Landau Ginzburg Research Articles

Extrinsic dielectric response due to domain wall motion in ferroelectric BaTiO[formula omitted]

BaTiO3 (BTO) is a prototypical perovskite ferroelectric, whose dielectric permittivity and loss spectra – which are strongly temperature and frequency dependent – include contributions from inhomogeneous polarization patterns, with domain walls (DWs) being the most common types. In order to elucidate how DWs influence dielectric response, we utilized a continuum approach based on the Landau–Ginzburg theory to model field-dependent properties of polydomain tetragonal phase of BTO near room temperature and above. A system with 180∘ DWs was evaluated as a case study, with both position-resolved and volume-averaged dielectric susceptibility and loss computed at different temperatures for a range of applied field frequencies and amplitudes. Our results demonstrate that cooperative dipole fluctuations in the vicinity of the DW provide a large (extrinsic) contribution to the system dielectric response relative to the intrinsic contribution stemming from within the domain. Dynamics of the DW profile fluctuations under applied field can be represented by a combination of breathing and sliding vibrational motions, with each exhibiting distinct dependence on the field frequency and amplitude. The implications of this behavior are important for understanding and improving control of coupled functional properties in ferroelectric materials, including their dielectric, electromechanical, and electrooptical responses. Furthermore, this investigation provides a computational benchmark for future studies and can be readily extended to other topological polarization patterns in ferroelectrics.

Investigation of Upper Critical Magnetic Field in 1111‐Type High‐Temperature Iron‐Based Superconductor SmFeAsO1−xFx

ABSTRACTIn this research work, we used a two‐band model to study the theoretical analysis of the upper critical magnetic field of a high‐temperature iron‐based superconductor . The graphs of the high‐temperature iron‐based superconductor's upper critical magnetic field (((T) and ) and angular dependence of the field () versus temperature were effectively plotted. The phase diagrams of the temperature‐dependent upper critical magnetic fields versus temperature were suppressed at the transitional temperature and decreased with rising temperature for both directions of the symmetry axis. Additionally, we plotted the phase diagrams and derived the Ginzburg–Landau (GL) parameters (( and ). At the superconducting critical temperature of the superconducting material, these GL parameters diverge at the transitional temperature. Furthermore, a phase diagram of GL characteristic parameter temperature dependence was plotted. By doping fluorine atoms into the parent compound Sm‐1111, the transitional temperature of this superconductor material increased, reaching a value of 54 K and above. Finally, our theoretical conclusion is consistent with the previous experimental results.

Correction: Analytical solution for ginzburg–landau equation in discrete solitons laser arrays lattices via non-perturbation methods

Correction: Analytical solution for ginzburg–landau equation in discrete solitons laser arrays lattices via non-perturbation methods

Defects and phase transitions to geometric phases of abelian GLSMs

We consider gauged linear sigma models with gauge group U(1) that exhibit a geometric as well as a Landau–Ginzburg phase. We construct defects that implement the transport of D-branes from the Landau–Ginzburg phase to the geometric phase. Through their fusion with boundary conditions these defects in particular provide functors between the respective D-brane categories. The latter map (equivariant) matrix factorizations to coherent sheaves and can be formulated explicitly in terms of complexes of matrix factorizations.

Nonlinear electrodynamics and its possible connection to relativistic superconductivity: an example

Abstract This work presents an illustrative example suggesting a potential connection between the Heisenberg–Euler (HE) model of nonlinear electrodynamics (NLED) and relativistic superconductivity. Within a cylindrical coordinate system, we derive nonlinear Maxwell’s equations from the HE Lagrangian to the fourth order in the electromagnetic (EM) field. By considering static electric and magnetic fields with Gaussian radial profiles, we compute the corresponding HE current density. In parallel, we explore relativistic type-II superconductivity in analogy with the Ginzburg–Landau (GL) theory. We calculate the vortex-supercurrent density of the condensate and propose a link between this current and the HE current. This connection enables the derivation of the relativistic order parameter state. The problem considered in this article may contribute to the understanding of superconductivity in strong EM environments within the broader framework of NLED.

Accurate compact nonlinear dynamical model for a volatile ferroelectric ZrO2 capacitor

We have measured the dynamical response of ZrO2 capacitors to applied triangular voltage waveforms with varying frequencies and amplitudes to determine the voltage and charge on the devices as a function of time. We have fit our experimental results to a Landau–Khalatnikov dynamical equation with a sixth order Landau–Ginzburg–Devonshire polynomial to represent the static charge-voltage behavior, and obtained coefficients of determination R2 > 0.99 for the fits. Analysis of the resulting quantitative model reveals an extremely small range of negative differential capacitance <16 mV. The hysteresis loops in the dynamical charge-voltage curves are found to result primarily from energy loss during the ferroelectric transitions, as represented by a frequency-dependent series resistance in the model.

Weakly non-linear stability analysis of g-jitter induced Rayleigh–Bénard convection under inclined surfaces

This study investigated the effect of g-jitter on the Rayleigh–Bénard convection between inclined surfaces whose lower layer is concentrated with a solute C. The problem is formulated using the Ginzburg–Landau (GL) equation, which is time-dependent non-autonomous ordinary differential equation and derived from a weakly non-linear theory and Fredholm solvability condition. The graphical solution of the GL equation is obtained with the help of MATHEMATICA by using the Runge–Kutta fourth-order method. The impact of various flow parameters on the convective rate of heat and mass transport has been discussed. The heat and mass transport is found to be advanced by the non-dimensional parameters viz. modulations’ amplitude (δ), Lewis number (Le), and solute Rayleigh number (RC), but it is suppressed by the angle of inclination ϕ.

Lump, periodic, multi-waves and interaction solutions to non-linear Landau–Ginzburg–Higgs model

Lump, periodic, multi-waves and interaction solutions to non-linear Landau–Ginzburg–Higgs model

Theoretical Studies on Off-Axis Phase Diagrams and Knight Shifts in UTe2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}: Tetra-Critical Point, d-Vector Rotation, and Multiple Phases

Inspired by recent remarkable sets of experiments on UTe2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}: discoveries of the fourth horizontal internal transition line running toward a tetra-critical point (TCP) at H = 15 T, the off-axis high-field phases, and abnormally large Knight shift (KS) drop below Tc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_\ extrm{c}$$\\end{document} for H‖a\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H \\parallel a$$\\end{document}-magnetic easy axis, we advance further our theoretical work on the field (H)-temperature (T) phase diagram for H‖b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H \\parallel b$$\\end{document}-magnetic hard axis which contains a positive sloped Hc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_\ extrm{c2}$$\\end{document} departing from TCP. A nonunitary spin-triplet pairing with three components explains these experimental facts simultaneously and consistently by assuming that the underlying normal electron system with a narrow bandwidth characteristic to the Kondo temperature ∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim$$\\end{document}30 K unsurprisingly breaks the particle-hole symmetry. This causes a special invariant term in Ginzburg–Landau (GL) free energy functional which couples directly with the 5f magnetic system, giving rise to the Tc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_\ extrm{c}$$\\end{document} splitting and ultimately to the positive sloped Hc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_\ extrm{c2}$$\\end{document} and the horizontal internal transition line connected to TCP. The large KS drop can be understood in terms of this GL invariance whose coefficient is negative and leads to a diamagnetic response where the Cooper pair spin is antiparallel to the applied field direction. The present scenario also accounts for the observed d-vector rotation phenomena and off-axis phase diagrams with extremely high Hc2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_\ extrm{c2}$$\\end{document}≳\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gtrsim$$\\end{document}70 T found at angles in between the b- and c-axes and between the bc-plane and a-axis, making UTe2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} a fertile playground for a possible topological superconductor.

Weakly nonlinear analysis of rotating magnetoconvection with anisotropic thermal diffusivity effect

The influence of anisotropic thermal diffusive coefficient on the stability of the horizontal fluid planar layer rotating about its vertical axis and permeated by the horizontal homogeneous magnetic field is studied. The linear stability analysis is carried out using the normal mode method. The stationary cross/oblique and parallel modes are calculated for different ranges of control parameters arising in the system. The SA (Stratification Anisotropy) parameter, α (the ratio of horizontal and vertical thermal diffusivities), plays a key role in deciding the boundaries between these modes and their instability regions when there is a combination of high and low rotation with weak and strong magnetic fields. The obtained isotropic results coincide with those obtained by pioneers in the literature. The weakly nonlinear behavior of the stationary convective motion in the vicinity of primary instability threshold is studied using the two-dimensional Landau–Ginzburg (LG) equation with cubic nonlinearity. This equation derived using the multiple scale analysis is similar to the one obtained in the literature having different relaxation time, nonlinear coefficient, and coherence lengths. These coefficients are used to study the heat transfer rate. In the case of high rotation, Nusselt number gets decreased from atmospheric (α &amp;lt; 1) to oceanic (α &amp;gt; 1) SA types. The domain for secondary instability of Eckhaus is obtained using the spatiotemporal LG equation and it is observed that the Eckhaus instability region decreases with increasing α.

Special representatives of complexified Kähler classes

Motivated by constructions appearing in mirror symmetry, we study special representatives of complexified Kähler classes, which extend the notions of constant scalar curvature and extremal representatives for usual Kähler classes. In particular, we provide a moment map interpretation, discuss a possible correspondence with compactified Landau–Ginzburg models, and prove existence results for such special complexified Kähler forms and their large volume limits in certain toric cases.

Dynamical study of optical soliton structure to the nonlinear Landau–Ginzburg–Higgs equation through computational simulation

Dynamical study of optical soliton structure to the nonlinear Landau–Ginzburg–Higgs equation through computational simulation

Structural and superconducting properties in hard Mo2BC

The utilization of high-hardness superconducting materials enhances and broadens the applications of superconductors. In this study, a high-hardness Mo2BC superconductor is synthesized using the high-pressure and high-temperature (HPHT) method. Our results demonstrate that it exhibits zero-resistance and Meissner effect below a superconducting critical temperature (Tc) of 7.0 K. The upper critical magnetic field of 4.3 T and the lower critical magnetic field of 226 Oe were obtained by data fitting, respectively. Type-II superconducting properties were confirmed by critical states analysis and Ginzburg-Landau (GL) parameters. Specific thermal properties revealed a Debye temperature as 565.1 K, while an electron-phonon coupling (EPC) parameter λ of 0.588 indicated properly coupled BCS conventional superconductivity. Mo2BC exhibits a Vickers hardness of up to 18.2 GPa, significantly surpassing that of traditional superconducting ceramics. It can be attributed to the robust covalent boron-zigzag-chains coupled with appropriate covalent [Mo6C] octahedrons within a non-centrosymmetric structure. The coexistence of both superconductivity and high hardness enables the versatility of Mo2BC, thereby laying the way for the development of high-hardness superconductors.

Influence of Stress on the Chiral Polarization and Elastrocaloric Effect in BaTiO3 with 180° Domain Structure

The polarization and elastrocaloric effect of chiral barium titanate (BaTiO3) with an Ising–Bloch-type domain wall under stress was investigated using the Landau–Ginzburg–Devonshire (LGD) theory. It has been shown that tensile stresses increase the magnitude of the Ising polarization component in barium titanate, together with a decrease in the domain wall width. Compressive stresses cause a reduction in the Ising polarization component and an increase in the domain width. Under compressive stress, barium titanate exhibits a negative elastrocaloric effect and temperature changes with increasing stress, while BaTiO3 exhibits a positive elastrocaloric effect under tensile stress. Bloch polarization shows angle-dependent polarization under external force, but the temperature change from the elastrocaloric effect is smaller than that of Ising polarization under stress. This work contributes to the understanding of polarization evolution under tension in ferroelectrics with chiral structure.

Topological solitons in charge-[formula omitted] flux quantized state of Kagome superconductors

A recent Little-Parks experiment on the new Kagome superconductor CsV3Sb5 demonstrated resistance oscillation with a period of ϕ0/3=hc/6e. This observation of charge-6e flux quantization is effectively explained by a three-component Ginzburg–Landau (GL) model that incorporates second-order Josephson-type couplings. Here, we numerically solve the GL model to present stable topological solitons. We reveal the structures of these solitons, characterized by closed domain walls with attached vortices. We identify two types of domain walls. These solitons possess multiple flux quanta and exhibit a ringlike geometry. Furthermore, we present the characteristic magnetic field distributions of these solitons, enabling their identification in, e.g., scanning Hall probe and scanning SQUID experiments.

Highly controllable stabilization and switching of multiple colliding soliton sequences with generic Ginzburg–Landau gain–loss

We investigate propagation of J soliton sequences in a nonlinear optical waveguide array with generic weak Ginzburg–Landau (GL) gain–loss and nearest-neighbor (NN) interaction. The propagation is described by a system of J perturbed coupled nonlinear Schrödinger (NLS) equations. The NN interaction property leads to the elimination of collisional three-pulse interaction effects, which prevented the observation of stable multisequence soliton propagation with J>2 sequences in the presence of generic GL gain–loss in all previous studies. We show that the dynamics of soliton amplitudes can be described by a generalized J-dimensional Lotka–Volterra (LV) model. Stability and bifurcation analysis for the equilibrium points of the LV model, which is augmented by an application of the Lyapunov function method, is used to develop setups that lead to robust and scalable transmission stabilization and switching for a general J value. The predictions of the LV model are confirmed by extensive numerical simulations with the perturbed coupled-NLS model with J=3, 4, and 5 soliton sequences. Furthermore, soliton stability and the agreement between the LV model’s predictions and the simulations are not reduced with increasing value of J. Therefore, our study provides the first demonstration of robust control of multiple colliding sequences of NLS solitons in the presence of generic weak GL gain–loss with an arbitrary number of sequences. Due to the robustness and scalability of the results, they can have important applications in stabilization and switching of broadband soliton-based optical waveguide transmission.

Critical Exponents and Universality for Fractal Time Processes above the Upper Critical Dimensionality

We study the critical behaviors of systems undergoing fractal time processes above the upper critical dimension. We derive a set of novel critical exponents, irrespective of the order of the fractional time derivative or the particular form of interaction in the Hamiltonian. For fractal time processes, we not only discover new universality classes with a dimensional constant but also decompose the dangerous irrelevant variables to obtain corrections for critical dynamic behavior and static critical properties. This contrasts with the traditional theory of critical phenomena, which posits that static critical exponents are unrelated to the dynamical processes. Simulations of the Landau–Ginzburg model for fractal time processes and the Ising model with temporal long-range interactions both show good agreement with our set of critical exponents, verifying its universality. The discovery of this new universality class provides a method for examining whether a system is undergoing a fractal time process near the critical point.

Manipulating Spin‐Lattice Coupling in Layered Magnetic Topological Insulator Heterostructure via Interface Engineering

AbstractInduced magnetic order in a topological insulator (TI) can be realized either by depositing magnetic adatoms on the surface of a TI or engineering the interface with epitaxial thin film or stacked assembly of 2D van der Waals (vdW) materials. Herein, the observation of spin‐phonon coupling in the otherwise non‐magnetic TI Bi2Te3 is reported, due to the proximity of FePS3 (an antiferromagnet (AFM), TN ≈ 120 K), in a vdW heterostructure framework. Temperature‐dependent Raman spectroscopic studies reveal deviation from the usual phonon anharmonicity originated from spin‐lattice coupling at the Bi2Te3/FePS3 interface at/below 60 K in the peak position (self‐energy) and linewidth (lifetime) of the characteristic phonon modes of Bi2Te3 (106 and 138 cm−1) in the stacked heterostructure. The Ginzburg‐Landau (GL) formalism, where the respective phonon frequencies of Bi2Te3 couple to phonons of similar frequencies of FePS3 in the AFM phase, is adopted to understand the origin of the hybrid magneto‐elastic modes. At the same time, the reduction of characteristic TN of FePS3 from 120 K in isolated flakes to 65 K in the heterostructure, possibly due to the interfacial strain, which leads to smaller Fe‐S‐Fe bond angles as corroborated by computational studies using density functional theory (DFT). Besides, inserting hexagonal boron nitride within Bi2Te3/FePS3 stacking regains the anharmonicity in Bi2Te3. Controlling interfacial spin‐phonon coupling in stacked heterostructure can have potential application in surface code spin logic devices.

Exact solutions of the Landau–Ginzburg–Higgs equation utilizing the Jacobi elliptic functions

The Landau–Ginzburg–Higgs equation is one of the significant evolution equation in physical phenomena. In this work, the exact solutions of this equation are gained by applying an analytical method depends on twelve Jacobi elliptic functions. This equation is turned into an ordinary differential equation by the proposed method. When solving the Landau–Ginzburg–Higgs equation, an auxiliary ordinary differential equation is considered. Some theorems and corollaries utilized in the solutions of this auxiliary equation are given. Using these solutions, the elliptic and elementary solutions of the Landau–Ginzburg–Higgs equation are obtained and illustrated by tables. Many solutions are given in the form of the complex, rational, hyperbolic, and trigonometric functions. The soliton solutions and the complex valued solutions are also found by proposed method. These solutions include the largest set of solutions in the literature. Some of them are shown graphically by 2-dimensional and 3-dimensional with the help of Mathematica software. The obtained solutions are beneficial for the farther development of a concerned model. The presented method does not need initial and boundary conditions, perturbation, or linearization. Besides, this method is easy, efficient, and reliable for solutions of many partial differential equations.

Construction of conservation laws for the Gardner equation, Landau–Ginzburg–Higgs equation, and Hirota–Satsuma equation

In this paper, two different methods for calculating the conservation laws are used, these are the direct construction of conservation laws and the conservation theorem proposed by Ibragimov. Using these two methods, we obtain the conservation laws of the Gardner equation, Landau–Ginzburg–Higgs equation and Hirota–Satsuma equation, respectively.