Landau Ginzburg Research Articles

Central charges of T-dual branes for toric varieties

Given any equivariant coherent sheaf L \mathcal {L} on a compact semi-positive toric orbifold X \mathcal {X} , its SYZ T-dual mirror dual is a Lagrangian brane in the Landau-Ginzburg mirror. We prove that the oscillatory integral of the equivariant superpotential in the Landau Ginzburg mirror over this Lagrangian brane is the genus-zero 1 1 -descendant Gromov-Witten potential with a Gamma-type class of L \mathcal {L} inserted.

Critical end point and universality class of neutron P23 superfluids in neutron stars

We study the thermodynamics and critical behavior of neutron $^3P_2$ superfluids in the inner cores of neutron stars. $^3P_2$ superfluids offer a rich phase diagram including uniaxial/biaxial nematic phases, the ferromagnetic phase, and the cyclic phase. Using the Bogoliubov-de Gennes (BdG) equation as superfluid Fermi liquid theory, we show that a strong (weak) magnetic field drives the first (second) order transition from the dihedral-two biaxial nematic phase to dihedral-four biaxial nematic phase in low (high) temperatures, and their phase boundaries are divided by the critical endpoint (CEP). We demonstrate that the set of critical exponents at the CEP satisfies the Rushbrooke, Griffiths, and Widom equalities, indicating a new universality class. At the CEP, the $^3P_2$ superfluid exhibits critical behavior with nontrivial critical exponents, indicating a new universality class. Furthermore, we find that the Ginzburg-Landau (GL) equation up to the 8th-order expansion satisfies three equalities and properly captures the physics of the CEP. This implies that the GL theory can provide a tractable way for understanding critical phenomena which may be realized in the dense core of realistic magnetars.

Pair-density-wave superconductivity of faces, edges, and vertices in systems with imbalanced fermions

We describe boundary effects in superconducting systems with Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting instability, using Bogoliubov-de-Gennes and Ginzburg-Landau (GL) formalisms. First, we show that in dimensions larger than one the standard GL functional formalism for FFLO superconductors is unbounded from below. This is demonstrated by finding solutions with zero Laplacian terms near boundaries. We generalize the GL formalism for these systems by retaining higher order terms. Next, we demonstrate that a cuboid sample of a superconductor with imbalanced fermions at a mean-field level has a sequence of the phase transitions. At low temperatures it forms Larkin-Ovchinnikov state in the bulk but has a different modulation pattern close to the boundaries. When temperature is increased the first phase transition occurs when the bulk of the material becomes normal while the faces remain superconducting. The second transition occurs at higher temperature where the system retains superconductivity on the edges. The third transition is associated with the loss of edge superconductivity while retaining superconducting gap in the vertices. We obtain the same sequence of phase transition by numerically solving the Bogoliubov-de Gennes model.

Giant electrocaloric response in compositional manipulated BaTiO3 relaxor–ferroelectric system

The compositional manipulation of the multiphase coexistence in relaxor–ferroelectrics has been reported to be an effective approach to generate the giant electrocaloric effect. In this work, we systemically investigate the temperature-dependent electrocaloric effect in BaZr0.18Ti0.82O3–BaSn0.11Ti0.89O3 relaxors, where Zr and Sn are introduced into BaTiO3 to develop the multiphase coexistence at the ferroelectric–paraelectric transition. Through the direct measurement by the heat flux sensor, a large temperature change around 4 K under an electric field of 10 MV m−1, combined with a broad temperature span (20 °C–60 °C), has been observed. For comparison, the electrocaloric properties are also indirectly deduced based on Maxwell equations and Landau–Ginzburg–Devonshire phenomenological theory, and the validity of the indirect methods in this relaxor–ferroelectric system has been discussed. This work would shed light on developing giant electrocaloric materials with a wide operating temperature range.

Spin-orbit coupling and spin-triplet pairing symmetry in Sr2RuO4

Spin-orbit coupling (SOC) plays a crucial role in determining the spin structure of an odd parity psedospin-triplet Cooper pairing state. Here, we present a thorough study of how SOC lifts the degeneracy among different p-wave pseudospin-triplet pairing states in a widely used microscopic model for $\mathrm{Sr_2 Ru O_4}$, combining a Ginzburg-Landau (GL) free energy expansion, a symmetry analysis of the model, and numerical weak-coupling renormalization group (RG) and random phase approximation (RPA) calculations. These analyses are then used to critically re-examine previous numerical results on the stability of chiral p-wave pairing. The symmetry analysis can serve as a guide for future studies, especially numerical calculations, on the pairing instability in $\mathrm{Sr_2 Ru O_4}$ and can be useful for studying other multi-band spin-triplet superconductors where SOC plays an important role.

Multicaloric effect in multiferroic EuTiO3 thin films

A modified Landau–Ginzburg–Devonshire phenomenological thermodynamic theory is used to investigate both the influence of biaxial compressive misfit strain between film and the substrate and the mechanical stress on the multicaloric response in epitaxial EuTiO3 thin films. The complicated compressive misfit strain–temperature phase diagram in the low-temperature region is developed. The excellent electrocaloric and elastocaloric effect can be achieved: $$ \Delta T(T_{\text{C}} ) = 3.66\,{\text{K}} $$, while $$ \Delta E = 100\,{\text{kV/cm}},u_{\text{m}} = - \,4.0{\%} $$; $$ \Delta T $$ = 5.31 K at 200 MPa. Besides, the maximal adiabatic temperature change $$ \Delta T(T_{\text{M}} ) = 17.3\,{\text{K}} $$, while $$ \Delta H = 5\,{\text{T}},u_{\text{m}} = - \,4.0{\%} $$, in the low-temperature region, which is comparable with the experimental result. Both the misfit strain and the external mechanical stress play a crucial role in the multicaloric response in EuTiO3 films. It may open more opportunities for practical application in refrigeration devices, especially for low-temperature solid-state multicaloric cooling.

Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers

In this work, we investigate the conformable space–time fractional complex Ginzburg–Landau (GL) equation dominated by three types of nonlinear effects. These types of nonlinearity include Kerr law, power law, and dual-power law. The symmetry case in the GL equation due to the three types of nonlinearity is presented. The governing model is dealt with by a straightforward mathematical technique, where the fractional differential equation is reduced to a first-order nonlinear ordinary differential equation with solution expressed in the form of the Weierstrass elliptic function. The relation between the Weierstrass elliptic function and hyperbolic functions enables us to derive two types of optical soliton solutions, namely, bright and singular solitons. Restrictions for the validity of the optical soliton solutions are given. To shed light on the behaviour of solitons, the graphical illustrations of obtained solutions are represented for different values of various parameters. The symmetrical structure of some extracted solitons is deduced when the fractional derivative parameters for space and time are symmetric.

Some Features of Critical Parameters Calculations of Nonhomogeneous Superconducting Films Using the Ginzburg–Landau Theory

A method for calculating the critical state of inhomogeneous superconducting films using the Ginzburg–Landau (GL) theory is proposed. From the condition of minimizing the functional of the GL free energy, a system of equations describing the superconducting state of an inhomogeneous plate is derived. The dependences of the critical current of the plate on the external magnetic field are numerically calculated. It is shown that the critical current in a zero external magnetic field decreases with increasing degree of film inhomogeneity, while the critical magnetic field (at a zero transport current) increases. An analysis of the calculated dependences of the product of the critical current and the external magnetic field (an analogue of the volume pinning force) of superconducting films on the external magnetic field shows that the maximum of this value shifts to stronger fields with increasing degree of inhomogeneity, i.e., an increase in inhomogeneity leads to an increase in the pinning force.

Four-Fold Anisotropy of the Parallel Upper Critical Magnetic Field in a Pure Layered d-Wave Superconductor at T = 0

It is well known that a four-fold symmetry of the parallel upper critical magnetic field disappears in the Ginzburg-Landau (GL) region in quasi-two-dimensional (Q2D) $d$-wave superconductors. Therefore, it has been accurately calculated so far as a correction to the GL results, which is valid close to superconducting transition temperature and is expected to be stronger at low temperatures. As to the case $T=0$, some approximated methods have been used, which are good only for closed electron orbits and unappropriate for the open orbits which exist in a parallel magnetic field in Q2D superconductors. For the first time, we accurately calculate the four-fold anisotropy of the parallel upper critical magnetic field in a pure Q2D $d$-wave superconductor at $T=0$, where it has the highest possible value. Our results are applicable to Q2D $d$-wave high-Tc and organic superconductors.

Superconductivity in 5d transition metal Laves phase SrIr2

We report here the superconducting properties of a Laves phase superconductor SrIr2, which has a cubic MgCu2 structure. SrIr2 is a type-II superconductor, with a Tc of 5.9 K. The estimated superconducting parameters of lower critical field µ0Hc1 and upper critical field µ0Hc2, coherence length ξ(0), penetration depth λ(0) and Ginzburg–Landau (GL) parameter κ(0) are approximately µ0Hc1 = 101 Oe, µ0Hc2(0) = 5.9 T, ξ(0) = 7.47 nm, λ(0) = 237 nm, and κ(0) = 31.7, respectively. The specific-heat data indicate that SrIr2 is a strong-coupling superconductor because the value of ΔC/γTc is approximately 1.71, which is larger than the value of 1.43 that is expected from the BCS theory. The physical properties obtained in this study are explained well by theoretical calculations including spin–orbit coupling (SOC). This result indicates that the physical properties of SrIr2 are strongly affected by the presence of SOC.

Paramagnetic Meissner Effect Observed in SrBi3 with κ Close to the Critical Regime

Vortex–vortex interaction plays an important role in determining the magnetic properties in different types of superconductors, among which rich phenomenons have been observed in superconductors with Ginzburg–Landau (GL) parameter κ close to the critical regime (between traditional type-I and type-II superconductors). Here, by using the flux method, we have grown a high-quality SrBi3 single crystal. The GL parameter has been determined to be 1.01 close to the phase transition temperature, making SrBi3 an ideal platform to study the nontrivial magnetic properties in relatively low-κ superconductors. The counterintuitive paramagnetic Meissner effect (PME) has been studied in our sample, and no giant PME is observed. Our results may suggest that vortex–vortex interaction plays a less dominant role in determining the PME compared with, for example, pinning and surface configurations.

Domain walls in neutron P23 superfluids in neutron stars

We work out domain walls in neutron $^{3}P_{2}$ superfluids realized in the core of neutron stars. Adopting the Ginzburg-Landau (GL) theory as a bosonic low-energy effective theory, we consider configurations of domain walls interpolating ground states, i.e., the uniaxial nematic (UN), ${\mathrm{D}}_{2}$-biaxial nematic (${\mathrm{D}}_{2}$-BN), and ${\mathrm{D}}_{4}$-biaxial nematic $({\mathrm{D}}_{4}$-BN) phases in the presence of zero, small and large magnetic fields, respectively. We solve the Euler-Lagrange equation from the GL free energy density, and calculate surface energy densities of the domain walls. We find that one extra Nambu-Goldstone mode is localized in the vicinity of a domain wall in the UN phase while a U(1) symmetry restores in the vicinity of one type of domain wall in the ${\mathrm{D}}_{2}$-BN phase and all domain walls in the ${\mathrm{D}}_{4}$-BN phase. Considering a pile of domain walls in the neutron stars, we find that the most stable configurations are domain walls perpendicular to the magnetic fields piled up in the direction along the magnetic fields in the ${\mathrm{D}}_{2}$-BN and ${\mathrm{D}}_{4}$-BN phases. We estimate the energy released from the deconstruction of the domain walls in the edge of a neutron star, and show that it can reach an astrophysical scale such as glitches in neutron stars.

The homological projective dual of

We study the derived category of a complete intersection $X$ of bilinear divisors in the orbifold $\operatorname{Sym}^{2}\mathbb{P}(V)$. Our results are in the spirit of Kuznetsov’s theory of homological projective duality, and we describe a homological projective duality relation between $\operatorname{Sym}^{2}\mathbb{P}(V)$ and a category of modules over a sheaf of Clifford algebras on $\mathbb{P}(\operatorname{Sym}^{2}V^{\vee })$. The proof follows a recently developed strategy combining variation of geometric invariant theory (VGIT) stability and categories of global matrix factorisations. We begin by translating $D^{b}(X)$ into a derived category of factorisations on a Landau–Ginzburg (LG) model, and then apply VGIT to obtain a birational LG model. Finally, we interpret the derived factorisation category of the new LG model as a Clifford module category. In some cases we can compute this Clifford module category as the derived category of a variety. As a corollary we get a new proof of a result of Hosono and Takagi, which says that a certain pair of non-birational Calabi–Yau 3-folds have equivalent derived categories.

Enhanced Anharmonic Oscillations in Cu0.5Tl0.5Ba2(Ca2−yMgy)Cu3−xCdxO10−δ (y = 0, 1; x = 0, 1.5) Superconductors

Cu0.5Tl0.5Ba2Ca2Cu3O10−δ (undoped), Cu0.5Tl0.5Ba2(CaMg)Cu3O10−δ (Mg-doped), Cu0.5Tl0.5Ba2Ca2Cu1.5Cd1.5O10−δ (Cd-doped), and Cu0.5Tl0.5Ba2(CaMg)Cu1.5Cd1.5O10−δ (Cd/Mg-codoped) samples were synthesized by two-step solid-state reaction at 860°C to investigate the possible role of anharmonic oscillations of atoms in the mechanism of high critical temperature (Tc) superconductivity. The samples showed orthorhombic crystal structure with smaller and larger unit cell volume for the Mg- and Cd/Mg-codoped samples, respectively, compared with the undoped sample. Tc observed by resistivity measurements decreased in the Cd-doped samples, but the maximum suppression was observed in the Cd/Mg-codoped sample showing semiconductor behavior. Fourier-transform infrared (FTIR) absorption spectroscopy revealed hardening of apical oxygen modes on the incorporation of Mg atoms as compared with the undoped sample and similarly with the doping of Mg atoms in the Cd-doped sample, confirming the intrinsic inclusion of these elements in the final compound. Excess conductivity analysis revealed suppression in the coherence length (ξc(0)), interlayer coupling (J), phase relaxation time (τφ) of carriers, Fermi velocity (VF) of carriers, Ginzburg–Landau (GL) parameter κ, breaking energy (Ebreak), and magnetic field penetration depth (λp.d) in Cd-doped samples. The values of Bc0(T), Bc1(T), and Jc(0) increased in the Cd-doped samples, showing enhancement of flux-pinning characteristics. It is proposed that Cd doping at CuO2-planar site induces anharmonic oscillation in the solid-state medium, which suppresses the density of phonons and thereby the density of Cooper pairs and hence superconductivity. These studies emphasize the essential role of electron–phonon interactions in the mechanism of high-Tc superconductivity.

Controlled Vortex Formation at Nanostructured Superconductor/Ferromagnetic Junctions

Stability and transport properties of superconducting/insulating/ferromagnetic nanostructures are decisively affected by vortex formation in the superconductor. Herein, the emergence of such vortices due to finite size and geometric effects is studied using a Landau–Ginzburg approach coupled to the magnetic layer via its stray field. Numerical simulations based on the finite‐element method evidence that magnetic vortices can be induced and coupled to each others upon appropriate nanostructuring of the magnetic films. These findings are of immediate relevance to transport properties of such structures.

Fluctuation diamagnetic susceptibility in type-II superconductors under magnetic field

Strong fluctuation effects were found in both low- and high-field regimes by recent measurements of magnetization on [Formula: see text] (LCCO) single crystals. The low-field fluctuation diamagnetic susceptibility data could not be fitted by simple Gaussian fluctuation theory using the lowest Landau level (LLL) approximation because of the slightly nonlinear behavior around the mean-field transition temperature [Formula: see text]. Self-consistent calculation of fluctuation diamagnetic susceptibility in high-temperature superconductors, based on the Ginzburg–Landau (GL) two-dimensional model and including all Landau levels, is presented. Our results are valid for arbitrary values of the magnetic field not too close to [Formula: see text]. The results agree well with the experimental data in a wide region around [Formula: see text], including both below and above [Formula: see text].

Higher-genus wall-crossing in Landau–Ginzburg theory

For a Fermat quasi-homogeneous polynomial, we study the associated weighted Fan–Jarvis–Ruan–Witten theory with narrow insertions. We prove a wall-crossing formula in all genera via localization on a master space, which is constructed by introducing an additional tangent vector to the moduli problem. This is a Landau–Ginzburg theory analogue of the higher-genus quasi-map wall-crossing formula proved by Ciocan-Fontanine and Kim. It generalizes the genus-0 result by Ross–Ruan and the genus-1 result by Guo–Ross.

An-harmonic Oscillations and Superconductivity in (Cu0.5-xKxTl0.5)Ba2Ca2Cu3-y-z ZnyCdzO10-δ (x = 0, 0.25; y = z = 0, 0.25, 0.5, 0.75, 1) Samples

(Cu0.5-xKxTl0.5)Ba2Ca2Cu3-y-z ZnyCdzO10-δ (x = 0, 0.25; y = z = 0, 0.25, 0.5, 0.75, 1) samples are synthesized for the investigation of role of an-harmonic oscillations in the mechanism of high Tc superconductivity. In the conducting planes, the carrier density is enhanced by K doping at the charge reservoir layer (Cu0.5Tl0.5)Ba2O4-δ by synthesizing (Cu0.25K0.25Tl0.5)Ba2Ca2Cu3-y-zZnyCdzO10-δ (y = z = 0, 0.25, 0.5, 0.75, 1) samples. The (Cu0.5-xKxTl0.5)Ba2Ca2Cu3-y-z ZnyCdzO10-δ (x = 0, 0.25; y = z = 0, 0.25, 0.5, 0.75, 1) samples were prepared by employing two-step solid-state reaction method accomplished at 860 °C and understand their superconducting properties by resistivity measurements, X-ray diffraction analysis, and FTIR absorption measurements. The orthorhombic unit cell of our samples was confirmed via XRD analysis. The analysis also reflected the increase in c-axis length and the volume of the unit cell with the enhanced dopants (Cd and Zn) concentration. The suppression of Tc(onset) and Tc(R = 0) was found with the increasing concentration of Zn and Cd. An improvement in the Tc(onset) observed in samples doped by K that arises due to increase in the density of free carriers supplied by alkali atoms. With the increasing content of Cd and Zn, the unit cell exhibits the softening of Cu(1)-OA-Cu(2) and Tl-OA-Cu(2) apical oxygen mode and hardening of planar oxygen mode. From FIC analysis, the Tcmf and T* and various cross over temperature were shifted towards lower temperature with the enhanced Zn and Cd dopant concentration. The value of α determining the defect density also increases with the increasing dopant (Zn and Cd) concentration. The numerical values of different parameter like Bc0(T), Bc1(T), Jc(0), and Ebreak showing increasing trend but the phase relaxation time of the carriers τφ points out decreasing trend with the enhanced doping of Cd and Zn. Moreover, these parameters reflected inferior values in K-doped samples relative to K-undoped samples. The value of other parameter like coherence length ξc(0) along c-axis, interlayer coupling J, magnetic field penetration depth λp.d, the Ginzburg Landau (GL) parameter κ, and the Fermi velocity VF of the carriers decreases as doping of Zn and Cd enhanced. These parameters show superior values in K-doped samples relative to K-undoped samples due to increase in the density of free carriers supplied by K atoms. The negative values of real part of dielectric constant suppress in both K undoped and K doped samples with increasing concentration of Cd and Zn. The imaginary part of dielectric constant and ac conductivity showing suppression in their negative values in K undoped samples while showing increase in absolute values in K doped samples with increasing concentration of Cd and Zn.

Mirror pairs of Calabi–Yau threefolds from mirror pairs of quasi-Fano threefolds

We present a new construction of mirror pairs of Calabi–Yau manifolds by smoothing normal crossing varieties, consisting of two quasi-Fano manifolds. We introduce a notion of mirror pairs of quasi-Fano manifolds with anticanonical Calabi–Yau fibrations using recent conjectures about Landau–Ginzburg models. Utilizing this notion, we give pairs of normal crossing varieties and show that the pairs of smoothed Calabi–Yau manifolds satisfy the Hodge number relations of mirror symmetry. We consider quasi-Fano threefolds that are some blow-ups of Gorenstein toric Fano threefolds and build 6518 mirror pairs of Calabi–Yau threefolds, including 79 self-mirrors.

Lattices for Landau–Ginzburg orbifolds

We consider a pair consisting of an invertible polynomial and a finite abelian group of its symmetries. Berglund, Hubsch, and Henningson proposed a duality between such pairs giving rise to mirror symmetry. We define an orbifoldized signature for such a pair using the orbifoldized elliptic genus. In the case of three variables and based on the homological mirror symmetry picture, we introduce two integral lattices, a transcendental and an algebraic one. We show that these lattices have the same rank and that the signature of the transcendental one is the orbifoldized signature. Finally, we give some evidence that these lattices are interchanged under the duality of pairs.