyacetylene is demonstrated by the analysis of the conventional line shape in time domain. Quantitative results of the hyperfine-coupling constant, the on-chain diffusion rate, and the off-chain hopping rate were extracted by nonlinear curve fitting to the time-domain signals, and they are consistent with the soliton model of polyacetylene.

Two-Polaron Solution and Its Stability in the Continuum Model of Polyacetylene

Explicit two-polaron solution is found in the continuum model of trans -polyacetylene. The solution is explored to examine stability of two polarons. It is found that two free polarons attract each other with a long range force until they form a single polaron with two carriers therein, which then dissociates into charged kink-antikink pair owing to a short range repulsion. Thus the reaction mechanism of two polarons into two charged kinks is clarified.

Lattice dynamics of polyacetylene as a one-dimensional system: Part I. The case of the trans perfect polymer

In this paper the lattice dynamics of trans-polyacetylene as a perfect one-dimensional crystal is treated. Dispersion curves, density of states and vibrational displacements are calculated. The results of the calculations are used to propose a vibrational assignment for (CH) x , (CD) x and ( 13CH) x . Calculations have been made with a quadratic simplified valence force field (SVFF). The relationship between SVFF and the electron-phonon coupling model for polyacetylene, generally adopted in the literature, is discussed. Comparison with the calculations of other authors is made.

SOLITON DIFFUSION IN POLYACETYLENE

Making use of the Su, Schrieffer and Heeger (SSH) model for polyacetylene, we study theoretically the soliton difusion in pristine trans-(CH)x. The soliton in the SSH model couples linearly both optical and acoustic phonons. Since the coupling to the optical phonon is stronger, the optical phonon dominates the soliton diffusion in high temperature (T>400K). However, below the room temperature the acoustic phonon dominates the soliton diffusion. For temperature T>To≡2mc2, where m is the soliton mass and c is the acoustic phonon velocity, the soliton relaxation is determined by the single phonon process. This process results in the diffusion constant DαT1/2(2-d), where d is the dimensionality of the acoustic phonon. For T

Optical absorption from polarons in a model of polyacetylene

We present a theoretical calculation, within a continuum electron-phonon-coupled model, of the optical absorption due to polarons in polyacetylene [${(\mathrm{CH})}_{x}$]. Our results can be applied to both trans- and cis-${(\mathrm{CH})}_{x}$, as well as potentially to other polymers (polypyroles, polyparaphenylenes) in which polarons are present. We establish that the essential signature of polaron absorption is the existence of three separate absorption peaks in the gap with qualitatively different features. For trans-${(\mathrm{CH})}_{x}$, we compare and contrast this structure with that from the kink solitons, which are expected to dominate the optical absorption at all but the lowest doping levels. For cis-${(\mathrm{CH})}_{x}$ and related polymers, we discuss polaron (and multipolaron) absorption and the relation of polarons to possible excitons in these materials. Finally, we evaluate briefly the existing experimental situation regarding optical absorption in polyacetylene and indicate possible future experiments that could confirm the existence of polarons in ${(\mathrm{CH})}_{x}$ and similar polymers.

Impurity states in dopedtrans-polyacetylene

We assess the importance of the impurity states of a doped trans-polyacetylene chain. The impurity potential is modeled by a point charge that is located off the chain and is screened phenomenologically. The common assumption that the dopant levels of a dimerized chain closely approximate the hydrogenic levels of a point charge is invalid if the impurity is not on the chain, even if the dopant is screened by the bulk dielectric constant. Additional nonhydrogenic states occur well into the gap. The formation energies for charged kink and polaron lattice distortions are found by solving the Su-Schrieffer-Heeger model for polyacetylene with an impurity added. The impurity states severely alter the structure and states of kink and polaron distortions. Moreover, the modifications depend sensitively on the form of the dopant potential. For the dopant screened isotropically by the bulk dielectric constant, the kink distortion has gap states inconsistent with the observed midgap optical absorption. In contrast, the polaron distortion is both stable and predicts a consistent optical threshold. The nature of doping polyacetylene will remain unclear until a realistic model for the dopant and its interaction with polyacetylene has been developed.

Hubbard versus Peierls and the Su-Schrieffer-Heeger model of polyacetylene

We have considered the competing effects of the electron-electron Hubbard repulsion and the electron-phonon interaction on the properties of a one-dimensional electron gas both within perturbation theory and by exact numerical solution of finite-length rings. We find that the perturbation-theory results provide a qualitatively correct description of the system over a considerable range of parameters. Among the more interesting conclusions we draw is that, so long as the repulsion $U$ is less than a critical value which depends on the strength of the electron-phonon interaction, the predictions of the Su-Schrieffer-Heeger model of polyacetylene are not profoundly affected by the electron-electron repulsion. A small splitting between the charged and neutral soliton-creation energies and minor shape changes are the principle effects.

Exactly soluble peierls models

Exactly soluble models for electrons on a deformable discrete chain are found. They include typical continuous Peierls models as special limits. The chain structure, electronic spectrum and thermodynamic functions in the ground state are found. The region of a nearly half filled band corresponding to the polyacetylene model is described in detail.

The importance of impurity states in doped transpolyacetylene

The authors assess the importance of the impurity states of a doped trans-polyacetylene chain. The impurity potential is modelled by a point charge that is located off the chain and screened phenomenologically with the bulk dielectric constant. The common assumption that the impurity levels of a dimerised chain closely approximate the hydrogenic levels of a point charge impurity in invalid when the impurity is not on the chain. Additional nonhydrogenic states occur. One of the new states is much deeper in the gap. The formation energies for charged soliton and charged polaron lattice distortions are found by solving the Su-Schrieffer-Haeger model for polyacetylene with an impurity added. The impurity states severely modify the structure of the soliton distortion. The charged polaron distortion, not the charged soliton distortion, is the most stable distortion that can be formed during doping with gap states consistent with the observed mid-gap absorption.

Boundary conditions and optical absorption in the soliton model of polyacetylene

In the present paper the boundary conditions and the optical absorption are studied for both the discrete and continuum models of solitions in polyacetylene. The topological property of the soliton is incorporated appropriately to derive the correct boundary conditions for the electronic wave functions which are essential for a proper calculation of optical absorption and other properties of the system. A general sum rule for the absorption coefficient is derived for the continuum model which is exactly satisfied by the result of the present calculation. The errors in the previous calculations are indicated. Finally, the theoretical results are compared with the experimental data.

Optical conductivity of solitons in polyacetylene

The soliton lattice solution of the continuum model for polyacetylene is used to derive the frequency dependent conductivity of charged solitons. The limit of low soliton density is explicitly evaluated and shown to be free of singularities. The conductivity sum rule is proven for the model Hamiltonian, and is shown to be satisfied by the explicit solution. Implications for polyacetylene and for TTF-TCNQ are discussed.

Real Time Dynamics in Polyacetylene

Abstract Dynamical solutios to a one-dimensional coupled electron-phonon model of polyacetylene are explored numerically. The results indicate that interesting objects in polyacetylene such as neutral spincarrying solitons, charged spinles solitons, polarons and breathers can be dynamically generated by single electron and electron pair tunneling, pgotoabsorption, and chain breaking

Electron Hopping Conduction in the Soliton Model of Polyacetylene

It is shown that at low temperatures a novel conduction mechanism, phonon assisted hopping between soliton bound states (intersoliton hopping), may be the dominant conduction process in lightly dop...

Electron Hopping Conduction in the Soliton Model of Polyacetylene

It is shown that at low temperatures a novel conduction mechanism, phonon assisted hopping between soliton bound states (intersoliton hopping), may be the dominant conduction process in lightly dop...

Two-soliton interaction energy and the soliton lattice in polyacetylene

Making use of a variational solution $\ensuremath{\Delta}(x)$ the dimerization pattern, we calculate the interaction energy of two solitons within the Su, Shrieffer, and Heeger model for polyacetylene. It is found that two solitons attract each other in general except for the case of two solitons having the same charge and the case of the spin triplet pair of neutral solitons. We have also studied the electronic structure of a regular array of solitons with the same charge.

Soliton dynamics in polyacetylene

The equations of motion of the coupled electron-phonon system are integrated in real time for the model of polyacetylene recently proposed. To illustrate the physical behavior of this nonlinear system we consider the time evolution starting from three physically relevant configurations: (i) end generated soliton, (ii) electron-hole pair generation of a charged soliton-antisoliton pair, and (iii) the dressing of an injected electron. The calculations show that the system relaxes within a time of order 10(-13) sec, converting excited electron-hole pairs into soliton-antisoliton pairs.