Chiral Soliton 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.

Emergent elasticity and wavelike to particle-like crossover in a magnetic chiral soliton lattice

Emergent elasticity and wavelike to particle-like crossover in a magnetic chiral soliton lattice

Chiral Bulk Solitons in Photonic Graphene with Decorated Boundaries

AbstractA chiral bulk soliton in a nonlinear photonic lattice with decorated boundaries, presenting a novel approach to manipulate photonic transport without extensive bulk modifications is proposed. Unlike traditional methods that rely on topological edge and corner modes, this strategy leverages the robust chiral propagation of bulk modes. By introducing nonlinearity into the system, a stable bulk soliton, akin to the topological valley Hall effects is found. The chiral bulk soliton exhibits remarkable stability; the energy does not decay even after a long‐distance propagation; and the corresponding Fourier spectrum confirms the absence of inter‐valley scattering indicating a valley‐locking property. The findings not only contribute to the fundamental understanding of nonlinear photonic systems but also hold significant practical implications for the design and optimization of photonic devices.

Modelling the Elliptical Instability of Magnetic Skyrmions

Two recently developed methods of modelling chiral magnetic soliton elliptical instability are applied in two novel scenarios: the tilted ferromagnetic phase of chiral magnets dominated by easy-plane anisotropy and the general case of the chiral magnet with tilted applied field and arbitrary uniaxial anisotropy. In the former case, the analytical predictions are found to exactly match previous numerical results. In the latter case, the instability of isolated chiral skyrmions has not yet been studied, although interestingly, the predictions correspond to previous numerical investigation into the phase diagram.

Propagation of wave insights to the Chiral Schrödinger equation along with bifurcation analysis and diverse optical soliton solutions

In this study, the modified Sardar sub-equation method is capitalised to secure soliton solutions to the (1+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1+1)$$\\end{document}-dimensional chiral nonlinear Schrödinger (NLS) equation. Chiral soliton propagation in nuclear physics is an extremely attractive field because of its wide applications in communications and ultrafast signal routing systems. Additionally, we perform bifurcation analysis to gain a deeper understanding of the dynamics of the chiral NLS equation. This highlights the complex behaviour of the system and exposes the conditions under which various types of bifurcations occur. Additionally, a sensitivity analysis is performed to assess how small changes in initial conditions and parameters influence the solutions, offering valuable perspectives on the stability and dependability of the acquired solutions. By employing the above-mentioned methodology, we derive a variety of exact solutions, including periodic, singular, dark, bright, mixed trigonometric, exponential, hyperbolic, and rational wave solutions. The study’s findings advance our theoretical knowledge of chiral NLS equations and have potential applications in optical communication and related fields.

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.

Stability analysis and soliton solutions of the (1+1)-dimensional nonlinear chiral Schrödinger equation in nuclear physics

The nonlinear Schrödinger equation equation is one of the most important physical models used in optical fiber theory to explain the transmission of an optical soliton. The field of chiral soliton propagation in nuclear physics is very interesting because of its numerous applications in communications and ultra-fast signal routing systems. The (1+1)-dimensional chiral dynamical structure that describes the soliton behaviour in data transmission is dealt with in this work using a variety of in-depth analytical techniques. This work has applications in particle physics, ionised science, nuclear physics, optics, and other applied mathematical sciences. We are able to develop a variety of solutions to demonstrate the behaviour of solitary wave structures, periodic soliton solutions, chiral soliton solutions, and bell-shaped soliton solutions with the use of applied techniques. Moreover, in order to verify the scientific calculations, the stability analysis for the observed solutions of the governing model is taken into consideration. In addition, the 3-dimensional, contour, and 2-dimensional visuals are supplied for a better understanding of the behaviour of the solutions. The employed strategies are dependable, uncomplicated, and effective; yet have not been utilised with the governing model in the literature that is now accessible. The resulting outcomes have impressive applications across a large number of study areas and computational physics phenomena representing real-world scenarios. The methods applied in this model are not utilized on the given models in previous literature so we can say that these describe the novelty of the work.

Simulation of time-crystal-like behavior for a few-boson chiral soliton model in a ring

We present numerical simulations for a chiral soliton model with N=2,3 bosons in a ring, which is a few-particle version of our previous mean-field model for a quantum time crystal. Following Syrwid, Kosior, and Sacha (SKS), the notion is that a precise position measurement of one particle can lead to spontaneous formation of a bright soliton that in a time crystal should rotate intact for at least a few revolutions around the ring. In their work SKS found spontaneous formation of a soliton due to the position measurement, but quantum fluctuations cause the soliton to subsequently decay before it has a chance to perform even one revolution of the ring. Based on this, they concluded that time-crystal dynamics are impossible for Wilczek's model of a bright soliton in a ring. In contrast, for our few-boson chiral soliton model, allowing for imprecise (weak) measurements of the particle position, we show that time-crystal-like behavior is possible, allowing for several revolutions of the spontaneously formed soliton around the ring. Published by the American Physical Society 2024

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.

Electric-field control of magnetic anisotropies: Applications to Kitaev spin liquids and topological spin textures

Magnetic anisotropies often originate from the spin-orbit coupling and determine magnetic ordering patterns. We develop a microscopic theory for dc electric-field controls of magnetic anisotropies in magnetic Mott insulators and discuss its applications to Kitaev materials and topological spin textures. Throughout this paper, we take a microscopic approach based on Hubbard-type lattice models, tight-binding models with onsite interactions. We derive a low-energy spin Hamiltonian from a fourth-order perturbation expansion of the Hubbard-type model. We show in the presence of a strong intra-atomic spin-orbit coupling that dc electric fields add non-Kitaev interactions such as a Dzyaloshinskii-Moriya interaction and an off-diagonal Γ′ interaction to the Kitaev-Heisenberg model and can induce a topological quantum phase transition between Majorana Chern insulating phases. We also investigate the interatomic Rashba spin-orbit coupling and its effects on topological spin textures. dc electric fields turn out to create and annihilate magnetic skyrmions, hedgehogs, and chiral solitons. We propose several methods of creating topological spin textures with external electromagnetic fields. Our theory clarifies that the strong but feasible electric field can control Kitaev spin liquids and topological spin textures. Published by the American Physical Society 2024

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.

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.

Chiral optical solitons in an electrically active multiferroic guiding structure.

A stack of a dielectric planar waveguide with a Kerr-type nonlinearity, sandwiched between two oxide-based helical multiferroic layers is shown to support electrically-controlled chiral solitons. These findings follow from analytical and full numerical simulations. The analytical scheme delivers explicit material parameters for the guided mode soliton and unveils how the soliton propagation characteristics are controlled by tuning the multiferroic helicity and amplitude of the injected electromagnetic wave. Silicon and CS2 are considered as the optical media in the guiding region enclosed by the multiferroic slabs. CS2 has very similar nonlinearity characteristics to silicon but in the linear regime it exhibits a smaller refractive index in the THz frequency range. The scattering simulations are performed using our developed numerical code based on the rigorous coupled wave method and the results for the dispersion curve for the guided mode agree very well with the analytical formula that we derive in this work. The results demonstrate a case of nonlinear pulse generation with field-controlled, nontrivial topological properties.

Novel transition dynamics of topological solitons

Continuous phase transitions can be classified into ones characterized by local-order parameters and others that need additional topological constraints. The critical dynamics near the former transitions have been extensively studied, but the latter is less understood. We fill this gap in knowledge by studying the transition dynamics to a parity-breaking topological ground state called the chiral soliton lattice in quantum chromodynamics at finite temperature, baryon chemical potential, and an external magnetic field. We find a slowing down of the soliton’s translational motion as the critical magnetic field approaches, while the local relaxation rate to the solitonic state remains finite. The time required to converge to the stationary state strongly depends on the symmetry of the initial configuration, determining whether translational motion occurs during the dynamic process. Published by the American Physical Society 2024

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.

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.

Chiral magnets from string theory

Chiral magnets with the Dzyaloshinskii-Moriya (DM) interaction have received quite an intensive focus in condensed matter physics because of the presence of a chiral soliton lattice (CSL), an array of magnetic domain walls and anti-domain walls, and magnetic skyrmions, both of which are important ingredients in the current nanotechnology. In this paper, we realize chiral magnets in type-IIA/B string theory by using the Hanany-Witten brane configuration (consisting of D3, D5 and NS5-branes) and the fractional D2 and D6 branes on the Eguchi-Hanson manifold. In the both cases, we put constant non-Abelian magnetic fluxes on higher dimensional (flavor) D-branes, turning them into magnetized D-branes. The O(3) sigma model with an easy-axis or easy-plane potential and the DM interaction is realized on the worldvolume of the lower dimensional (color) D-branes. The ground state is the ferromagnetic (uniform) phase and the color D-brane is straight when the DM interaction is small compared with the scalar mass. However, when the DM interaction is larger, the uniform state is no longer stable and the ground state is inhomogeneous: the CSL phases and helimagnetic phase. In this case, the color D-brane is no longer straight but is snaky (zigzag) when the DM interaction is smaller (larger) than a critical value. A magnetic domain wall in the ferromagnetic phase is realized as a kinky D-brane. We further construct magnetic skyrmions in the ferromagnetic phase, realized as D1-branes (fractional D0-branes) in the former (latter) configuration. We see that the host D2-brane is bent around the position of a D0-brane as a magnetic skyrmion. Finally, we construct, in the ferromagnetic phase, domain-wall skyrmions, that is, composite states of a domain wall and skyrmions, and find that the domain wall is no longer flat in the vicinity of the skyrmion. Consequently, a kinky D2-brane worldvolume is pulled or pushed in the vicinity of the D0-brane depending on the sign of the skyrmion topological charge.

Anisotropic microwave response in Cr1∕3TaS2 hosting chiral magnetic soliton

Chromium-intercalated hexagonal Cr1∕3TaS2 possesses exotic properties, such as high-temperature magnetic soliton, crossover of critical behavior, and nontrivial magnetism. In this study, we employ the electron spin resonance (ESR) technique to modulate and study the chiral magnetic soliton lattice (CSL) in Cr1∕3TaS2 using microwave at X-band. The experimental results show that Cr1∕3TaS2 has a particularly strong microwave response when H⊥c but very weak feedback when H//c, revealing an anisotropic microwave response. When H⊥c, the resonance peak at lower fields results from the surface barrier induced by the competition between Dzyaloshinsky–Moriya interaction, Zeeman energy, and exchange energy. The dominant resonance is caused by the ferromagnetic mode with the twisted region as the boundary condition, which transforms into a paramagnetic resonance above the phase transition temperature (TC). Furthermore, an unusual temperature dependence of ESR spectra is revealed. The crystalline electric field (CEF) excitation owing to large strong spin–orbit coupling results in the widening of the ESR linewidth above TC. Furthermore, an abrupt shift in the resonance field Hr2 and ESR linewidth ΔHPP2 is observed around TC, which is attributed to a sudden change in spin-exchange interactions and magnetic anisotropy around TC, as Cr1∕3TaS2 was previously observed for spin interaction transition from strong anisotropic 3D-Ising type to isotropic 3D-Heisenberg magnetic interaction below TC. This work demonstrates that the ESR can detect the CSL state and investigate materials with nontrivial magnetism.

Characteristics of stochastic solutions for the chiral NLSE through Brownian motion process

In this work, we produce some new stochastic chiral solitons for the chiral nonlinear Schrödinger equation through Brownian motion process. Specifically, we use the unified approach to produce these soliton solutions. These solutions are so important in quantum mechanics, optical fiber communication, heat transfer, applications of energy, etc. These solutions behave in qualitatively distinct structural ways, based on physical coefficients parameters and the noise parameter. The results of the solitary structures of this system agree well with the properties of the nonlinear Schrödinger systems used to investigate dispersive modes and higher-order chiral systems. We introduce some plots for the deterministic and stochastic cases in order to show the behavior of waves in both cases. Namely, we used Matlab 18 to create comprehensive configurations to highlight the physical dynamical description of the solutions as well as provide further information. The dominance of the noise term in all wave conversion, growth, and damping of envelopes and shocks has been verified. Finally, our analysis can be outspread to several equations arising in natural science.

Observation and Characterization of Multiple Resonance Modes in a Chiral Helimagnet CrNb3S6.

The chiral helimagnet CrNb3S6 hosts various temperature- and magnetic-field-stabilized chiral soliton lattices (CSLs) and corresponding exotic collective spin resonance modes, which make it an ideal candidate for future magnetic storage/memory and magnon-based information processing. While most studies have focused on characterizing various static spin textures in this chiral helimagnet, its corresponding collective dynamics have rarely been explored. This study systematically investigates the temperature- and magnetic-field-dependent magnetic dynamics of a single crystal of CrNb3S6 using broadband microwave spectroscopy. We observe an optical mode with a temperature-independent mode number in addition to Kittel-like ferromagnetic resonance (FMR) modes in the CSL phase, consistent with the temperature-independent normalized CSL period L(H)/L(0) based on the 1D chiral sine-Gordon model. Furthermore, combining theoretical model fitting and micromagnetic simulation, we provide a detailed phase diagram and temporal-spatial resolution of dynamic modes, which may help to develop high-frequency exchange-coupling-based spintronic devices.