Soliton Defects Research Articles

Thermally Induced Crossover from 2D to 1D Behavior in an Array of Atomic Wires: Silicon Dangling-Bond Solitons in Si(553)-Au.

The self-assembly of submonolayer amounts of Au on the densely stepped Si(553) surface creates an array of closely spaced "atomic wires" separated by 1.5nm. At low temperature, charge transfer between the terraces and the row of silicon dangling bonds at the step edges leads to a charge-ordered state within the row of dangling bonds with ×3 periodicity. Interactions between the dangling bonds lead to their ordering into a fully two-dimensional (2D) array with centered registry between adjacent steps. We show that as the temperature is raised, soliton defects are created within each step edge. The concentration of solitons rises with increasing temperature and eventually destroys the 2D order by decoupling the step edges, reducing the effective dimensionality of the system to 1D. This crossover from higher to lower dimensionality is unexpected and, indeed, opposite to the behavior in other systems.

Soliton defects and topological -periodic superconductivity from an orbital magnetic field effect in edge Josephson junctions

Recently, much research has been dedicated to understanding topological superconductivity and Majorana zero modes induced by a magnetic field in hybrid proximity structures. This paper proposes a realization of topological superconductivity in a short Josephson junction at an edge of a 2D topological insulator subject to a perpendicular magnetic field. The magnetic field effect is entirely orbital, coming from a gradient of the order parameter phase at the edge, which results in a soliton defect at the junction with a pair of gapless Andreev bound states. The latter are reducible to Majorana zero modes by a unitary rotation and protected by a chiral symmetry. Furthermore, both ground state and excitations are quasiperiodic in the magnetic flux enclosed in the junction, with the period equal to the double flux quantum . This behaviour follows from the gauge invariance of the —phase periodicity of the Majorana states and manifests itself as —spaced magnetic oscillations of the critical current. Another proposed observable is a persistent current occurring in the absence of an external phase bias. Beside the oscillations, it shows a sign reversal prompted by the neutral Majorana zero modes. These findings offer the possibility to access topological superconductivity through low-field dc magnetotransport measurements.

Controlling the stability of nonlinear optical modes via electromagnetically induced transparency

We propose a scheme to generate and stabilize the high-dimensional spatial solitons via electromagnetically induced transparency (EIT). The system we consider is a resonant atomic ensemble having $\mathrm{\ensuremath{\Lambda}}$ configuration. We illustrate that under EIT conditions the equation satisfied by the probe field envelope is reduced to a saturable nonlinear Schr\odinger equation with the trapping potential, provided by a far-detuned laser field and a random magnetic field. We present high-dimensional soliton solutions exhibiting many interesting characteristics, including diversity (i.e., many different types of soliton solutions can be found, including bright, ring multipole bright, ring multipole defect mode, multiring bright, multiring defect mode, and vortices solitons), the phase transition between bright soliton and higher-order defect modes (i.e., the phase transition can be realized by controlling the nonlinear coefficient or the intensity of the trapping potential), and stability (i.e., various solitons can be stabilized by the Gaussian potential provided by the far detuned laser field, or the random potential provided by the magnetic field). We also find that some solitons are the extension of the linear eigenmode, whereas others entirely derive from the role of nonlinearity. Compared with previous studies, we not only show the diverse soliton solutions in the same system but also find the boundary of the phase transition for the type of solitons. In addition, we present the possibility of using the random potential to stabilize various solitons and vortices.

The effect of the negative particle velocity in a soliton gas within Korteweg–de Vries-type equations

The effect of changing the direction of motion of a defect (a soliton of small amplitude) in soliton lattices described by the Korteweg–de Vries and modified Korteweg–de Vries integrable equations (KdV and mKdV) was studied. Manifestation of this effect is possible as a result of the negative phase shift of a small soliton at the moment of nonlinear interaction with large solitons, as noted in [1], within the KdV equation. In the recent paper [2], an expression for the mean soliton velocity in a “cold” KdV-soliton gas has been found using kinetic theory, from which this effect also follows, but this fact has not been mentioned. In the present paper, we will show that the criterion of negative velocity is the same for both the KdV and mKdV equations and it can be obtained using simple kinematic considerations without applying kinetic theory. The averaged dynamics of the “smallest” soliton (defect) in a soliton gas consisting of solitons with random amplitudes has been investigated and the average criterion of changing the sign of the velocity has been derived and confirmed by numerical solutions of the KdV and mKdV equations.

A tractable prescription for large-scale free flight expansion of wavefunctions

A numerical recipe is given for obtaining the density image of an initially compact quantum mechanical wavefunction that has expanded by a large but finite factor under free flight. The recipe given avoids the memory storage problems that plague this type of calculation by reducing the problem to the sum of a number of fast Fourier transforms carried out on the relatively small initial lattice. The final expanded state is given exactly on a coarser magnified grid with the same number of points as the initial state. An important application of this technique is the simulation of measured time-of-flight images in ultracold atom experiments, especially when the initial clouds contain superfluid defects. It is shown that such a finite-time expansion, rather than a far-field approximation is essential to correctly predict images of defect-laden clouds, even for long flight times. Examples shown are: an expanding quasicondensate with soliton defects and a matter-wave interferometer in 3D.

Chiral asymmetry in propagation of soliton defects in crystalline backgrounds

By applying Darboux-Crum transformations to a Lax pair formulation of the Korteweg-de Vries (KdV) equation, we construct new sets of multi-soliton solutions to it as well as to the modified Korteweg-de Vries (mKdV) equation. The obtained solutions exhibit a chiral asymmetry in propagation of different types of defects in crystalline backgrounds. We show that the KdV solitons of pulse and compression modulation types, which support bound states in semi-infinite and finite forbidden bands in the spectrum of the perturbed quantum one-gap Lame system, propagate in opposite directions with respect to the asymptotically periodic background. A similar but more complicated picture also appears for the multi-kink-antikink mKdV solitons that propagate with a privileged direction over topologically trivial or topologically nontrivial crystalline background in dependence on position of energy levels of the trapped bound states in the spectral gaps of the associated Dirac system. An exotic N=4 nonlinear supersymmetric structure incorporating Lax-Novikov integrals of a pair of perturbed Lame systems is shown to underlie the Miura-Darboux-Crum construction. It unifies the KdV and mKdV solutions, detects the defects and distinguishes their types, and identifies the types of crystalline backgrounds.

Soliton defects in one-gap periodic system and exotic supersymmetry

By applying Darboux--Crum transformations to the quantum one-gap Lam\'e system, we introduce an arbitrary countable number of bound states into forbidden bands. The perturbed potentials are reflectionless and contain two types of soliton defects in the periodic background. The bound states with a finite number of nodes are supported in the lower forbidden band by the periodicity defects of the potential well type, while the pulse-type bound states in the gap have an infinite number of nodes and are trapped by defects of the compression modulations nature. We investigate the exotic nonlinear $\mathcal{N}=4$ supersymmetric structure in such paired Schr\"odinger systems, which extends an ordinary $\mathcal{N}=2$ supersymmetry and involves two bosonic generators composed from Lax--Novikov integrals of the subsystems. One of the bosonic integrals has a nature of a central charge and allows us to liaise the obtained systems with the stationary equations of the Korteweg--de Vries and modified Korteweg--de Vries hierarchies. This exotic supersymmetry opens the way for the construction of self-consistent condensates based on the Bogoliubov--de Gennes equations and associated with them new solutions to the Gross--Neveu model. They correspond to the kink or kink-antikink defects of the crystalline background in dependence on whether the exotic supersymmetry is unbroken or spontaneously broken.

Detailed comparison of numerical methods for the perturbed sine-Gordon equation with impulsive forcing

The properties of various numerical methods for the study of the perturbed sine-Gordon (sG) equation with impulsive forcing are investigated. In particular, finite difference and pseudo-spectral methods for discretizing the equation are considered. Different methods of discretizing the Dirac delta are discussed. Various combinations of these methods are then used to model the soliton–defect interaction. A comprehensive study of convergence of all these combinations is presented. Detailed explanations are provided of various numerical issues that should be carefully considered when the sG equation with impulsive forcing is solved numerically. The properties of each method depend heavily on the specific representation chosen for the Dirac delta—and vice versa. Useful comparisons are provided that can be used for the design of the numerical scheme to study the singularly perturbed sG equation. Some interesting results are found. For example, the Gaussian approximation yields the worst results, while the domain decomposition method yields the best results, for both finite difference and spectral methods. These findings are corroborated by extensive numerical simulations.

Exploring the competition between localization and delocalization of the neutral soliton defect in polyenyl chains with the orbital optimized second order opposite spin method

Theory and implementation of the analytical nuclear gradient is presented for orbital optimized scaled opposite-spin perturbation theory (O2). Evaluation of the O2 analytical gradient scales with the 4th power of molecular size, like the O2 energy. Since the O2 method permits optimization of the orbitals in the presence of wavefunction-based electron correlation, it is suitable for problems where correlation effects determine the competition between localization and delocalization of an odd electron, or hole. One such problem is the description of a neutral soliton defect on an all-trans polyacetylene chain with an odd number of carbon atoms. We show that the results of the O2 method compare well to benchmark values for small polyenyl radicals. O2 is also efficient enough to be applied to longer chains where benchmark coupled cluster methods are unfeasible. For C(41)H(43), unrestricted orbital O2 calculations yield a soliton length of about 9 carbon atoms, while other unrestricted orbital methods such as Hartree-Fock, and the B3LYP and ωB97X-D density functionals, delocalize the soliton defect over the entire chain. The O2 result is about half the width inferred experimentally.

A new perspective on optoelectric conversion in conjugated polymers**Project supported by the Special Funds of the National Natural Foundation of China (Grant No. 11047148), and the Jining University Research Program, China (Grant No. 2010QNKJ04).

Photoexcitation of a neutral soliton will create a polaron and a charged soliton. According to a tight-binding model and a nonadiabatic method, we investigate the dynamical process of these two photogenerated charge carriers in an external electric field. It is found that the polaron and the soliton can pass through each other, which excludes the possibility of carrier recombination that usually occurs in existing organic solar cells. The results indicate a more efficient way to realize the optoelectric conversion by photoexciting polymer materials with soliton defects. On the other hand, it is found that solitons take on greater stability than polarons during collision.

Dynamical simulations of charged soliton transport in conjugated polymers with the inclusion of electron-electron interactions

We present numerical studies of the transport dynamics of a charged soliton in conjugated polymers under the influence of an external time-dependent electric field. All relevant electron-phonon and electron-electron interactions are nearly fully taken into account by simulating the monomer displacements with classical molecular dynamics and evolving the wave function for the pi electrons by virtue of the adaptive time-dependent density matrix renormalization group simultaneously and nonadiabatically. It is found that after a smooth turn on of the external electric field the charged soliton is accelerated at first up to a stationary constant velocity as one entity consisting of both the charge and the lattice deformation. An Ohmic region (6 mV/A</=E(0)</=12 mV/A) where the stationary velocity increases linearly with the electric field strength is observed. The relationship between electron-electron interactions and charged soliton transport is also investigated in detail. We find that the dependence of the stationary velocity of a charged soliton on the on-site Coulomb interactions U and the nearest-neighbor interactions V is due to the extent of delocalization of the charged soliton defect.

Trapping Bragg solitons by a pair of defects

We study collisions of moving solitons in a fiber Bragg grating with a structure composed of two local defects of the grating, attractive or repulsive. Results are summarized in the form of diagrams showing the share of the trapped energy as a function of the soliton's velocity and defects' strength. The moving soliton can be trapped by a cavity bounded by repulsive defects; a well-defined region of the most efficient trapping is identified. The trapped soliton performs persistent oscillations in the cavity, with the frequency in the GHz range. For attractive defects, essential differences are found from the earlier studied case of the collision of a soliton with a single defect: in this case, too, there appears a well-defined region of the most efficient trapping, and the largest velocity, up to which the soliton can be captured, increases. The findings may be significant for experiments aimed at the creation of "standing-light" pulses in the fiber gratings and for related applications. Collisions between identical solitons moving across the two-defect structure are also studied. On the attractive set, soliton-soliton collisions may give rise to symmetric capture of the solitons by both defects or merger into a single pulse trapped at one defect.

Polarizability and second hyperpolarizability of open-shell π-conjugated compounds from spin projection method calculations

The Löwdin spin projection technique has been applied to the calculation of the polarizability ( α) and second hyperpolarizability ( γ) of polyacetylene (PA) chains bearing neutral soliton or charged polaron defects. For both types of systems, α and γ smoothly evolve when successive spin contaminations are removed and converge towards a non-spin-contaminated value. Comparisons between the α and γ of these open-shell systems and their corresponding closed-shell analogs, i.e. regular PA chains and PA chains bearing a positively charged soliton, demonstrate the dual role of spin pairing and charge on the linear and non-linear responses of π-conjugated systems.

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.

Interaction of sine-Gordon kinks with defects: the two-bounce resonance

A model of soliton–defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov theory is used to derive a critical velocity for strong interactions, which is shown to be exponentially small for weak defects. Matched asymptotic expansions for nearly heteroclinic orbits are constructed for the initial value problem, which are then used to derive analytical formulas for the locations of the well known two- and three-bounce resonance windows, as well as several other phenomena seen in numerical simulations.

Proton ENDOR Studies of Soliton Wave Functions and Dynamics in Polyacetylenes

Electron nuclear double resonance (ENDOR) studies were carried out over a range of temperatures for five different preparations of polyacetylenes (PAs): Shirakawa (trans-PA), Shirakawa (cis-PA), Durham PA, Naarmann PA, and “enolic PA”. EPR and magnetic susceptibility (SQUID) measurements were also performed and correlated with ENDOR measurements. Whereas the same quasi-delocalized paramagnetic defect (“soliton”) appears to give rise to the ENDOR spectra for all preparations, the extent and dynamics of the soliton defect vary significantly with different preparations illustrating the importance of the lattice (cross-links, residual catalyst, elimination products, adjacent polyene chains, etc.) surrounding and terminating a soliton in defining apparent delocalization of the observed soliton. The analysis of the temperature dependence of ENDOR spectra is complicated by the relatively high concentration of paramagnetic solitons, which may facilitate exchange narrowing of ENDOR spectra. The ambiguity of wheth...

Strong NLS soliton–defect interactions

We consider the interaction of a nonlinear Schrödinger soliton with a spatially localized (point) defect in the medium through which it travels. Using numerical simulations, we find parameter regimes under which the soliton may be reflected, transmitted, or captured by the defect. We propose a mechanism of resonant energy transfer to a nonlinear standing wave mode supported by the defect. Extending Forinash et al. [Phys. Rev. E 49 (1994) 3400], we then derive a finite-dimensional model for the interaction of the soliton with the defect via a collective coordinates method. The resulting system is a three degree-of-freedom Hamiltonian with an additional conserved quantity. We study this system both numerically and using the tools of dynamical systems theory, and find that it exhibits a variety of interesting behaviors, largely determined by the structures of stable and unstable manifolds of special classes of periodic orbits. We use this geometrical understanding to interpret the simulations of the finite-dimensional model, compare them with the nonlinear Schrödinger simulations, and comment on differences due to the finite-dimensional ansatz.

Structural properties of doped polyacetylene chains: a comparative theoretical investigation using Hartree–Fock, Møller–Plesset second-order perturbation theory, and density functional theory approaches

The effect of doping on the geometrical structure of polyacetylene chains containing up to 101 carbon atoms has been investigated theoretically by using the Hartree–Fock approach, the second-order Møller–Plesset perturbation theory as well density functional theory with the hybrid B3LYP exchange–correlation functional. In all cases, the transfer of charge associated with doping induces important geometrical modifications as a result of the large electron–phonon coupling characterizing these π-conjugated systems. The geometrical modifications are mostly described by variations of the bond length alternation following a hyperbolic tangent relation. For chains bearing a positive charge, the Hartree–Fock scheme overestimates the defect localization with respect to the Møller–Plesset scheme where the soliton spans a 36 CH unit region. On the other hand, the B3LYP approach predicts the soliton to be excessively delocalized. When a counterion is added, the soliton defect is more localized. The soliton width goes from 5 ± 2 CH units when the counterion is a Li atom to 9 ± 2 CH units when it is a Cl atom. Moreover, in the presence of a counterion, the three approaches provide much similar bond length alternation and charge distribution patterns.

Erratum: Thermal and quantum fluctuations around domain walls [Phys. Rev. D65, 065021 (2002)

We compute thermal and quantum fluctuations in the background of a domain wall in a scalar field theory at finite temperature using the exact scalar propagator in the subspace orthogonal to the wall's translational mode. The propagator makes it possible to calculate terms of any order in the semiclassical expansion of the partition function of the system. The leading term in the expansion corresponds to the fluctuation determinant, which we compute for arbitrary temperature in space dimensions 1,2, and 3. Our results may be applied to the description of thermal scalar propagation in the presence of soliton defects (in polymers, magnetic materials, etc.) and interfaces which are characterized by kinklike profiles. They lead to predictions as to how classical free energies, surface tensions, and interface profiles are modified by fluctuations, allowing for comparison with both numerical and experimental data. They can also be used to estimate transition temperatures. Furthermore, the simple analytic form of the propagator may simplify existing calculations, and allow for more direct comparisons with data from scattering experiments.

Thermal and quantum fluctuations around domain walls

We compute thermal and quantum fluctuations in the background of a domain wall in a scalar field theory at finite temperature using the exact scalar propagator in the subspace orthogonal to the wall's translational mode. The propagator makes it possible to calculate terms of any order in the semiclassical expansion of the partition function of the system. The leading term in the expansion corresponds to the fluctuation determinant, which we compute for arbitrary temperature in space dimensions $1,$ $2,$ and $3.$ Our results may be applied to the description of thermal scalar propagation in the presence of soliton defects (in polymers, magnetic materials, etc.) and interfaces which are characterized by kinklike profiles. They lead to predictions as to how classical free energy differences, surface tensions, and interface profiles are modified by fluctuations, allowing for comparison with both numerical and experimental data. They can also be used to estimate transition temperatures. Furthermore, the simple analytic form of the propagator may simplify existing calculations, and allow for more direct comparisons with data from scattering experiments.