Soliton Lattice Research Articles

Solitonic ground state in supersymmetric theory in background

A solitonic ground state called a chiral soliton lattice (CSL) is realized in a supersymmetric theory with background magnetic field and finite chemical potential. To this end, we construct, in the superfield formalism, a supersymmetric chiral sine-Gordon model as a neutral pion sector of a supersymmetric two-flavor chiral Lagrangian with a Wess-Zumino-Witten term. The CSL ground state appears in the presence of either a strong magnetic field and/or large chemical potential, or a background fermionic condensate in the form of a fermion bilinear consisting of the gaugino and a superpartner of a baryon gauge field.

Tilted-chiral-state-induced topological Hall effect in chiral magnetic soliton host Cr1/3TaS2

Chromium-intercalated Cr1/3TaS2 is well known for hosting a nontrivial chiral magnetic soliton lattice (CSL) with the reported highest Curie temperature (TC∼151 K) and strongest spin–orbit coupling, which has significant applications in gigahertz and high-speed spintronic devices. Herein, we thoroughly investigate the magneto-electrical transport properties of Cr1/3TaS2 single crystals. For H//ab, our magnetoresistance (MR) measurements reveal distinctive step-like behaviors, which are attributed to the formation and annihilation of chiral magnetic solitons. When under an oblique field, similar but weaker MR behaviors are observed compared to H//ab, indicating the appearance of an inclination-field-induced tilted-CSL. A topological Hall effect is observed under an oblique field, which is suggested to be induced by a nonzero topological charge density resulting from the tilted chiral states. The Cr1/3TaS2 offers an intriguing platform for studying the impact of chiral magnetic structures on magneto-electrical properties, which holds promise for both future spintronic device applications and fundamental investigation.

Effective spin dynamics of spin-orbit coupled matter-wave solitons in optical lattices

Abstract We consider matter-wave solitons in spin-orbit coupled Bose-Einstein condensates embedded in optical lattice and study dynamics of soliton within the framework of Gross-Pitaevskii equations. We express spin components of the soliton pair in terms of nonlinear Bloch equation and investigate effective spin dynamics. It is seen that the effective magnetic field that appears in the Bloch equation is affected by the optical lattices, and thus the optical lattice influences the precessional frequency of the spin components. We make use of numerical approaches to investigate the dynamical behavior of density profiles and center-of-mass of the soliton pair in presence of the optical lattice. It is shown that the spin density is periodically varying due to flipping of spinors between the two states. The amplitude of spin flipping oscillation increases with lattice strength. We find that the system can also exhibit interesting nonlinear behavior for chosen values of parameters. We present a fixed point analysis to study the effects of optical lattices on the nonlinear dynamics of the spin components. It is seen that the optical lattice can act as a control parameter to change the dynamical behavior of the spin components from periodic to chaotic.

Envelope vector solitons in nonlinear flexible mechanical metamaterials

In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model the system, we formulate discrete equations that describe the longitudinal and rotational displacements of each individual rigid unit mass using a lump element approach. By applying the multiple-scales method in the context of a semi-discrete approximation, we derive an effective nonlinear Schrödinger equation that characterizes the evolution of rotational and slowly varying envelope waves from the aforementioned discrete motion equations. We thus show that this flexible mechanical metamaterial chain supports envelope vector solitons where the rotational component has the form of either a bright or a dark soliton. In addition, due to nonlinear coupling, the longitudinal displacement displays kink-like profiles thus forming the 2-components vector soliton. These findings, which include specific vector envelope solutions, enrich our knowledge on the nonlinear wave solutions supported by flexible mechanical metamaterials and open new possibilities for the control of nonlinear waves and vibrations.

A complete dynamical analysis of discrete electric lattice coupled with modified Zakharov–Kuznetsov equation

The behavior of nonlinear waves within a modified Zakharov–Kuznetsov equation and their interactions with discrete electric lattice structures are examined in this study. The ϕ6−model expansion method is utilized to acquire substantial knowledge into the complex dynamics of the system under consideration, particularly with regard to the discrete electric lattice and analytical electrical solitons. By incorporating higher-order effects and improving accuracy in representing specific physical conditions, the study achieves a more realistic portrayal of nonlinear wave dynamics. The investigation also sheds light on the relationship between non-linearity, discreteness, and equation dynamics by exploring the conditions that lead to the formation of solitons and other nonlinear structures. In addition, a unique set of electrical solitons is defined to explore dynamic behaviors such as chaotic, quasi-periodic, and periodic motions under various parameterized conditions, including an external damping force. Phase plane analysis is visualized by using dynamic structure 3D and 2D phase plots, is used for bifurcation and sensitivity inspections. Finally, time series graphs are offered as mathematical depictions of solitary waves, and Lyapunov exponents with real and complex eigenvalues are used to study the stability and chaotic behaviors of the system.

Two-dimensional flat-band solitons in superhoneycomb lattices

Abstract Flat-band periodic materials are characterized by a linear spectrum containing at least one band where the propagation constant remains nearly constant irrespective of the Bloch momentum across the Brillouin zone. These materials provide a unique platform for investigating phenomena related to light localization. Meantime, the interaction between flat-band physics and nonlinearity in continuous systems remains largely unexplored, particularly in continuous systems where the band flatness deviates slightly from zero, in contrast to simplified discrete systems with exactly flat bands. Here, we use a continuous superhoneycomb lattice featuring a flat band in its spectrum to theoretically and numerically introduce a range of stable flat-band solitons. These solutions encompass fundamental, dipole, multi-peak, and even vortex solitons. Numerical analysis demonstrates that these solitons are stable in a broad range of powers. They do not bifurcate from the flat band and can be analyzed using Wannier function expansion leading to their designation as Wannier solitons. These solitons showcase novel possibilities for light localization and transmission within nonlinear flat-band systems.

Photovoltaic spatial gap solitons in biased photorefractive optical lattices

We investigate the existence and characteristics of spatially confined optical gap solitons within an optical lattice embedded in a biased bulk photovoltaic photorefractive crystal. The Floquet-Bloch theory is used to analyze the uniform lattice and derive the optical lattice band structure. In the photonic band gaps, which are typically opaque to light transmission, the photorefractive nonlinearity permits the formation of solitons. The paraxial Helmholtz equation is set up and solved thereby discovering single hump and double hump soliton states in both band gaps. Interestingly, we have not found any multi peak solitons to exist in this particular case. We examine the characteristics of these gap solitons, finding that the soliton width (an indicator of nonlinearity) and intensity depend on their location within the band gap. We find that the magnitude of the external electric field profoundly affects the gap soliton characteristics. Additionally, the Vakhitov-Kolokolov (VK) criterion, perturbation analysis and numerical techniques are used to analyze the stability of the various types of the spatial gap solitons in both the band gaps.

On Long Waves and Solitons in Particle Lattices with Forces of Infinite Range

On Long Waves and Solitons in Particle Lattices with Forces of Infinite Range

Non-Abelian chiral soliton lattice in rotating QCD matter: Nambu-Goldstone and excited modes

The ground state of QCD with two flavors at a finite baryon chemical potential under rapid rotation is a chiral soliton lattice (CSL) of the η meson, consisting of a stack of sine-Gordon solitons carrying a baryon number, due to the anomalous coupling of the η meson to the rotation. In a large parameter region, the ground state becomes a non-Abelian CSL, in which due to the neutral pion condensation each η soliton decays into a pair of non-Abelian sine-Gordon solitons carrying S2 moduli originated from Nambu-Goldstone (NG) modes localized around it, corresponding to the spontaneously broken vector symmetry SU(2)V. There, the S2 modes of neighboring solitons are anti-aligned, and these modes should propagate in the transverse direction of the lattice due to the interaction between the S2 modes of neighboring solitons. In this paper, we calculate excitations including gapless NG modes and excited modes around non-Abelian and Abelian (η) CSLs, and find three gapless NG modes with linear dispersion relations (type-A NG modes): two isospinons (S2 modes) and a phonon corresponding to the spontaneously broken vector SU(2)V and translational symmetries around the non-Abelian CSL, respectively, and only a phonon for the Abelian CSL because of the recovering SU(2)V. We also find in the deconfined phase that the dispersion relation of the isospinons becomes of the Dirac type, i.e. linear even at large momentum.

Domain-wall Skyrmion phase in a rapidly rotating QCD matter

Based on the chiral perturbation theory at the leading order, we show a signal of the presence of a new phase in rapidly rotating QCD matter with two flavors, that is a domain-wall Skyrmion phase. Based on the chiral Lagrangian with a Wess-Zumino-Witten (WZW) term responsible for the chiral anomaly and chiral vortical effect, it was shown that the ground state is a chiral soliton lattice (CSL) consisting of a stack of η-solitons in a high density region under rapid rotation. In a large parameter region, a single η-soliton decays into a pair of non-Abelian solitons, each of which carries SU(2)V/U(1) ≃ ℂP1 ≃ S2 moduli as a consequence of the spontaneously broken vector symmetry SU(2)V. In such a non-Abelian CSL, we construct the effective world-volume theory of a single non-Abelian soliton to obtain a d = 2 + 1 dimensional ℂP1 model with a topological term originated from the WZW term. We show that when the chemical potential is larger than a critical value, a topological lump supported by the second homotopy group π2(S2) ≃ ℤ has negative energy and is spontaneously created, implying the domain-wall Skyrmion phase. This lump corresponds in the bulk to a Skyrmion supported by the third homotopy group π3[SU(2)] ≃ ℤ carrying a baryon number. This composite state is called a domain-wall Skyrmion, and is stable even in the absence of the Skyrme term. An analytic formula for the effective nucleon mass in this medium can be written only in terms of the meson’s constants as 42πfπfη/mπ~1.21\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 4\\sqrt{2}\\pi {f}_{\\pi }{f}_{\\eta }/{m}_{\\pi}\\sim 1.21 $$\\end{document} GeV with the decay constants fπ and fη of the pions and η meson, respectively, and the pion mass mπ. This is reasonably heavier than the nucleon mass in the QCD vacuum.

Quantum Liquid States of Spin Solitons in a Ferroelectric Spin-Peierls State.

In this study, we performed high-magnetic-field magnetization, dielectric, and ultrasound measurements on an organic salt showing a ferroelectric spin-Peierls (FSP) state, which is in close proximity to a quantum critical point. In contrast to the sparsely distributed gaslike spin solitons typically observed in conventional spin-Peierls (SP) states, the FSP state exhibits dense liquidlike spin solitons resulting from strong quantum fluctuations, even at low fields. Nevertheless, akin to conventional SP systems, a magnetic-field-induced transition is observed in the FSP state. In conventional high-field SP states, an emergent wave vector results in the formation of a spin-soliton lattice. However, in the present high-field FSP state, the strong quantum fluctuations preclude the formation of such a soliton lattice, causing the dense solitons to remain in a quantum-mechanically melted state. This observation implies the realization of a quantum liquid-liquid transition of topological particles carrying spin and charge in a ferroelectric insulator.

Robust inverse scattering analysis of discrete high-order nonlinear Schrödinger equation

Abstract In this study, we present the rigorous theory of the robust inverse scattering method for the discrete high-order nonlinear Schrödinger (HNLS) equation with a nonzero boundary condition (NZBC). Using the direct scattering problem, we deduce the analyticity, symmetries, and asymptotic behaviors of the Jost solutions and scattering matrix. We also formulate the inverse scattering problem using the matrix Riemann–Hilbert problem (RHP). Furthermore, utilizing the loop group theory, we construct the multi-fold Darboux transformation (DT) within the framework of the robust inverse scattering transform. Additionally, we develop the corresponding Bäcklund transformation (BT) to obtain the multi-fold lattice soliton solutions. To derive the high-order rational solutions, we further construct the high-order DT. Finally, we theoretically and graphically analyze these solutions, which exhibit lattice breather waves, W-shape lattice solitons, high-order lattice rogue waves (RW), and their interactions.

Evidence of 3D Topological-Domain Dynamics in KTN:Li Polarization-Supercrystal Formation.

We experimentally and theoretically investigate thermal domain evolution in near-transition KTN:Li. Results allow us to establish how polarization supercrystals form, a hidden 3D topological phase composed of hypervortex defects. These are the result of six converging polarization vortices, each associated to one orientation of the 3D broken inversion symmetry. We also identify rescaling soliton lattices and domain patterns that replicate on different scales. Findings shed light on volume domain self-organization into closed-flux patterns and open up new scenarios for topologically protected noise-resistant ferroelectric memory bits.

Chiral Soliton Lattice turns into 3D crystal

Chiral perturbation theory predicts the chiral anomaly to induce a so-called Chiral Soliton Lattice at sufficiently large magnetic fields and baryon chemical potentials. This state breaks translational invariance in the direction of the magnetic field and was shown to be unstable with respect to charged pion condensation. Improving on previous work by considering a realistic pion mass, we employ methods from type-II superconductivity and construct a three-dimensional pion (and baryon) crystal perturbatively, close to the instability curve of the Chiral Soliton Lattice. We find an analogue of the usual type-I/type-II transition in superconductivity: along the instability curve for magnetic fields eB > 0.12 GeV2 and chemical potentials μ < 910 MeV, this crystal can continuously supersede the Chiral Soliton Lattice. For smaller magnetic fields the instability curve must be preceded by a discontinuous transition.

Three-dimensional Bose–Einstein gap solitons in optical lattices with fractional diffraction

Compared with low-dimensional solitons that are widely studied in various realizable nonlinear physical systems, the properties and dynamics of three-dimensional solitons and vortices have not been well disclosed yet. Using numerical simulations and theoretical analysis, we here address the existence, structural property, and dynamics of three-dimensional gap solitons and vortices (with topological charge s=1) of Bose–Einstein condensates moving by Lévy flights (characterized by fractional diffraction operators, Lévy index 1<α≤2) in optical lattices. We stress that previously the localized modes have only been revealed in low-dimensional nonlinear fractional systems in one- and two-dimensional periodic potentials, our study presented here thus drives the associated nonlinear-wave research into three-dimensional configurations. The three-dimensional optical lattices exhibit a nontrivial wide band-gap feature, within which the matter-wave localized gap modes could be excited. The stability and instability regions of both three-dimensional gap modes are obtained via direct perturbed simulations, shedding light on multidimensional soliton physics in nonlinear fractional systems with periodic potentials.

Dual Higgs modes entangled into a soliton lattice in CuTe

Recently discovered Higgs particle is a key element in the standard model of elementary particles and its analogue in materials, massive Higgs mode, has elucidated intriguing collective phenomena in a wide range of materials with spontaneous symmetry breaking such as antiferromagnets, cold atoms, superconductors, superfluids, and charge density waves (CDW). As a straightforward extension beyond the standard model, multiple Higgs particles have been considered theoretically but not yet for Higgs modes. Here, we report the real-space observations, which suggest two Higgs modes coupled together with a soliton lattice in a solid. Our scanning tunneling microscopy reveals the 1D CDW state of an anisotropic transition metal monochalcogenide crystal CuTe is composed of two distinct but degenerate CDW structures by the layer inversion symmetry broken. More importantly, the amplitudes of each CDW structure oscillate in an out-of-phase fashion to result in a regular array of alternating domains with repeating phase-shift domain walls. This unusual finding is explained by the extra degeneracy in CDWs within the standard Landau theory of the free energy. The multiple and entangled Higgs modes demonstrate how novel collective modes can emerge in systems with distinct symmetries broken simultaneously.

Magnetic Helicity in a Chiral‐Polar Magnet Ni2InSbO6

The class of chiral‐polar magnets has recently captured significant interest in scientific study due to their intriguing physical phenomena. Among all the chiral‐polar magnets, Ni2InSbO6 stands out because of its unique attributes, such as the emergence of the topological chiral soliton lattice in the presence of an external magnetic field perpendicular to the chiral‐polar axis. However, the magnetic structure of Ni2InSbO6 at zero field has not been well understood yet. This work presents an analysis including polarized optical microscopy and polarized neutron diffraction on a carefully chosen Ni2InSbO6 crystal. Results confirm the predominance of a single chiral‐polar domain within the crystal and indicate the likelihood of cycloidal magnetic ordering under zero magnetic field, alongside the observation of net magnetic helicity. The existence of both a dominant chiral‐polar domain and a dominant cycloidal magnetic domain within Ni2InSbO6 provides an excellent platform for further exploration of its unconventional physical attributes.

Transmission and control of band gap vortex solitons in fractional-order diffraction honeycomb lattices

In this paper, the existence and transmission characteristics of gap vortex optical solitons in a honeycomb lattice are investigated based on the fractional nonlinear Schrödinger equation. Firstly, the band-gap structure of honeycomb lattice is obtained by the plane wave expansion method. Then the gap vortex soliton modes and their transmission properties in the fractional nonlinear Schrödinger equation with the honeycomb lattice potential are investigated by the modified squared-operator method, the split-step Fourier method and the Fourier collocation method, respectively. The results show that the transmission of gap vortex solitons is influenced by the &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ {\mathrm{L}}\acute{{\mathrm{e}}}{\mathrm{v}}{\mathrm{y}} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20232005_M3.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20232005_M3.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; index and the propagation constant. The stable transmission region of gap vortex soliton can be obtained through power graphs. In the stable region, the gap vortex soliton can transmit stably without being disturbed. However, in the unstable region, the gap vortex soliton will gradually lose ring structure and evolves into a fundamental soliton with the transmission distance increasing. And the larger the &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$ {\mathrm{L}}\acute{{\mathrm{e}}}{\mathrm{v}}{\mathrm{y}} $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20232005_M4.jpg"/&gt;&lt;graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20232005_M4.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; index, the longer the stable transmission distance and the lower the power of the bandgap vortex soliton. When multiple vortex solitons transmit in the lattice, the interaction between them is influenced by the lattice position and phase. Two vortex solitons that are in phase and located at adjacent lattices, are superimposed with sidelobe energy, while two vortex solitonsthat are out of phase are cancelled with sidelobe energy. These vortex solitons will gradually lose ring structure and evolve into dipole modes in the transmission process. And they are periodic rotation under the azimuth angle modulating. When two vortex solitons located at non-adjacent lattice, vortex solitons can maintain a ring-shaped structure due to the small influence of sidelobes. When three gap vortex solitons are located at non-adjacent lattices, the solitons can also maintain their ring-like structures. However, when there are more than three gap vortex solitons, the intensity distribution of vortex solitons are uneven due to the sidelobe energy superimposed. These vortex solitons will form dipole modes and rotate under the azimuthal angle modulating in the transmission process. These results can offer theoretical guidance for transmitting and controlling the gap vortex solitons in the lattice.

Analytical discovery of dark soliton lattices in (2+1)-dimensional generalized fractional Kundu-Mukherjee-Naskar equation

&lt;p&gt;This research explored optical soliton solutions for the (2+1)-dimensional generalized fractional Kundu-Mukherjee-Naskar equation (gFKMNE), which is a nonlinear model for explaining pulse transmission in communication structures and optical fibers. Two enhanced variants of $ (\frac{G'}{G}) $-expansion method were employed, namely, extended $ (\frac{G'}{G}) $-expansion method and the generalized $ (r+\frac{G'}{G}) $-expansion method, based on the wave transformation of the model into integer-order nonlinear ordinary differential equations (NODEs). By assuming a series-form solution for the resultant NODEs, these strategic methods further translated them into a system of nonlinear algebraic equations. Solving these equations provided optical soliton solutions for gFKMNE using the Maple-13 tool. Through 3D and contour visuals, it was revealed that the constructed soliton solutions are periodically arranged in the optical medium, forming dark soliton lattices. These dark soliton lattices are significant in several domains, such as optical signal processing, optical communications, and nonlinear optics.&lt;/p&gt;

Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice

QCD matter in strong magnetic field exhibits a rich phase structure. In the presence of an external magnetic field, the chiral Lagrangian for two flavors is accompanied by the Wess-Zumino-Witten (WZW) term containing an anomalous coupling of the neutral pion π0 to the magnetic field via the chiral anomaly. Due to this term, the ground state is inhomogeneous in the form of either chiral soliton lattice (CSL), an array of solitons in the direction of magnetic field, or domain-wall Skyrmion (DWSk) phase in which Skyrmions supported by π3[SU(2)] ≃ ℤ appear inside the solitons as topological lumps supported by π2(S2) ≃ ℤ in the effective worldvolume theory of the soliton. In this paper, we determine the phase boundary between the CSL and DWSk phases beyond the single-soliton approximation, within the leading order of chiral perturbation theory. To this end, we explore a domain-wall Skyrmion chain in multiple soliton configurations. First, we construct the effective theory of the CSL by the moduli approximation, and obtain the ℂP1 model or O(3) model, gauged by a background electromagnetic gauge field, with two kinds of topological terms coming from the WZW term: one is the topological lump charge in 2+1 dimensional worldvolume and the other is a topological term counting the soliton number. Topological lumps in the 2+1 dimensional worldvolume theory are superconducting rings and their sizes are constrained by the flux quantization condition. The negative energy condition of the lumps yields the phase boundary between the CSL and DWSk phases. We find that a large region inside the CSL is occupied by the DWSk phase, and that the CSL remains metastable in the DWSk phase in the vicinity of the phase boundary.