Model Of Polyacetylene Research Articles

Phase Transition in the Peierls Model for Polyacetylene

We consider the Peierls model for closed polyactetylene chains with an even number of carbon atoms as well as infinite chains, in the presence of temperature. We prove the existence of a critical temperature below which the chain is dimerized and above which it is 1-periodic. The chain behaves like an insulator below the critical temperature and like a metal above it. We characterize the critical temperature in the thermodynamic limit model and prove that it is exponentially small in the rigidity of the chain. We study the phase transition around this critical temperature.

Understanding Topological Insulators in Real Space.

A real space understanding of the Su–Schrieffer–Heeger model of polyacetylene is introduced thanks to delocalization indices defined within the quantum theory of atoms in molecules. This approach enables to go beyond the analysis of electron localization usually enabled by topological insulator indices—such as IPR—enabling to differentiate between trivial and topological insulator phases. The approach is based on analyzing the electron delocalization between second neighbors, thus highlighting the relevance of the sublattices induced by chiral symmetry. Moreover, the second neighbor delocalization index, , also enables to identify the presence of chirality and when it is broken by doping or by eliminating atom pairs (as in the case of odd number of atoms chains). Hints to identify bulk behavior thanks to are also provided. Overall, we present a very simple, orbital invariant visualization tool that should help the analysis of chirality (independently of the crystallinity of the system) as well as spreading the concepts of topological behavior thanks to its relationship with well-known chemical concepts.

Duality and domain wall dynamics in a twisted Kitaev chain

The Ising chain in transverse field is a paradigmatic model for a host of physical phenomena, including spontaneous symmetry breaking, topological defects, quantum criticality, and duality. Although the quasi-1D ferromagnet CoNb$_2$O$_6$ has been put forward as the best material example of the transverse field Ising model, it exhibits significant deviations from ideality. Through a combination of THz spectroscopy and theory, we show that CoNb$_2$O$_6$ in fact is well described by a different model with strong bond dependent interactions, which we dub the {\it twisted Kitaev chain}, as these interactions share a close resemblance to a one-dimensional version of the intensely studied honeycomb Kitaev model. In this model the ferromagnetic ground state of CoNb$_2$O$_6$ arises from the compromise between two distinct alternating axes rather than a single easy axis. Due to this frustration, even at zero applied field domain-wall excitations have quantum motion that is described by the celebrated Su-Schriefer-Heeger model of polyacetylene. This leads to rich behavior as a function of field. Despite the anomalous domain wall dynamics, close to a critical transverse field the twisted Kitaev chain enters a universal regime in the Ising universality class. This is reflected by the observation that the excitation gap in CoNb$_2$O$_6$ in the ferromagnetic regime closes at a rate precisely twice that of the paramagnet. This originates in the duality between domain walls and spin-flips and the topological conservation of domain wall parity. We measure this universal ratio `2' to high accuracy -- the first direct evidence for the Kramers-Wannier duality in nature.

Axionic band topology in inversion-symmetric Weyl-charge-density waves

In recent theoretical and experimental investigations, researchers have linked the low-energy field theory of a Weyl semimetal gapped with a charge-density wave (CDW) to high-energy theories with axion electrodynamics. However, it remains an open question whether a lattice regularization of the dynamical Weyl-CDW is in fact a single-particle axion insulator (AXI). In this Letter, we use analytic and numerical methods to study both lattice-commensurate and incommensurate minimal (magnetic) Weyl-CDW phases in the mean-field state. We observe that, as previously predicted from field theory, the two inversion- ($\mathcal{I}$-) symmetric Weyl-CDWs with $\phi = 0,\pi$ differ by a topological axion angle $\delta\theta_{\phi}=\pi$. However, we crucially discover that $neither$ of the minimal Weyl-CDW phases at $\phi=0,\pi$ is individually an AXI; they are instead quantum anomalous Hall (QAH) and "obstructed" QAH insulators that differ by a fractional translation in the modulated cell, analogous to the two phases of the Su-Schrieffer-Heeger model of polyacetylene. Using symmetry indicators of band topology and non-abelian Berry phase, we demonstrate that our results generalize to multi-band systems with only two Weyl fermions, establishing that minimal Weyl-CDWs unavoidably carry nontrivial Chern numbers that prevent the observation of a static magnetoelectric response. We discuss the experimental implications of our findings, and provide models and analysis generalizing our results to nonmagnetic Weyl- and Dirac-CDWs.

Subsonic and supersonic polarons in one-electron model of polyacetylene

Free-moving polarons are investigated in the framework of new one-electron model of conjugated polymers. It is shown that on a dimerized lattice there exist free (in the absence of an external force like an electric field) stationary polarons, both subsonic and supersonic. Subsonic free polarons are observed in the velocity range from 0 to the speed of sound. Supersonic free polarons are observed in a limited range of velocities. There is a range of forbidden velocities between subsonic and supersonic free polarons. An analytical expression for the free polaron shape at different velocities is derived and confirmed in molecular dynamics simulations. The dynamics of subsonic and supersonic polarons in an electric field is different. It is shown that the subsonic polaron motion is not stationary and the velocity oscillations are associated with the periodic emission of tensile impulses in front of the polaron, taking away the energy received from the electric field. The supersonic polaron motion is stationary and the energy gained from the electric field is permanently transformed into oscillations behind the polaron.

A Topological View on Optical and Phononic Fabry–Perot Microcavities through the Su–Schrieffer–Heeger Model

Advances in nanofabrication technologies have enabled the study of acoustic wave phenomena in the technologically relevant GHz–THz range. First steps towards applying concepts from topology in nanophononics were made with the proposal of a new topological acoustic resonator, based on the concept of band inversion. In topology, the Su–Schrieffer–Heeger (SSH) model is the paradigm that accounts for the topological properties of many one-dimensional structures. Both the classical Fabry–Perot resonator and the reported topological resonators are based on Distributed Bragg Reflectors (DBRs). A clear and detailed relation between the two systems, however, is still lacking. Here, we show how a parallelism between the standard DBR-based acoustic Fabry–Perot type cavity and the SSH model of polyacetylene can be established. We discuss the existence of surface modes in acoustic DBRs and interface modes in concatenated DBRs and show that these modes are equivalent to Fabry–Perot type cavity modes. Although it is not possible to assign topological invariants to both acoustic bands enclosing the considered minigap in the nanophononic Fabry–Perot case, the existence of the confined mode in a Fabry–Perot cavity can nevertheless be interpreted in terms of the symmetry inversion of the Bloch modes at the Brillouin zone edge.

Floquet topological transitions in a driven one-dimensional topological insulator

The Su--Schrieffer--Heeger model of polyacetylene is a paradigmatic Hamiltonian exhibiting nontrivial edge states. By using Floquet theory we study how the spectrum of this one-dimensional topological insulator is affected by a time-dependent potential. In particular, we provide evidence of the competition among different photon-assisted processes and the native topology of the unperturbed Hamiltonian to settle the resulting topology at different driving frequencies. While some regions of the quasienergy spectrum develop new gaps hosting Floquet edge states, the native gap can be dramatically reduced and the original edge states may be destroyed or replaced by new Floquet edge states. Our study is complemented by an analysis of the Zak phase applied to the Floquet bands. Besides serving as a simple example for understanding the physics of driven topological phases, our results could find a promising testing ground in cold-matter experiments.

Bond alternation in infinite periodic polyacetylene: Dynamical treatment of the anharmonic potential

The potential energy of the infinite periodic chain model of polyacetylene (pPA) is symmetric with two equivalent minima separated by the Peierls’ stabilization barrier. In this work it is shown how an energy scale and vibrational energy levels for this highly anharmonic Peierls’ degree of freedom can be estimated. Particular attention is given to the potential energy increase for large deformations. Two empirical methods and direct periodic boundary condition (PBC) density functional theory (DFT) calculations are in semi-quantitative agreement with each other. Each lead to the conclusion that pPA has a zero-point level that is above the Peierls’ barrier. The argument does not depend critically on the barrier height or the other parameters of the model or the computation method. It is concluded that pPA will not exhibit bond alternation since two stable structures are not possible due primarily to the stiffness of the underlying CC sigma bond system.

Chiral Topological Phases and Fractional Domain Wall Excitations in One-Dimensional Chains and Wires

According to the general classification of topological insulators, there exist one-dimensional chirally (sublattice) symmetric systems that can support any number of topological phases. We introduce a zigzag fermion chain with spin-orbit coupling in magnetic field and identify three distinct topological phases. Zero-mode excitations, localized at the phase boundaries, are fractionalized: two of the phase boundaries support ±e/2 charge states while one of the boundaries support ±e and neutral excitations. In addition, a finite chain exhibits ±e/2 edge states for two of the three phases. We explain how the studied system generalizes the Peierls-distorted polyacetylene model and discuss possible realizations in atomic chains and quantum spin Hall wires.

Nonempirical studies of the electronic properties of highly conducting polymers

We present ab initio calculations on the electronic structure of highly conducting polymers. A Hartree-Fock study of the lithium doping of all-trans polyacetylene demonstrates that the bond alternation, present in the undoped chain is dramatically reduced as the charge transfer from the lithium atom increases. At ˜0.1e transferred per CH unit, we predict equal bond lengths. The relationship of these results to the soliton model for polyacetylene is discussed. Nonempirical effective Hamiltonian calculations on undoped polyacetylene, polydiacetylene, poly (p-phenylene) and derivatives including poly (p-phenylene sulfide) are described. These calculations provide reliable bandwidths and ionization potentials. The ionization potential results are in good agreement with experimental estimates; the bandwidth results yield a satisfying qualitative correlation to the conductivities obtained on doping for the various systems considered.

Critical dopant concentration in polyacetylene and phase diagram from a continuous four-Fermi model

The Optimized Perturbation Theory (OPT) method, at finite temperature and finite chemical potential, is applied to the field theory model for polyacetylene. The critical dopant concentration in trans-polyacetylene is evaluated and compared with the available experimental data and with previous calculations. The results obtained within the OPT go beyond the standard mean field (or large-N) approximation (MFA) by explicitly including finite N effects. A critical analysis of the possible theoretical prescriptions to implement and interpret these corrections to the mean field results, given the available data, is given. For typical temperatures probed in the laboratory, our results show that the critical dopant concentration is only weakly affected by thermal effects.

Structural phases of coupled polyacetylene chains with impurities

AbstractThe study of quasi‐particles in conducting polymers is concentrated in single‐chain works. It is shown in the present study that interchain interactions can be determinant in the relative presence of solitons, polarons, or bipolarons in conjugated polymers. We consider a modified version of the SSH model for polyacetylene. The results show that the presence of different impurities, bonded to different chains sites, led to quite different relative chains configurations and phases related to bond alignment order, presence of quasi‐particles, and their respective charges. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Quantum chemical investigation of biexcitons in conjugated polymers

The formation of biexcitons in conjugated polymers is examined within the Pariser–Parr–Pople (PPP) model of polyacetylene. The calculations are done using a scattering formalism that provides a size-consistent description of excited states containing both single and double electron–hole pair excitations. The excited-state absorption spectrum from the 1 1Bu exciton state was calculated and examined for signatures of biexciton formation. Calculations were performed on polyenes with up to 9 unit cells, and on long chains using periodic boundary conditions. While polyenes with 7 to 31 unit cells exhibit states with some of the features expected for biexcitons, such states are not seen in the limit of long chains. This suggests that, within the two-band model considered here, exciton–exciton interactions are not of sufficient strength to lead to biexciton formation in the limit of long chains, and that their presence in shorter chains is due to confinement effects. In the long-chain limit, transitions are found to states consisting of overlapping electron–hole pairs, but these states have energies above that required to make two free excitons. These states may result from scattering resonances between excitons.

Intermediate neglect of differential overlap excited state calculations in periodic boundary conditions: The absorption spectrum of poly(para-phenylene vinylene)

Much of our current theoretical understanding of the electronic structure of conjugated polymers is based on two-band systems, such as the π-electron model of polyacetylene. But poly(para-phenylene vinylene) (PPV) and many other systems exhibit a number of bands, and this raises new and interesting questions that are beginning to be addressed. Such studies are complicated by the large number of model parameters, and the sensitivity of the predictions to the values used. While the intermediate neglect of differential overlap (INDO) method provides a systematic and tested approach for deriving these parameters from the chemical structure, previous tools could be applied only to oligomers, making it difficult to put the results in the context of other well-studied models. Here, we report INDO calculations on oligomers of PPV as well as long chains with periodic boundary conditions. The long-chain calculations are used to assign the spectral features to transitions between bands, and these assignments are transferred to oligomers by examining how the calculated oligomer spectra evolve with chain length. The effects of various electron–hole symmetry breaking mechanisms on the intensity of peak II (at 3.7 eV) relative to peak III (at 4.7 eV) in the optical absorption spectrum are examined. INDO theory on planar unsubstituted PPV breaks electron–hole symmetry due to inclusion of next-nearest neighbor transfer integrals, giving peak II about 4% of the intensity observed for peak III in the long-chain limit. Alkoxy substitution at the 2 and 5 positions of the phenyl ring is modeled using hydroxy groups (OH-PPV). (This approach is confirmed by replacing the hydroxy substituents with methoxy substituents.) For a planar OH-PPV structure, peak II has 8% of the intensity of peak III. AM1 calculations indicate that in OH-PPV, the vinylene rotates out of the plane of the phenyl rings by 20°, and this raises the intensity of peak II to 15% that of peak III. Finally, finite-chain effects cause oligomers of OH-PPV with between 4 and 8 phenylene units to have a peak II intensity that is 25% that of peak III. Oligomers exhibit additional transitions in the vicinity of peak II, but these have a strong dependence on the length of the oligomer and merge with the lowest-energy peak in the long-chain limit.

Electron fractionalization

A largely qualitative, and rather idiosyncratic discussion of electron fractionalization in condensed matter physics is presented, including some historical reflections and some speculations concerning future application of these ideas. Particular attention is paid to systems which exhibit spin–charge separation, i.e. the electron can decay into separate excitations which carry the electron spin and the electron charge; the soliton model of polyacetylene is treated as a paradigmatic example. This paper is based on a talk given at a symposium honoring A.J. Heeger, A.C. MacDiarmid, and H. Sirikawa, the winners of the year 2000 Nobel Prize in Chemistry.

Comment on “Density-matrix renormalization-group method for excited states”

In a Physical Review B paper Chandross and Hicks claim that an analysis of the density-density correlation function in the dimerised Hubbard model of polyacetylene indicates that the optical exciton is bound, and that a previous study by Boman and Bursill that concluded otherwise was incorrect due to numerical innacuracy. We show that the method used in our original paper was numerically sound and well established in the literature. We also show that, when the scaling with lattice size is analysed, the interpretation of the density-density correlation function adopted by Chandross and Hicks in fact implies that the optical exciton is unbound.

Relaxation Paths and Dynamics of Photoexcited Polyene Chains: Evidence for Creation and Annihilation of Neutral Soliton Pairs

In recent work, we have demonstrated that the excited-state paths for radiationless deactivation and trans → cis isomerization for a series of polyenes involve a point of conical intersection between the covalent excited and ground states. In this paper we show how motion through this point can “trigger” the production of a transient π-diradical species (on the ground state) featuring an inverted double bond/single bond pattern. The computations have been carried out using an ab initio CAS−SCF approach and a hybrid molecular mechanics−valence bond (MM−VB) force field on three polyenes of increasing chain length: hexa-1,3,5-triene, octa-1,3,5,7-tetraene, and dodeca-1,3,5,7,9,11-hexaene (C12H14). Our computations show that production of the π-diradical must be a general feature of photoexcited polyenes. The investigation of the geometrical and electronic structure of these species indicates that they correspond to a pair of neutral solitons carrying unpaired electrons. Semiclassical trajectory computations on the “minimal” polyacetylene model C12H14 are used to model the creation, evolution, and annihilation dynamics of these transient entities.

Major intermolecular effects on nonlinear electrical response in a hexatriene model of solid state polyacetylene

Through detailed model studies, benchmarked by extensive ab initio calculations, we show (1) how sizable medium effects on molecular electrical response of polymeric solids can arise; (2) that classical electrostatics accurately reproduces a full quantum treatment; and (3) that for a large bundle of hexatriene molecules taken as a model of polyacetylene, the medium effect will lead to as much as a 95% reduction in the second hyperpolarizability and a 50% reduction in the polarizability. For designing organic materials with enhanced nonlinear optical (NLO) properties, the results reveal features that might be optimized and point to a sound model for selecting other features.

Calculation of oscillator strengths using the density matrix renormalisation group method

We present a scheme for the calculation of oscillator strengths between the salient molecular states in correlated models of conjugated polymers using the density matrix renormalisation group method. The accuracy of the method is demonstrated by comparison with exact solutions. The method is applied to a model of polyacetylene in order to identify the dominant transitions, and hence the key states participating in non-linear optical properties.

Towards understanding the ultra-fast dynamics of rhodopsin

Abstract