Solitons In Polyacetylene Research Articles

Rigorous index theory for one-dimensional interacting topological insulators

We present a rigorous but elementary index theory for a class of one-dimensional systems of interacting (and possibly disordered) fermions with U(1)⋊Z2 symmetry defined on the infinite chain. The class includes the Su–Schrieffer–Heeger (SSH) model [Su et al., “Solitons in polyacetylene,” Phys. Rev. Lett. 42, 1698 (1979); Su et al., “Soliton excitations in polyacetylene,” Phys. Rev. B 22, 2099 (1983); and Asbóth et al., A Short Course on Topological Insulators: Band-Structure Topology and Edge States in One and Two Dimensions, Lecture Notes in Physics (Springer, 2016)] as a special case. For any locally unique gapped (fixed-charge) ground state of a model in the class, we define a Z2 index in terms of the sign of the expectation value of the local twist operator. We prove that the index is topological in the sense that it is invariant under continuous modification of models in the class with a locally unique (fixed-charge) gapped ground state. This establishes that any path of models in the class that connects the two extreme cases of the SSH model must go through a phase transition. Our rigorous Z2 classification is believed to be optimal for the class of models considered here. We also show an interesting duality of the index and prove that any topologically nontrivial model in the class has a gapless edge excitation above the ground state when defined on the half-infinite chain. The results extend to other classes of models, including the extended Hubbard model. Our strategy to focus on the expectation value of local unitary operators makes the theory intuitive and conceptually simple. This paper also contains a careful discussion about the notion of unique gapped ground states of a particle system on the infinite chain. (There are two lecture videos in which the main results of this paper are discussed [H. Tasaki, “Rigorous index theory for one-dimensional interacting topological insulators: A brief introduction,” online lecture (21:41), November, 2021, seehttps://www.gakushuin.ac.jp/~881791/OL/#Index1DTI2021S and https://youtu.be/ypGVb3eYrpg and H. Tasaki, “Rigorous index theory for one-dimensional interacting topological insulators: With a pedagogical introduction to the topological phase transition in the SSH model,” online lecture (49:07), November, 2021, see https://www.gakushuin.ac.jp/~881791/OL/#Index1DTI2021L and https://youtu.be/yxZYOevV2Y].

A Peierls Transition in Long Polymethine Molecular Wires: Evolution of Molecular Geometry and Single-Molecule Conductance

Molecules capable of mediating charge transport over several nanometers with minimal decay in conductance have fundamental and technological implications. Polymethine cyanine dyes are fascinating molecular wires because up to a critical length, they have no bond-length alternation (BLA) and their electronic structure resembles a one-dimensional free-electron gas. Beyond this threshold, they undergo a symmetry-breaking Peierls transition, which increases the HOMO-LUMO gap. We have investigated cationic cyanines with central polymethine chains of 5-13 carbon atoms (Cy3+-Cy11+). The absorption spectra and crystal structures show that symmetry breaking is sensitive to the polarity of the medium and the size of the counterion. X-ray crystallography reveals that Cy9·PF6 and Cy11·B(C6F5)4 are Peierls distorted, with high BLA at one end of the π-system, away from the partially delocalized positive charge. This pattern of BLA distribution resembles that of solitons in polyacetylene. The single-molecule conductance is essentially independent of molecular length for the polymethine salts of Cy3+-Cy11+ with the large B(C6F5)4- counterion, but with the PF6- counterion, the conductance decreases for the longer molecules, Cy7+-Cy11+, because this smaller anion polarizes the π-system, inducing a symmetry-breaking transition. At higher bias (0.9 V), the conductance of the shorter chains, Cy3+-Cy7+, increases with length (negative attenuation factor, β = -1.6 nm-1), but the conductance still drops in Cy9+ and Cy11+ with the small polarizing PF6- counteranion.

Electron Correlation Effects on Topological Phases

Topological insulators are found in materials that have elements with strong spin orbit interaction. However, electron Coulomb repulsion also potentially generates the topological insulators as well as Chern insulators by the mechanism of spontaneous symmetry breaking, which is called topological Mott insulators. The quantum criticality of the transition to the topological Mott insulators from zero-gap semiconductors follows unconventional universality distinct from the Landau-Ginzburg-Wilson scenario. On the pyrochlore lattice, the interplay of the electron correlation and the spin orbit interaction provides us in a rich phase diagram not only with simple topological insulators but also with Weyl semimetal and topologically distinct antiferromagnetic phases. Magnetic domain wall of the all-in-all-out type antiferromagnetic order offers a promising candidate of magnetically controlled transport, because, even when the Weyl points disappears, the domain wall maintains robust gapless excitations with Fermi surfaces around it embedded in the bulk insulator and bears uniform magnetization simultaneously. The ingap state is protected by a mechanism similar to the solitons in polyacetylene. Puzzling experimental results of pyrochlore iridates are favorably compared with the prediction of the domain wall theory.

Metallic Interface Emerging at Magnetic Domain Wall of Antiferromagnetic Insulator: Fate of Extinct Weyl Electrons

Topological insulators, in contrast to ordinary semiconductors, accompany protected metallic surfaces described by Dirac-type fermions. Here, we theoretically show another emergent two-dimensional metal embedded in the bulk insulator is realized at a magnetic domain wall. The domain wall has long been studied as ingredients of both old-fashioned and leading-edge spintronics. The domain wall here, as an interface of seemingly trivial antiferromagnetic insulators, emergently realizes a functional interface preserved by zero modes with robust two-dimensional Fermi surfaces, where pyrochlore iridium oxides proposed to host condensed-matter realization of Weyl fermions offer such examples at low temperatures. The existence of ingap states pinned at domain walls, theoretically resembling spin/charge solitons in polyacetylene, and protected as the edge of hidden one-dimensional weak Chern insulators characterized by a zero-dimensional class A topological invariant, solves experimental puzzles observed in R2Ir2O7 with rare earth elements R. The domain wall realizes a novel quantum confinement of electrons and embosses a net uniform magnetization, which enables magnetic control of electronic interface transports beyond semiconductor paradigm.

ChemInform Abstract: Chemical Reactions Induced and Probed by Positive Muons

The application of μ+ science, collectively called μSR, but encompassing a variety of methods including muon spin rotation, muon spin relaxation, muon spin repolarization, muon spin resonance and level-crossing resonance, to chemistry is introduced emphasizing the special aspects of processes which are “induced and probed” by the μ+ itself. After giving a general introduction to the nature and methods of muon science and a short history of muon chemistry, selected topics are given. One concerns the usefulness of muonium as hydrogen-like probes of chemical reactions taking polymerization of vinyl monomers and reaction with thiosulphate as examples. Probing solitons in polyacetylene induced and probed by μ+ is also an important example which shows the unique nature of muonium. Another important topic is “lost polarization”. Although this term is particular to muon chemistry, the chemistry underlining the phenomenon of lost polarization has an importance to both radiation and hot atom chemistries.

Spin current in the Möbius cyclacene belts

We report on density functional theory studies of the electronic structure and magnetic properties of Möbius-[ n]cyclacenes. The geometry of Möbius bands presents a modulation of bond lengths that is needed to accommodate the twist. This modulation takes the form of bond alternation defects analogous to those of solitons in polyacetylene. The ground state of all Möbius bands is a triplet, with a spin density distribution that follows the bond length modulation. A molecular dynamics simulation of the Möbius cyclacene at 300 K shows that the twist travels around the belt inducing a magnetic current.

Vanishing conductivity of quantum solitons in polyacetylene

Quantum solitons or polarons are supposed to play a crucial role in the electric conductivity of polyacetylene, in the intermediate doping regime. We present an exact fully quantized calculation of the quantum soliton conductivity in polyacetylene and show that it vanishes exactly. This is obtained by applying a general method of soliton quantization, based on order–disorder duality, to a Z(2)-symmetric complex extension of the TLM dimerization effective field theory. We show that, in this theory, polyacetylene solitons are sine-Gordon solitons in the phase of the complex field.

Spin distribution in neutral polyene radicals: Pariser–Parr–Pople model studied with the density matrix renormalization group method

The geometries and pi electron spin distributions induced by neutral soliton defects in trans-polyacetylene radicals (from C(7)H(9) to C(49)H(51)) are studied using Pariser-Parr-Pople (PPP) model, solved by the density matrix renormalization group (DMRG) method. Comparisons with other quantum chemical methods as well as the experimental observations on heptatrienyl (C(7)H(9)) and nonatetraenyl (C(9)H(11)) radical species show that the semiempirical PPP method is in the list of the very few theories that can give correct description of the spin distributions for such extended pi-conjugated systems. By virtue of DMRG's power in dealing with large one-dimensional systems, we predicted that the half-width of a neutral spin soliton in polyacetylene is about 14 atoms, and the spin distributions in the center of the soliton is calculated as rho(0)=0.25, rho(1)=-0.12 with rho(1)rho(0)=-0.48, rho(-)rho(+)=-0.52, which agree well with the results from electron-nuclear double resonance experiments.

ESR and ENDOR studies of solitons and polarons in conjugated polymers

Nonlinear excitations such as solitons and polarons in conjugated polymers carry spins. In this case electron spin resonance (ESR) and electron-nuclear double resonance (ENDOR) provide unique methods to determine their wave functions. In this review article, the case of solitons in polyacetylene, CHx, and polarons in an electroluminescent polymer, poly(paraphenylene vinylene) (PPV) are discussed as typical examples. High-resolution proton ENDOR spectra, obtained with stretch-oriented samples, yield the half extension of the excitations of 18 carbon atoms and 4 phenyl rings for CHx and PPV, respectively. These extensions are well described by the theories in the case of finite electron correlation. In addition, light-induced ESR technique is shown to be useful in obtaining site-selective information of spin distribution in the case of PPV derivatives, as well as the excitation spectra of polarons.

Excitation spectrum for ultrafast photogeneration of charged solitons in polyacetylene

Ultrafast photoinduced absorption by IRAV modes is used to detect charged solitons in oriented polyacetylene. We find that soliton pairs are photogenerated within our time resolution of ∼250 fs with -100% quantum efficiency (Φ ch ). The excitation spectrum of Φ ch shows an onset at 1.0 eV, with a weak photon energy dependence up to 4.7 eV. These results agree with the ultrafast soliton formation predicted by Su and Schrieffer and with the SSH threshold of 2E g /π for soliton pair production.

Spin soliton dynamics and magnetic susceptibility of (DMe-DCNQI) 2Li by ESR under pressure

At ambient pressure, a 1/4 filled spin-Peierls system (DMe-DCNQI) 2Li shows spin-Peierls transition at T sp ∼65 K , which increases by about 15 K at 10 kbar. Below T sp, Curie susceptibility emerges. We measured a frequency dependence of ESR line width of Curie spins, and found a quasi-one-dimensional (Q1D) diffusive motion. We propose that the Curie spins are spin solitons as a domain wall spread over several units. The chains with 4 N+ n units, where N=integer, n=1, 2, or 3, caused by possible structural defects could provide the spin solitons. The average domain size is ∼100 DCNQI molecules deduced from the Curie constant and the extension of domain wall is found to be several units from the frequency dependence of ESR line width at 4.2 K. The diffusion rate of the spin solitons increases with temperature, suggesting a motion of the spin soliton dominated by phonons, which is similar to the neutral solitons in polyacetylene. It was also found that the pressure tends to suppress the spin soliton motion.

Excitation spectrum for ultrafast photogeneration of charged solitons in polyacetylene

Ultrafast photoinduced absorption by infrared-active vibrational modes is used to detect charged solitons in oriented trans-polyacetylene. Soliton pairs are photogenerated within ;250 fs with quantum efficiencies (fch) approaching unity. The excitation spectrum of fch shows an onset at ;1.0 eV with a weak photon energy dependence up to 4.7 eV. The results are consistent with the ultrafast soliton formation predicted by Su and Schrieffer and with the Su-Scrieffer-Heeger threshold of 2Eg /p for soliton pair production. The recombination dynamics of charged solitons is very fast ~initial decay,1 ps) with a modest dependence on the pump photon energy.

Statistical properties of charged interfaces

We consider the equilibrium statistical properties of interfaces submitted tocompeting interactions: a long-range repulsive Coulomb interaction inherent tothe charged interface and a short-range, anisotropic, attractive one due to eitherelasticity or confinement. We focus on one-dimensional interfaces such as strings.Model systems considered for applications are mainly aggregates of solitons inpolyacetylene and other charge-density wave systems, domain lines inuniaxial ferroelectrics and the stripe phase of oxides. At zero temperature,we find a shape instability which leads, via phase transitions, to tiltedphases. Depending on the regime, elastic or confinement, the order of thezero-temperature transition changes. Thermal fluctuations lead to a pure Coulombroughening of the string, in addition to the usual one, and to the presenceof angular kinks. We suggest that such instabilities might explain thetilting of stripes in cuprate oxides. The three-dimensional problem of thecharged wall is also analysed. The latter experiences instabilities towardsvarious tilted phases separated by a tricritical point in the elastic regime. Inthe confinement regime, the increase of dimensionality favours either themelting of the wall into a Wigner crystal of its constituent charges or astrongly inclined wall which might have been observed in nickelate oxides.

ESEEM study on a stable paramagnetic center in polydiacetylene having a π-conjugated ladder structure

Using two-, three- and five-pulse methods, we have measured the electron spin echo envelope modulation (ESEEM) of a stable paramagnetic center existing in a non-doped ladder polymer, in which two polydiacetylenes are conjugated in each repeating unit. A relatively deep modulation effect owing to weak hyperfine interaction with protons was observed. The number of interacting protons was estimated to be a few tens based on the analysis of the modulation amplitude. The interaction with many protons implies that the paramagnetic center in the ladder polydiacetylene also possesses a wavefunction delocalized on several units in the π-conjugated system like the spin solitons in polyacetylene.

Attempts to model neutral solitons in polyacetylene by ab initio and density functional methods. The nature of the spin distribution in polyenyl radicals

Different quantum chemical methods have been examined, in order to test their abilities to model long polyenyl radicals and, in the limit, a neutral soliton in polyacetylene. For polyenyl radicals up to C9H11, it was possible to use a range of methods up to CCSD(T). A number of interesting features of the geometries and spin distributions were found in these radicals. Coupled cluster methods reproduced rather well the experimental ratios of the spins at each of the carbons in allyl, pentadienyl, and heptatrienyl radicals. In contrast, both restricted and unrestricted Hartree–Fock methods gave very poor results. CASSCF gave good geometries and π spin distributions, but only if all the π MOs were included in the active space. Both pure (BLYP) and hybrid (B3LYP) DFT methods were found to over-estimate the widths of solitons in long polyenyl chains.

Collisions of solitons in polyacetylene

The dynamics of collisions of structural defects in polyacetylene are studied numerically using the Su-Schrieffer-Heeger model extended to include the influence of an external electric field. The electric field is used to accelerate charged solitons in polyacetylene and it is introduced in terms of a time-dependent vector potential. Collisions between solitons with different charges in a soliton network are considered. It is found that although two isolated solitons on a chain may exchange their moments in a collision, several solitons work like a barrier attenuating the transfer moment. A charge oscillation is observed between the colliding solitons and partial charge transfers. It is also found that if the colliding solitons hold different charges (charged soliton-charged soliton or neutral soliton-charged soliton), the pair is more stable, surviving the collision. Neutral solitons are unstable against collisions and make a dynamic bound state. The energies involved are also discussed.

Effects of Site-Type and Bond-Type Disorders on the Dynamics of Charged and Neutral Solitons

The effects of a site-type impurity potential and a bond-type disorder on the dynamical behaviors of charged and neutral solitons in polyacetylene are studied numerically. The charged soliton feels the site-type potential in the same way as an electron does, except for the broadening of the potential range due to the finite width of the soliton. While the neutral soliton goes through the site-type impurity potential as if there is nothing, reflecting the fact that the excess electron density vanishes everywhere in this case. On the other hand, there is no essential difference between the effects of the bond-type disorder on both solitons. The effective potential in this case looks like a step function, which can be explained in terms of matching or mismatching of the disorder with the dimerization pattern in the region outside of the soliton.

Insulator-to-metal transition driven by clustering of solitons in polyacetylene

It's believed that the simple Su-Schrieffer-Heeger Hamiltonian can not predict the insulator to metal transition of trans-polyacetylene (t-PA). The soliton lattice configuration at a doping level y=6% still has a semiconductor gap. Disordered distributions of solitons close the gap, but the electronic states around the Fermi energy are localized. However, within the same framework, it is possible to show that a cluster of solitons can produce dramatic changes in the electronic structure, allowing an insulator-to-metal transition.

Effects of the nonlinear electron-lattice interaction on the electronic states and localized modes around a soliton in polyacetylene

We have investigated the energy spectra, the electronic states and the localized modes of soliton by considering the effects of the square term of the electron-lattice interactions in the SSH model. Only the midgap state has been found, and the two bound states near the edge of the valence band and the conduction band obtained in the standard SSH models, disappear. The energy gap and the dimerization increase, but the total width of the energy band does not change. All five localized modes survive, and their localizations are strengthened and the frequencies are shifted.

Semi-Phenomenological Analysis of Dynamics of Nonlinear Excitations in One-Dimensional Electron-Phonon System

The structure of moving nonlinear excitations in one-dimensional electron-phonon systems is studied semi-phenomenologically by using an effective action in which the width of the nonlinear excitation is treated as a dynamical variable. The effective action can be derived from Su, Schrieffer and Heeger's model or its continuum version proposed by Takayama, Lin-Liu and Maki with an assumption that the nonlinear excitation moves uniformly without any deformation except the change of its width. The form of the action is essentially the same as that discussed by Bishop and coworkers in studying the dynamics of the soliton in polyacetylene, though some details are different. For the moving excitation with a velocity $v$, the width is determined by minimizing the effective action. A requirement that there must be a minimum in the action as a function of its width provides a maximum velocity. The velocity dependence of the width and energy can be determined. The motions of a soliton in p olyacetylene and an acoustic polaron in polydiacetylene are studied within this formulation. The obtained results are in good agreement with those of numerical simulations.