Doped Trans-polyacetylene Research Articles

Evidence for solitonic spin excitations from a charge-lattice-coupled ferroelectric order.

Topological defects have been explored in different fields ranging from condensed matter physics and particle physics to cosmology. In condensed matter, strong coupling between charge, spin, and lattice degrees of freedom brings about emergent excitations with topological characteristics at low energies. One-dimensional (1D) systems with degenerate dimerization patterns are typical stages for the generation of topological defects, dubbed "solitons"; for instance, charged solitons are responsible for high electrical conductivity in doped trans-polyacetylene. Here, we provide evidence based on a nuclear magnetic resonance (NMR) study for mobile spin solitons deconfined from a strongly charge-lattice-coupled spin-singlet ferroelectric order in a quasi-1D organic charge-transfer complex. The NMR spectral shift and relaxation rate associated with static and dynamic spin susceptibilities indicate that the ferroelectric order is violated by dilute solitonic spin excitations, which were further demonstrated to move diffusively by the frequency dependence of the relaxation rate. The traveling solitons revealed here may promise the emergence of anomalous electrical and thermal transport.

Engineering of robust topological quantum phases in graphene nanoribbons.

Boundaries between distinct topological phases of matter support robust, yet exotic quantum states such as spin-momentum locked transport channels or Majorana fermions1-3. The idea of using such states in spintronic devices or as qubits in quantum information technology is a strong driver of current research in condensed matter physics4-6. The topological properties of quantum states have helped to explain the conductivity of doped trans-polyacetylene in terms of dispersionless soliton states7-9. In their seminal paper, Su, Schrieffer and Heeger (SSH) described these exotic quantum states using a one-dimensional tight-binding model10,11. Because the SSH model describes chiral topological insulators, charge fractionalization and spin-charge separation in one dimension, numerous efforts have been made to realize the SSH Hamiltonian in cold-atom, photonic and acoustic experimental configurations12-14. It is, however, desirable to rationally engineer topological electronic phases into stable and processable materials to exploit the corresponding quantum states. Here we present a flexible strategy based on atomically precise graphene nanoribbons to design robust nanomaterials exhibiting the valence electronic structures described by the SSH Hamiltonian15-17. We demonstrate the controlled periodic coupling of topological boundary states18 at junctions ofgraphene nanoribbons with armchair edges to create quasi-one-dimensional trivial and non-trivial electronic quantum phases. This strategy has the potential to tune the bandwidth of the topological electronic bands close to the energy scale of proximity-induced spin-orbit coupling19 or superconductivity20, and may allow the realization of Kitaev-like Hamiltonians3 and Majorana-type end states21.

Phonon Conductance of Potassium- and Sodium-Doped Transpolyacetylene Chain

A theoretical approach for the study of phonon dynamics and scattering properties of doped transpolyacetylene chain is presented. The coherent reflection and transmission scattering cross-sections for phonons incident on the doped unit cell boundary are calculated in accordance with the Landauer-Buttiker electron scattering description, using the matching procedure with the nearest and next nearest neighbor elastic force constants. This is done for two different dopants, namely, the potassium and sodium atoms. Our numerical results yield an understanding of the transpolyacetylene chain dynamical properties and the effects on phonon conductance due to phonon incident on the doped unit cell boundary. The coherent reflection and transmission coefficients show characteristic spectral features, depending on the cutoff frequencies for the propagating phonons and on the nature of the dopants. They illustrate the occurrence of Fano resonances in the scattering spectra that result from the interactions of propagating elastic waves of the undoped transpolyacetylene chain with the localized modes due to the breakdown of the translation symmetry in the x direction.

Asymmetrically doped one-dimensional trans-polymers

Abstract More than 30 years ago [H. Shirakawa, E.J. Louis, A.G. MacDiarmid, C.K. Chiang, A.J. Heeger, J. Chem. Soc. Chem. Comm. 578 (1977); S. Etemad, A.J. Heeger, Ann. Rev. Phys. Chem. 33 (1982) 443] it was discovered that doped trans-polyacetylene ( CH ) x , a one-dimensional (1D) conjugated polymer, exhibits electrical conductivity. In this work we show that an asymmetrically doped 1D trans-polymer has non-conventional properties, as compared to symmetrically doped systems. Depending on the level of asymmetry between the chemical potentials of the two involved fermionic species, the polymer can be in a partially or fully spin polarized state. Some possible experimental consequences of doped 1D trans-polymers used as 1D organic polarized conductors are discussed.

Correlation induced insulator to metal transition: A systematic density functional study on highly doped n-type trans-polyacetylene

Since its discovery in 1977, a number of quantum chemical calculations have been attempted to simulate the metallic state of highly doped trans-polyacetylene. These simulations have focused on the possible closure of the band gap at high doping level due to a charge-induced elimination of Peierls distortion; however, conclusive demonstration of a metallic state has not been achieved. The present study presents density functional theory calculations of the band structure of highly doped trans-polyacetylene with explicit inclusion of the metal atoms in a one-dimensional periodic structure. The results indicate (i) small lattice dimerization, i.e., remnant of Peierls distortion exists even in the heavily doped trans-polyacetylene sample, (ii) charge induced closure of the Peierls gap is not a necessary condition to arrive at a metallic state in such systems, and (iii) electronic correlation, as described at the density functional theory level, with a charge induced small Peierls distortion is sufficient to achieve metallic state of highly doped n-type trans-polyacetylene even in one dimension. Furthermore, comparison of functionals that include differing degrees of electron correlation suggest that correlation promotes formation of the metallic state.

Relationships between the Raman Excitation Photon Energies and Its Wavenumbers in Doped trans-Polyacetylene

The resonance Raman spectra of trans-polyacetylene films doped heavily with electron donor (Na) and acceptor (HClO4) have been measured with excitation wavelengths between 488- and 1320-nm, and the relationships between the Raman excitation photon energies (2.54-0.94 eV) and its wavenumbers were discussed. We found the linear dependence of the Raman shifts with the exchanges of excitation photon energies. In particular, the Raman wavenumbers in the C=C stretching <TEX>$(V_1$</TEX> band) showed a dramatic decrease with the increase in Raman excitation photon energies. In the case of acceptor doping, its change is larger than that of donor doping. The observed wavenumber (1255-1267 <TEX>$cm^{-1}$</TEX>) of the <TEX>$V_2$</TEX> band (CC stretch) of Na-doped form is lower than that of the corresponding band (1290-1292 <TEX>$cm^{-1}$</TEX>) of its pristine trans-polyacetylene, whereas the contrary is the case for the HClO4 doped form (1295-1300 <TEX>$cm^{-1}$</TEX>). The origin of doping-induced Raman bands is discussed in terms of negative and positive polarons.

Electronic structure of doped trans-polyacetylene

The behavior of electronic structures of doped trans-polyacetylene is revealed by a simple method. (C24H26)+n is used to simulate p-type doped trans-polyacetylene at various doping concentrations. The electronic structure is calculated, by CNDO/2 method. These calculations show that at low doping level, the decrease of electronic energy compensates the increase of elastic energy, thus the bond alternation exists, and the charge carriers are solitons. When doping level is high, the increase of elastic energy is larger than the decrease, of electronic energy, the bond alternation disappears, solitons no longer exist, and polyacetylene is in a metalic state.

A study of iodine-doped transpolyacetylene

With a view to elucidate and develop a model for the mechanism of conduction in doped transpolyacetylene (t-PA) we have carried out an ab initio study of the ground and excited state of transoctatetraene in the presence of an Iodine atom. While the ground state is calculated as characterized by a slightly distorted alternating bond geometry with Iodine remaining largely neutral atop the plane of the polyene near roughly the midpoint of chain axis, the excited state has the geometry characterized by a solitonic distortion with the octatetraene carrying a net positive charge close to .7e. The bandgap (HOMO-LUMO gap) is computed to be nearly .8 eV. Moreover, the excited state energy appears very insensitive to the position of Iodine along the axis of the octatetraene chain. As an extension of an earlier calculation on the transport of charge by a charged soliton, a similar calculation is performed on a C 8Hi 10 + “kink” travelling along the backbone of C 12H 14 + yielding very similar results. We have extended the ab initio calculations also to the infinite chain.

Soliton Lattice in Trans-Polyacetylene with Random Site-Type impurities11The project supported by National Natural Science Foundation of China with Grant No. 1947007 and the Trans-Century Training Programme Foundation for the Talents by the State Education Commission of China

In order to understand the effect of disorder of impurities in doped trans-polyacetylene, we investigate the electronic states of trans-PA with random site-type impurities, especially, taken into account the Coulomb interaction between impurity ions. The randomness of impurity ions can obviously affect the electronic structures of trans-PA chain for the intermediate doping regime (%). With increasing doping level, this in turn leads to widen the soliton band and narrow the band gap. Moreover, the upper gap will appear a maximum at the critical doping level ( 6%). In addition, when the doping concentration is larger than 12%, the random distribution of impurities tends to be uniform because of being concerned with the Coulomb interaction between ions. Meanwhile, the order parameter configuration indicates that it will appear soliton lattice.

Carrier transport in polyacetylene with intermediate doping.

By use of a modified version of Naarmann's method, we have synthesized polyacetylene (CH${)}_{\mathit{x}}$. The doping was carried out in liquid phases of iodine and iron chloride, and the samples obtained were [CH(${\mathrm{I}}_{3}$${)}_{\mathit{y}}$${]}_{\mathit{x}}$ and [CH(${\mathrm{FeCl}}_{4}$${)}_{\mathit{y}}$${]}_{\mathit{x}}$, respectively. The dopant concentration y is between 0.01 and 0.05, and belongs to the intermediate doping region. The temperature dependence of the dc conductivity for the different dopant concentrations is measured. In doped trans-polyacetylene, charged and neutral soliton pairs are produced in the chains. The conduction mechanism, which is based on the intersoliton hopping of electrons, is the same for polyacetylene with intermediate or light doping. For this reason, Kivelson's model of the average hopping rate, the Hamiltonian of trans-polyacetylene explored by Su, Schrieffer, and Heeger, and the method of Ambegaokar, Halperin, and Langer, which is related to the average transition rate, are used and the relation between the average hopping rate and the transition rate obtained. Finally, in the light of percolation theory and the variable-range-hopping model, the formula for conductivity is derived. The theory is in good agreement with the experiments.

Density-functional study of undoped and doped trans-polyacetylene.

We report a self-consistent linear-combination-of-Gaussian-orbitals study of the electronic states and ground-state geometry of an undoped and doped single, infinite chain of trans-polyacetylene using the density-functional theory in the local-density approximation. We find a dimerized ground state for an undoped chain with a dimerization amplitude of about 0.01 \AA{}, which is lower than the experimental value of 0.023\char21{}0.03 \AA{}. A pure Hartree calculation neglecting all exchange and correlation gives a much smaller dimerization amplitude of less than 0.005 \AA{}. The local exchange-correlation energy thus significantly favors the dimerization although its effect is not strong enough. In the calculations of the doped chains, the dopant ions were approximated by a uniform background charge. We find that the undimerized state becomes energetically more favorable than any uniformly dimerized state at a critical doping level of about 0.04 (0.03) extra holes (electrons) per CH unit. The band structures and total energies of polaron and soliton lattices at a higher doping level of 0.2 holes per CH unit are calculated and compared with those of the uniformly dimerized and undimerized lattices, and possible models of the metallic state of trans-polyacetylene are discussed. According to our study, the bonds become increasingly similar with increasing doping. The undimerized chain model seems to be a good approximation for the metallic state of trans-polyacetylene at high doping levels although the possibility for a marginal soliton lattice cannot be fully excluded.

Charge storage states in polyenes

Changes in the geometric and electronic structure of polyenes upon sodium doping have been studied in detail. A short polyene containing three double bonds, hexatriene, forms a charge transfer complex with a maximum of one sodium ion. The interaction results in the formation of a polaron (radical anion) on the polyene chain. This type of charge storage state is shown to be unstable relative to the formation of a hexatriene dimer when interaction between two polyenes is allowed for; the two polyenes are then bound to each other via a carbon–carbon single bond. The charge storage states in this case correspond to two singly charged, spinless defects, one on each polyene segment of the dimer molecule. Decapentaene, which contains five carbon–carbon double bonds, is shown to be able to accept two electrons from a pair of sodium atoms. Similar to the case of doped trans-polyacetylene, the charges are stored as a soliton–antisoliton pair. However, when there is an excess of the number of polyene molecules relative to the number of sodium atoms, i.e., below saturation doping, this type of charge storage state is also unstable towards the formation of a decapentaene dimer of the same type as in hexatriene.

Effects of the impurity potential on the band structure of doped trans-polyacetylene

In order to understand the drastic effect of impurity doping on the transport properties of polyacetylene, the authors investigate in detail how the impurity ion potential alone affects the band structure of electrons and the order parameter in doped polyacetylene by a self-consistent numerical calculation based upon the Su-Schrieffer-Heeger Hamiltonian plus the impurity potential. Their results show that the potential has only a small effect on gap closure, which is mainly determined by the larger overlap between the electronic wavefunctions in the nearest soliton states. They also find that the order parameter does not go to zero in the heavily doped region where there is no gap, and it is almost unaffected by the impurity potential.

Some density-functionalLMTO studies of electronic properties of quasi-one-dimensional systems

Results of first-principles, density-functional, LMTO calculations on quasi-one-dimensional systems are presented. Special emphasis is put on the problems related with studying the properties of real materials by means of electronic structure calculations. As examples we discuss undoped and doped trans polyacetylene, an MX chain compound, CaNiN, and a comparison between polycarbonitrile and hydrogen cyanide. It is argued that single-chain calculations on undoped polyacetylene predict a bond-length alternation, whereas this may be suppressed in multichain calculations. For an MX chain we demonstrate the importance of including the full ligand structure, whereas many properties of CaNiN can be understood as intrinsic to single chains. A comparison between the covalently bonded polycarbonitrile and the hydrogen-bonded hydrogen cyanide reveals differences between delocalized and localized electrons but also inaccuracies in the relative total energies. Finally, results for doped trans polyacetylene indicate relatively large electronic dopant-polymer hopping integrals as well as problems in describing electron transfers for weakly interacting systems when using a local-density approximation. In total it is demonstrated that reliable and useful informations are obtained in most cases, but also that one has to be careful in choosing the idealized system that is to represent the real material and that certain aspects of the local-density approximation should be improved. © 1993 John Wiley & Sons, Inc.

Extended states in disordered doped polyacetylene chains

In this work we study the electronic structure of ordered and disordered distributions of soliton-type defects along large, finite chains of trans-polyacetylene ( trans-PA), as a function of the concentration of defects. The Negative Factor Counting method was used in a tight-binding parameterization with the geometrical data from Austin Method 1 calculations. Our results show the presence of extended (conducting) states at the Fermi level that could explain the semiconductor-metal transition for highly doped trans-polyacetylene, in accordance with the experimentally observed infrared-active vibrational states.

Ab initio Hartree—Fock studies of the binding energy of a soliton to a sodium counterion in doped trans-polyacetylene

We have performed split valence ab initio Hartree—Fock calculations of the total binding energy, E B, of charged solitons to donor impurities in doped trans-polyacetylene. The total energy is calculated for a system with the soliton pinned to the impurity and for a system where the soliton is isolated from the impurity. E B is taken to be the difference between the optimized total energies of these two systems. For a sodium counterion we obtain a total binding energy of E B = 3.18 eV. This value reduces to 2.25 eV when Møller—Plesset second-order perturbation corrections are included. The energy of the soliton level relative to the valence band edge is found to decrease by 0.22 eV in the presence of a sodium counterion, a result which correlates well with optical absorption data.

The effect of inter-chain coupling properties of doped trans-polyacetylene

The evolution of the Pauli susceptibility versus the doping concentration for the highly doped trans-polyacetylene chains is studied. The analysis is focused on the inter-chain interactions that have been added to the Su-Shrieffer-Haeger (SSH) Hamiltonian. The calculations are restricted to the finite (100–500 sites) chains of the polyacetylene. It is shown that the additional coupling corrects a character of the insulator-metal phase transition observed in trans-polyacetylene.

Electronic properties of highly doped trans-polyacetylene.

The evolution of the density of states at the Fermi energy for a single chain of highly doped trans-polyacetylene is studied as a function of the dopant concentration. The studies are focused on the metallic state of the polymer, which is obtained for dopant concentrations above y\ensuremath{\sim}6%. Two types of lattice structures are considered: the soliton lattice and the polaron lattice. An effective potential due to the dopant counterions is included. The calculations are restricted to perfectly ordered samples. It is shown that the soliton lattice exhibits metallic properties only at very high doping levels. The polaron lattice is shown to exhibit a finite density of states at the Fermi energy, which in the metallic regime compares favorably with the experimental result both in magnitude and as concerns the evolution with increasing dopant concentration.

Ab initio calculations of trans-polyacetylene clusters including sodium counterions

The geometrical and electronic properties of a negatively charged soliton in trans-polyacetylene are calculated at the ab initio Hartree-Fock level. The optimized geometry of a system including a sodium counterion is compared with that of a negatively charged soliton with no counterion present. It is shown that in the presence of the dopant, the characteristics width of the soliton is reduced by a factor of 2.5. For higher doping levels, a single counterion does not represent the dopant potential accurately. Instead, the situation of high doping concentration is represented by a cluster of three polymer chains, carrying one solition each and surrounding a channel of three sodium ions. In our calculations, only one of these chains is treated quantum mechanically. Theother two chains are represented by an array of point charges located at the carbon sites of these chains. When the electrostatic interaction with these point charges is taken into account, as well as the full interaction with the sodium ions, the soliton width is increased as compared to the case of the soliton interacting with a single counterion. Due to the attractive potential of soliton-counterion complexes on neighboring chains, additional geometrical distortions in the soliton geometry occur. This effect must be considered when discussing the transition into a metallic state for highly doped trans-polyacetylene.

A density-functional study of undoped and doped trans polyacetylene

The first-principles, density-functional, full-potential, LMTO method for helical polymers is applied to trans polyacetylene, yielding an optimized structure with non-vanishing CC bond-length alternation in good agreement with experiments and in disagreement with another recent density-functional study. It is further demonstrated that the method gives realistic photo-electron spectra without any adjustment, and that information about the energy-loss function can be extracted. Moreover, results of Compton scattering are predicted, and, finally, preliminary results on highly doped polyacetylene are presented.