Landau Ginzburg Research Articles

Vortex state study of superconducting Fe(Te, Se) thin films deposited on SrTiO3 substrate by pulsed laser deposition technique

Superconducting thin films of two thicknesses have been fabricated on (100) oriented SrTiO3 (STO) substrates using the target of composition Fe1.05Te0.50Se0.50 by pulsed laser deposition technique. The structural and transport properties of the fabricated thin films have been investigated and the results indicate the enhancement in the superconducting properties with increasing thickness of the thin films. The onset of the superconducting transition temperature of the grown thin films of thicknesses ∼78 nm and ∼177 nm are ∼12.10 and 12.62 K at 0 T magnetic field, respectively. To estimate the upper critical fields HC2(0), thermally activated energy (TAE) and vortex phase diagram, the magnetoresistance measurements have been performed in the magnetic field range of 0 - 8 T. HC2(0) have been calculated by Ginzburg Landau (GL) theory and Werthamer-Helfand-Hohenberg model by taking the criterion of 90%, 50% and 10% of normal state resistivity and the corresponding GL coherence lengths have also been calculated. In the present work, the TAE has been estimated by conventional Arrhenius relation and modified thermally activated flux flow (TAFF) theory. The power law dependence of TAE, shows prominently the possible planer defects in the system. From the modified TAFF model, the values of fitting parameter ‘q’ suggests the 3 dimensional behaviour of the vortices for both the grown thin films. The vortex phase diagram study reveals the transition from the vortex liquid to vortex glass state.

Flexocaloric Effect in Thin Plates of Barium Titanate and Strontium Titanate

Based on the Love–Kirchhoff approach, the flexoelectric effect in a thin plate of a ferroelectric with cubic symmetry is studied. The electric and elastic fields in the ferroelectric are described within the framework of the Landau–Ginzburg thermodynamic potential. The influence of inhomogeneity of the polarization distribution in the plate is taken into account. The obtained values for the plate bending caused by applying the electric field make it possible to calculate the dependence of changes in entropy on temperature in plates of barium titanate and strontium titanate (the flexocaloric effect).

Elliptic genera andq-series development in analysis, string theory, andN=2 superconformal field theory

In this paper, we examine the Ruelle-type spectral functions [Formula: see text], which define an overall description of the content of the work. We investigate the Gopakumar–Vafa reformulation of the string partition functions, describe the [Formula: see text] Landau–Ginzburg model in terms of Ruelle-type spectral functions. Furthermore, we discuss the basic properties satisfied by elliptic genera in [Formula: see text] theories, construct the functional equations for [Formula: see text], and analyze the modular transformation laws for the elliptic genus of the Landau–Ginzburg model and study their properties in details.

Hierarchy of domain reconstruction processes due to charged defect migration in acceptor doped ferroelectrics

Evolution of a stripe array of polarization domains triggered by the oxygen vacancy migration in an acceptor doped ferroelectric is investigated in a self-consistent manner. A comprehensive model based on the Landau–Ginzburg–Devonshire approach includes semiconductor features due to the presence of electrons and holes, and effects of electrostriction and flexoelectricity especially significant near the free surface and domain walls. A domain array spontaneously formed in the absence of an external field is shown to undergo a reconstruction in the course of the gradual oxygen vacancy migration driven by the depolarization fields. The charge defect accumulation near the free ferroelectric surface causes a series of phenomena: (i) symmetry breaking between the positive and negative c-domains, (ii) appearance of an effective dipole layer at the free surface followed by the formation of a surface electrostatic potential, (iii) tilting and recharging of the domain walls, especially pronounced at higher acceptor concentrations. An internal bias field determined by the gain in the free energy of the structure exhibits dependences of its amplitude on time and dopant concentration well comparable with available experimental results on aging in BaTiO3.

Stochastic Landau–Ginzburg equation with white-noise boundary conditions of Robin type

We consider stochastic nonlinear Landau–Ginzburg equations on the half-line with Robin-type white-noise boundary conditions. We establish the existence and uniqueness of a solution to the initial boundary value problem with values in an appropriate weighted space. We are also interested in the regularity behavior of the solution, especially near the origin.

Modified transverse Ising model for the dielectric properties of SrTiO3 films and interfaces

The transverse Ising model (TIM), with pseudospins representing the lattice polarization, is often used as a simple description of ferroelectric materials. However, we demonstrate that the TIM, as it is usually formulated, provides an incorrect description of SrTiO3 films and interfaces because of its inadequate treatment of spatial inhomogeneity. We correct this deficiency by adding a pseudospin anisotropy to the model. We demonstrate the physical need for this term by comparison of the TIM to a typical Landau–Ginzburg–Devonshire model. We then demonstrate the physical consequences of the modification for two model systems: a ferroelectric thin film, and a metallic LaAlO3/SrTiO3 interface. We show that, in both cases, the modified TIM has a substantially different polarization profile than the conventional TIM. In particular, at low temperatures the formation of quantized states at LaAlO3/SrTiO3 interfaces only occurs in the modified TIM.

More non-Abelian mirrors and some two-dimensional dualities

In this paper, we extend the non-Abelian mirror proposal of two of the authors from two-dimensional gauge theories with connected gauge groups to the case of [Formula: see text] gauge groups with discrete theta angles. We check our proposed extension by counting and comparing vacua in mirrors to the known dual two-dimensional [Formula: see text] gauge theories. The mirrors in question are Landau–Ginzburg orbifolds, and for mirrors to [Formula: see text] gauge theories, the critical loci of the mirror superpotential often intersect fixed-point loci, so that to count vacua, one must take into account the twisted sector contributions. This is a technical novelty relative to the mirrors of gauge theories with connected gauge groups, for which critical loci do not intersect fixed-point loci and so no orbifold twisted sector contributions are pertinent. The vacuum computations turn out to be a rather intricate test of the proposed mirrors, in particular as untwisted sector states in the mirror to one theory are often exchanged with twisted sector states in the mirror to the dual. In cases with nontrivial IR limits, we also check that the central charges computed from the Landau–Ginzburg mirrors match those expected for the IR SCFTs.

Finite element implementation based on explicit, Galerkin and Crank–Nicolson methods to phase field theory for thermal- and surface- induced martensitic phase transformations

In this paper, a nonlinear finite element approach is used to solve the time-dependent phase field or Ginzburg–Landau (GL) equation for phase transformations (PTs) at the nanoscale. The utilized Helmholtz energy includes a third-degree polynomial of the phase variable which results in a nonlinear dependence on the order parameter in the GL equation. The method of weighted residuals is used to derive the corresponding finite element formulation. Using the divergence theorem, the Laplace term in the GL equation is reduced to the first-order term which can represent both the isolated and variable surface energy boundary conditions, allowing for surface-induced phenomena. In order to apply the Dirichlet boundary condition, i.e., constant phase order parameter, the penalty method is used. Quadrilateral elements have been used in the Cartesian coordinate system, and irregular elements for complex geometries are transformed to regular ones by using natural coordinates. Four-point Gaussian integral has been used for integral calculations. The alpha family and both the explicit and implicit methods (Crank–Nicolson and Galerkin methods) are used for time discretization. Thus, the Picard and Newton–Raphson methods are used to linearize the nonlinear equation and their computational efficiencies are compared. In the explicit method, in order to calculate the inverse of the stiffness matrix, the lumping technique has been used which transforms it into a modified diagonal matrix, and this significantly reduced the computation time. In the implicit methods of Picard and Newton–Raphson, both the exact and numerical approaches were used to calculate the tangential matrix for the unknown order parameter and no difference in results between them was found. The convergence for both the Picard and Newton–Raphson methods was studied and compared. Cubic to tetragonal, thermal- induced transformation in NiAl is considered. The order parameter profile and the width and velocity of austenite (A)–martensite (M) interface are calculated and verified with previous works. Examples of thermal- and surface-induced PTs in nanosized samples without hole and with it are studied, presenting planar and nonplanar interfaces. The developed algorithm and code present a proper tool to solve more advanced phase field problems for PTs at the nanoscale with complex geometries and including mechanics effects and with considering complex interactions.

Reconstructing GKZ via Topological Recursion

In this article, a novel description of the hypergeometric differential equation found from Gel’fand–Kapranov–Zelevinsky’s system (referred to as GKZ equation) for Givental’s J-function in the Gromov–Witten theory will be proposed. The GKZ equation involves a parameter $$\hbar $$, and we will reconstruct it as a quantum curve from the classical limit $$\hbar \rightarrow 0$$ via the topological recursion. In this analysis, the spectral curve (referred to as GKZ curve) plays a central role, and it can be described by the critical point set of the mirror Landau–Ginzburg potential. Our novel description is derived via the duality relations of the string theories, and various physical interpretations suggest that the GKZ equation is identified with the quantum curve for the brane partition function in the cohomological limit. As an application of our novel picture for the GKZ equation, we will discuss the Stokes phenomenon for the equivariant $${\mathbb {C}}\mathbf{P }^{1}$$ model, and the wall-crossing formula for the total Stokes matrix will be examined. And as a byproduct of this analysis, we will study Dubrovin’s conjecture for this equivariant model.

Effect of Cd intercalation on the superconducting properties of (Cu0.5-yKyTl0.5)Ba2Ca2Cu3-xCdxO10-δ (y = 0, 0.25; x = 0, 0.5, 1.0, 1.5, 2.0) superconductors

(Cu0.5Tl0.5)Ba2Ca2 Cu3-xCdxO10-δ (x = 0, 0.5, 1.0, 1.5, 2.0) samples are synthesized for the investigation of role of an-harmonic oscillations in the mechanism of high Tc superconductivity. The density of carriers in the conducting planes is enhanced with the doping of K at the (Cu0.5Tl0.5)Ba2O4-δ by synthesizing (Cu0.25K0.25Tl0.5)Ba2Ca2Cu3-xCdxO10-δ (x = 0, 0.5, 1.0, 1.5, 2.0) samples. These samples were synthesized by two step solid state reaction method accomplished at 860 °C and studied their superconducting properties by resistivity measurements, X-ray diffraction analysis and FTIR absorption measurements. The planar reflections observed in the XRD analysis of the samples are best fitted to the orthorhombic crystal structure. The c-axis length and the volume of the unit cell increases with the enhanced doping of Cd in the final compound. The onset temperature of superconductivity Tc (onset) and the zero-resistivity critical temperature Tc (R = 0) suppresses with the increased doping of Cd in the final compound. An improvement in the Tc (onset) and Tc (R = 0) is observed in K-doped samples that arises due to increase in the density of free carriers supplied by alkali atoms. A softening of apical oxygen mode of type Cu(1)‒OA‒Cu(2)/Cd is observed with the increased doping of Cd at the CuO2 planar sites. The apical oxygen mode of type Tl‒OA‒Cu(2)/Cd is, however, did not change with the doping of Cd in the final compound. The planar oxygen mode (545 ‒ 570 cm−1) is hardened with the enhanced doping of Cd in the final compound. The excess conductivity analyses of conductivity data have shown a shift in the various cross-over temperatures, Tcmf and T* towards lower temperatures with the enhanced doping of Cd in the final compound. The value of α determining the defect density also increases with the increased doping of Cd in the final compound. The coherence length along the c-axis ξc(0), interlayer coupling J, magnetic field penetration depth λp.d and Ginzburg Landau (GL) parameter κ decreased with the increase doping of Cd. The phase relaxation time of the carriers Ꞇϕ, the Fermi velocity VF of the carriers decreased while Bc0(T), Bc1(T) and Jc (0) are enhanced with increase doing of Cd in the final compound.

Thermal induced nanovoid evolution in the vicinity of an immobile austenite-martensite interface

In this paper, thermal induced nanovoid evolution in the vicinity of an immobile austenite (A)-martensite (M) interface is studied. The phase field approach (PFA) to martensitic phase transformation (PT) is presented and the coupled Ginzburg-Landau (GL) and mechanics equations are solved to resolve an A-M interface. Then, the solution is stopped when the interface reached its finite width under thermal loading to keep the interface immobile. Next, the PFA for nanovoid evolution is presented and the coupled Cahn-Hilliard (CH) and mechanics equations are solved for the sample consisting of the obtained immobile A-M nanostructure. As a novelty, the mobility coefficient and the formation energy of nanovoids are considered phase dependent. The finite element method and the COMSOL code are used to solve the coupled GL and mechanics equations for single martensitic variant PTs as well as the coupled CH and mechanics equations for nanovoid evolution. The presented models and the numerical procedure are verified with the existing analytical and experimental data. The effect of the phase dependent energy barrier and the mobility coefficient of nanovoids, the transformation strain and the A-M interface width size on the nanovoid evolution is in detail investigated and the nanovoid structures and stress fields are presented. Mainly, the obtained nanostructures show that the nanovoids which appear at the interface grow only in martensite while they are suppressed in austenite, resulting in an oval shape for the nanovoids. Also, the nanovoids which appear in the martensite away from the interface and move toward it are suppressed at the interface. No nanovoid formation is found in austenite. The obtained results agree with the existing experimental data. The current model and the results can help for a better understanding of nanovoid evolution in different neighboring phases and the effect of different PT characteristics on the nanovoid evolution. Thus, they can be used to build the model for the interaction of nanovoids and the PT at the nanoscale.

Borcea–Voisin mirror symmetry for Landau–Ginzburg models

Fan–Jarvis–Ruan–Witten theory is a formulation of physical Landau–Ginzburg models with a rich algebraic structure, rooted in enumerative geometry. As a consequence of a major physical conjecture, called the Landau–Ginzburg/Calabi–Yau correspondence, several birational morphisms of Calabi–Yau orbifolds should correspond to isomorphisms in Fan–Jarvis–Ruan–Witten theory. In this paper, we exhibit some of these isomorphisms that are related to Borcea–Voisin mirror symmetry. In particular, we develop a modified version of Berglund–Hübsch–Krawitz mirror symmetry for certain Landau–Ginzburg models. Using these isomorphisms, we prove several interesting consequences in the corresponding geometries.

Continuum limit in numerical simulations of the $\mathcal{N}=2$ Landau–Ginzburg model

Abstract The $\mathcal{N}=2$ Landau–Ginzburg description provides a strongly interacting Lagrangian realization of an $\mathcal{N}=2$ superconformal field theory. It is conjectured that one such example is given by the two-dimensional $\mathcal{N}=2$ Wess–Zumino model. Recently, the conjectured correspondence has been studied by using numerical techniques based on lattice field theory; the scaling dimension and the central charge have been directly measured. We study a single superfield with a cubic superpotential, and give an extrapolation method to the continuum limit. Then, on the basis of a supersymmetric-invariant numerical algorithm, we perform a precision measurement of the scaling dimension through a finite-size scaling analysis.

Conductivity Fluctuation and Some Parameters of High temperature Superconductor Polycrystalline Y1Ba2Cu3O7−δ doped with Silver Nanoparticles

In this study, we report the effect of Ag nanoparticles doping on the dimensional fluctuations of superconducting order parameters, crystal structure, and some parameters of Y1Ba2Cu3O7−δ + × Ag (x = 0.0, 0.06, 0.1, 0.3, and 0.6 wt%) polycrystalline ceramics. By increasing the content of Ag in YBCO matrix, X-ray diffraction (XRD) with the Rietveld refinement technique revealed that the crystal lattice parameters changed and the orthorhombicity decreased slightly. Also, the increase of Ag wt% caused a decrease of superconducting transition temperatures (Tc) which are determined from the standard four-probe method and dropped abruptly. Aslamazov–Larkin (AL) model was used to analyze excess conductivity fluctuation. Lawerence–Doniach (LD) temperature named TLD which is responsible for the dimensional nature of fluctuation inside the grains is influenced by nano-silver combination in the compound. Crossover temperature from 2D to 3D (TLD) decreased in the mean-field region as a resultant dominance of 3D region by increasing of Ag in YBCO matrix. The decrease in zero-resistance critical temperature (Tc zero), zero-temperature coherence length along the c-axis ξc(0), and super layer length d values implies the degradation of inter-grain weak links, more disorder state of samples and unsettling of the mean free path for the charge carriers respectively with addition of silver nanoparticles. The calculations based on AL and LD model showed the highest anisotropy (γ = 1.34681) for the x = 0.6 sample. The size of the Ag ions, being larger compared to Cu ions, and the number of substitution sites affects the coupling between the CuO2 planes and that results in higher anisotropy. Critical magnetic fields Bc1(0), Bc2(0), and critical current density Jc(0) were indirectly calculated from the Ginzburg–Landau (GL) number and GL equations. By increasing the doping level of silver nanoparticle, these parameters were found to be higher in Ag-added YBCO samples compared to the pure Y123, meaning better intrinsic flux pinning properties of doped Y123. The silver nanoparticle inclusion reduces the grain size and increases the strength and hardness of the parent compound.

Graded tilting for gauged Landau–Ginzburg models and geometric applications

In this paper we develop a graded tilting theory for gauged Landau-Ginzburg models of regular sections in vector bundles over projective varieties. Our main theoretical result describes - under certain conditions - the bounded derived category of the zero locus $Z(s)$ of such a section $s$ as a graded singularity category of a non-commutative quotient algebra $\Lambda/\langle s\rangle$: $D^b(\mathrm{coh} Z(s))\simeq D^{\mathrm{gr}}_{\mathrm{sg}}(\Lambda/\langle s\rangle)$. Our geometric applications all come from homogeneous gauged linear sigma models. In this case $\Lambda$ is a non-commutative resolution of the invariant ring which defines the $\mathbb{C}^*$-equivariant affine GIT quotient of the model. We obtain purely algebraic descriptions of the derived categories of the following families of varieties: - Complete intersections. - Isotropic symplectic and orthogonal Grassmannians. - Beauville-Donagi IHS 4-folds.

Giant caloric effects enhanced by the helix polarization at the 180° domain wall in tetragonal BaTiO3

The electrocaloric and elastocaloric properties at the 180° domain wall in the tetragonal BaTiO3 are studied using the Landau–Ginzburg–Devonshire model as a function of the domain wall rotation angle α. The Ising-Bloch character is predicted at the 180° domain wall in tetragonal BaTiO3 under the flexoelectric effect. The electric field-induced adiabatic temperature change (ΔTE) which is induced by the Bloch-type polarization component depends on α, and a giant positive ΔTE appears at α = (π + 12n)/24 where n is an integer. The asymmetry of ΔTE is found around the Bloch-type domain wall. The Bloch-type polarization component has a little contribution to the stress-induced adiabatic temperature change. This calculation indicates a contribution of helix polarization at the domain wall on the caloric effects (CEs) in the ferroelectric materials.

Determining Coefficients in an Expansion of the Electric Energy of A2ВХ4 Group Crystals According to Polarization by Studying the Dynamics of Repolarization via Harmonic Analysis

Coefficients of the expansion of electrical energy $${{W}_{c}}$$ in the ferroelectric phase near phase transition temperature $${{T}_{c}}$$ are determined from an even power series according to polarization $${{P}_{c}}$$ by studying the dynamics of repolarization in A2BX4 group crystals according to the Landau–Ginzburg–Devonshire theory. Experimental results are compared to the theoretical concepts of the Landau–Ginzburg–Devonshire theory describing dependences $${{W}_{c}}({{P}_{c}})$$ in static.

Pseudotoric structures and special Lagrangian torus fibrations on certain flag varieties

We construct pseudotoric structures (à la Tyurin, 2010) on the two-step flag variety Fℓ1,n−1;n, and explain a general relation between pseudotoric structures and special Lagrangian torus fibrations, the latter of which are important in the study of SYZ mirror symmetry (Strominger et al., 1996). As an application, we speculate how our constructions can explain the number of terms in the superpotential of Rietsch’s Landau–Ginzburg mirror (Rietsch, 2008; Marsh and Rietsch; Pech and Rietsch, 2018; Pech et al., 2016).

Reexamining Ginzburg-Landau theory for neutron P23 superfluidity in neutron stars

The Ginzburg-Landau (GL) effective theory is a useful tool to study a superconductivity or superfluidity near the critical temperature, and usually the expansion up to the fourth-order in terms of order parameters is sufficient for the description of the second-order phase transition. In this paper, we discuss the GL equation for the neutron $^{3}P_{2}$ superfluidity relevant for interior of neutron stars. We derive the GL expansion up to the eighth order in the condensates and find that this order is necessary for the system to have the unique ground state, unlike the ordinary cases. Starting from the $LS$ potential, which provides the dominant attraction between two neutrons at the high density, we derive the GL equation in the path-integral formalism, where the auxiliary field method and the Nambu-Gor'kov representation are used. We present the detailed description for the trace calculation necessary in the derivation of the GL equation. As numerical results, we show the phase diagram of the neutron $^{3}P_{2}$ superfluidity on the plane spanned by the temperature and magnetic field, and we find that the eighth-order terms lead to a first-order phase transition, whose existence was predicted in the Bogoliubov-de Gennes equation but has not been found thus far within the framework of the GL expansion up to the sixth order. The first-order phase transition will affect the interior structures inside the neutron stars.

3-D Properties in (RE)BCO Tapes Measured in Fields up to 35T

We have measured the temperature and angular dependence of the upper critical field (BC 2 ) for three state of the art (RE)BCO HTS tapes using variable-temperature ac susceptibility measurements in applied fields up to 35 T. The three tapes measured were a Fujikura tape without artificial pinning centers and Superpower tapes with and without artificial pinning centers. We have obtained fits to our B C2 (T , θ) data using both the anisotropic Ginzburg-Landau (G-L) and Klemm's models for layered superconductors. Our calculations suggest that these tapes are three-dimensional (3-D) at all temperatures in zero field but become 2-D in magnetic fields above a crossover field of 457/γ T, where γ = √m c /m ab is the G-L anisotropy parameter. The values of γ were measured and show that the 3-D-2-D crossover fields in these tapes are at least 130 T.