Landau Energy Research Articles

Domain Dynamics Response to Polarization Switching in Relaxor Ferroelectrics.

Nanoscale polar regions, or nanodomains (NDs), are crucial for understanding the domain structure and high susceptibility of relaxors. However, unveiling the evolution and function of NDs during polarization switching at the microscopic level is of great challenge. The experimental in situ characterization of NDs under electric-field perturbations, and computational accurate prediction of the dipole switching within a sufficiently large supercell, are notoriously tricky and tedious. These difficulties hinder a full understanding of the link between micro domain dynamics and macro polarization switching. Herein, the real-time evolution of NDs at the nanoscale is observed and visualized during polarization switching in an exemplary relaxor system of Bi5- xLaxMg0.5Ti3.5O15. Two fundamentally different domain switching pathways and dynamic characteristics are revealed: one steep, bipolar-like switching between two degenerate polarization states; and another flat, multi-step switching process with a thermodynamically stable non-polar mesophase mediating the degenerate polarization states. The two are determined by the distinct Landau energy landscapes that are strongly dependent on the intrinsic domain configurations and interdomain interactions. This work bridges the gap between micro domain dynamics and macro polarization switching, providing a guiding principle for the strategic design and optimization of relaxors.

Ultrahigh Capacitive Energy Storage in a Heterogeneous Nanolayered Composite

AbstractFerroelectric polymers with robust electrical polarization have been extensively investigated for capacitive energy storage. However, their inherent ferroelectric hysteresis loss limits the discharged energy density and compromises energy efficiency. Here, a heterogeneous nanolayered composite of ferroelectric polymer poly(vinylidene fluoride‐trifluoroethylene) (P(VDF‐TrFE)) and Al2O3 is presented, which effectively mitigates ferroelectric hysteresis loss while maintaining high polarization and enhanced breakdown strength. Phase‐field simulations indicate that the polarization behaviors of the heterogeneous layered structure are jointly influenced by the thickness and dielectric constant of each component, which balances the electrical energy and Landau energy within the heterogeneous system. Guided by the theoretical simulations, optimized polarization behaviors are achieved with a significant reduction in remnant polarization and ferroelectric loss in the P(VDF‐TrFE)/Al2O3 composites through careful control of P(VDF‐TrFE) thickness at nanometer scale. Moreover, the presence of multiple interfaces in the layered composites leads to a remarkable enhancement in polarization and breakdown strength. Consequently, an ultrahigh energy density of about 108 J cm−3 is achieved with a high charge–discharge efficiency of exceeding 80%. This work not only presents a straightforward approach to modify the polarization behaviors of ferroelectric polymers but also demonstrates a promising strategy for developing high‐energy‐density polymer nanocomposites.

Enhancing piezoelectric coefficient and thermal stability in lead-free piezoceramics: insights at the atomic-scale

Given the highly temperature-sensitive nature of the polymorphic phase boundaries, attaining excellent piezoelectric coefficient with superior temperature stability in lead-free piezoceramics via direct compositional design remains a formidable challenge. We demonstrate the synergistic improvement of piezoelectric coefficient and thermal stability in lead-free piezoceramics via atomic-scale local ferroelectric structure design. Via modulation of the local Landau energy barrier at doping sites, we effectively mitigate fluctuations in piezoelectric d33. Our approach achieves an impressive d33 of ~430 pC/N with a minimal temperature fluctuation range (△d33 ~ 7%) across the room temperature to 100 °C in potassium sodium niobate ceramics. Further optimization through annealing extends this temperature up to 150 °C (△d33 ~ 8%) while maintaining a high d33 of ~380 pC/N, rivaling the performance of classic temperature stable lead zirconate titanate. This work establishes a framework for addressing the dilemma between high piezoelectric coefficient and inadequate temperature stability in lead-free piezoceramics.

Neutron dynamics in ultra-strong electromagnetic fields: an example model

Abstract This work is concerned with the relativistic quantum dynamics of a self-interacting neutron in the presence of an external ultra-strong electromagnetic (EM) field in a cylindrical inertial frame. We first regard the Dirac–Pauli (DP) Lagrangian to study the planar dynamics of a neutron polarized along the z-axis subjected to a confining external static EM field composed of a homogeneous magnetic field in the z-direction and a linear radial electric field in the polar plane. The corresponding discrete Landau energy levels are found. As a nonlinear (NL) example model, we introduce a 1-flavor Nambu Jona–Lasinio (NJL) mass term into the DP Lagrangian. The continuous ground-state Landau levels are determined. We readily obtain modified Maxwell’s equations associated with these levels. We consider a simple application of the model related to the dynamics of neutrons in the presence of strong-QED fields inside the surface of aligned neutron stars. We briefly comment on possible classical solitonic solutions of the model.

Superfine Nanodomain Engineering Unleashing Ferroelectricity in Incipient Ferroelectrics.

Incipient ferroelectrics have emerged as an attractive class of functional materials owing to their potential to be engineered for exotic ferroelectric behavior, holding great promise for expanding the ferroelectric family. However, thus far, their artificially engineered ferroelectricity has fallen far short of rivaling classic ferroelectrics. In this study, we address this challenge by developing a superfine nanodomain engineering strategy. By applying this approach to representative incipient ferroelectric of SrTiO3-based films, we achieve unprecedentedly strong ferroelectricity, not only surpassing previous records for incipient ferroelectrics but also being comparable to classic ferroelectrics. The remanent polarization of the thin film reaches up to 17.0 μC cm-2 with an ultrahigh Curie temperature of 973 K. Atomic-scale investigations elucidate the origin of this robust ferroelectricity in the emergent high-density superfine nanodomains spanning merely 3-10 unit cells. Combining experimental results with theoretical assessments, we unveil the underlying mechanism, where the intentionally introduced diluted foreign Fe element creates a deeper Landau energy well and promotes a short-range ordering of polarization. Our developed strategy significantly streamlines the design of unconventional ferroelectrics, providing a versatile pathway for exploring new and superior ferroelectric materials.

Error Bounds for Discrete Minimizers of the Ginzburg–Landau Energy in the High-\(\boldsymbol{\kappa }\) Regime

Error Bounds for Discrete Minimizers of the Ginzburg–Landau Energy in the High-\(\boldsymbol{\kappa }\) Regime

Orbital stability of the black soliton for the quintic Gross–Pitaevskii equation

In this work, a proof of the orbital stability of the black soliton solution of the quintic Gross–Pitaevskii equation in one spatial dimension is obtained. We first build and show explicitly black and dark soliton solutions and we prove that the corresponding Ginzburg–Landau energy is coercive around them by using some orthogonality conditions related to perturbations of the black and dark solitons. The existence of suitable perturbations around black and dark solitons satisfying the required orthogonality conditions is deduced from an implicit function theorem. In fact, these perturbations involve dark solitons with sufficiently small speeds and some proportionality factors arising from the explicit expression of their spatial derivative.

Understanding magnetoelectric switching in BiFeO3 thin films

In this work we use a phenomenological theory of ferroelectric switching in BiFeO3 thin films to uncover the mechanism of the two-step process that leads to the reversal of the weak magnetization of these materials. First, we introduce a realistic model of a BiFeO3 film, including the Landau energy of isolated domains as well as the constraints that account for the presence of the substrate and the multidomain configuration found experimentally. We use this model to obtain statistical information about the switching behavior—by running dynamical simulations based on the Landau-Khalatnikov time-evolution equation, including thermal fluctuations—and we thus identify the factors that drive the two-step polarization reversal observed in the experiments. Additionally, we apply our model to test potential strategies for optimizing the switching characteristics. Published by the American Physical Society 2024

Triply periodic minimal surfaces based topology optimization for the hydrodynamic and convective heat transfer

Triply periodic minimal surfaces (TPMS), possessing diverse and crucial properties for thermal convection analysis, hold significant promise for topology optimization in convective and hydrodynamic systems. This study aims to develop an innovative topology optimization method based on TPMS for channel shape design. We focus on maximizing heat dissipation and mass flux while maintaining a constant mean curvature. The channel structures undergo free evolution during the optimization process, resulting in efficient and intricate geometries based on the TPMS assumption. To incorporate TPMS properties, we modify the original energy formulation, which comprises kinetic energy, thermal energy, and Ginzburg–Landau energy. The governing system encompasses the phase field model, the Darcy–Stokes model, and the reaction–diffusion heat transfer model. The hydrodynamic response within the phase change structure is computed by solving the transient Darcy–Stokes equation augmented with a temperature-dependent diffusion term. To achieve second-order temporal and spatial accuracy, we employ the Crank–Nicolson method for the time scale and the central difference method for the spatial scale. Through the utilization of the Lagrange multiplier method, we establish the unconditional decrease of the discretized original energy. This implies that the proposed scheme can utilize a large time step. To verify the robustness of our proposed method, we conduct several numerical tests from both qualitative and quantitative perspectives. The results demonstrate the effectiveness of our method in enhancing heat and mass transfer capabilities.

Stability and convergence of relaxed scalar auxiliary variable schemes for Cahn–Hilliard systems with bounded mass source

Abstract The scalar auxiliary variable (SAV) approach of Shen et al. (2018), which presents a novel way to discretize a large class of gradient flows, has been extended and improved by many authors for general dissipative systems. In this work we consider a Cahn–Hilliard system with mass source that, for image processing and biological applications, may not admit a dissipative structure involving the Ginzburg–Landau energy. Hence, compared to previous works, the stability of SAV-discrete solutions for such systems is not immediate. We establish, with a bounded mass source, stability and convergence of time discrete solutions for a first-order relaxed SAV scheme in the sense of Jiang et al. (2022), and apply our ideas to Cahn–Hilliard systems with mass source appearing in diblock co-polymer phase separation, tumor growth, image inpainting, and segmentation.

The Ginzburg–Landau energy with a pinning term oscillating faster than the coherence length

The aim of this article is to study the magnetic Ginzburg–Landau functional with an oscillating pinning term. We consider here oscillations of the pinning term that are much faster than the coherence length \varepsilon>0 , which is also the inverse of the Ginzburg–Landau parameter. We study both the case of a periodic potential and of a random stationary ergodic one. We prove that we can reduce the study of the problem to the case where the pinning term is replaced by its average in the periodic case and by its expectation with respect to the random parameter in the random case. In order to do that, we use a decoupling of the energy (detailed in Lassoued and Mironescu’s 1999 paper) that leads us to the study of the convergence of a scalar positive minimizer of the Ginzburg–Landau energy with pinning term and with homogeneous Neumann boundary conditions. We prove uniform convergence of this minimizer towards the mean value of the pinning term by using a blowup argument and a Liouville-type result for non-vanishing entire solutions of the real Ginzburg–Landau/ Allen–Cahn equation, due to the results of Farina (2003).

Electromagnetism of one-component plasmas of massless fermions

We present a theoretical study of two- and three-dimensional massless Dirac one-component plasmas embedded in a constant uniform magnetic field. We determine the wavefunctions and Landau energy levels of a massless Dirac fermion in a constant magnetic field. On this basis we consider magnetism of Fermi fluids of massless charged particles. We show that such a three-dimensional Dirac plasma consisting of fermions with the same helicity has its own magnetic moment. We also consider the limit of strong magnetic fields and investigate the De Haas–van Alphen effect. We derive the Kubo formula for the electrical conductivity tensor of massless Dirac plasmas and consider the Shubnikov–de Haas effect. In addition, we propose a model of the static conductivity tensor and employ the matrix version of the classical method of moments to derive a Drude-like formula for the dynamic conductivity tensor for massless Dirac plasmas. We find that the electrical conductivity tensor for Dirac fermions with the right helicity is not isotropic in the plane perpendicular to the magnetic field.

Asymptotic Stability for Diffusion with Dynamic Boundary Reaction from Ginzburg–Landau Energy

Asymptotic Stability for Diffusion with Dynamic Boundary Reaction from Ginzburg–Landau Energy

On minimizers of the 2D Ginzburg–Landau energy with tangential anchoring

We analyze Ginzburg–Landau minimization problems in two dimensions with either a “strong or weak” tangential boundary condition. These problems are motivated by experiments in liquid crystals with boundary defects. The imposition of classical boundary conditions on a liquid crystal surface is referred to as “strong anchoring”, while “weak anchoring” refers to the inclusion of boundary energy terms. In the singular limit when the correlation length tends to zero, we show that boundary defects will be observed for weak anchoring, while both boundary and interior vortices are possible for strong anchoring.

COMPACTNESS AND STRUCTURE OF ZERO-STATES FOR UNORIENTED AVILES–GIGA FUNCTIONALS

AbstractMotivated by some models of pattern formation involving an unoriented director field in the plane, we study a family of unoriented counterparts to the Aviles–Giga functional. We introduce a nonlinear $\operatorname {\mathrm {curl}}$ operator for such unoriented vector fields as well as a family of even entropies which we call ‘trigonometric entropies’. Using these tools, we show two main theorems which parallel some results in the literature on the classical Aviles–Giga energy. The first is a compactness result for sequences of configurations with uniformly bounded energies. The second is a complete characterization of zero-states, that is, the limit configurations when the energies go to 0. These are Lipschitz continuous away from a locally finite set of points, near which they form either a vortex pattern or a disclination with degree 1/2. The proof is based on a combination of regularity theory together with techniques coming from the study of the Ginzburg–Landau energy. Our methods provide alternative proofs in the classical Aviles–Giga context.

New magneto-polaron resonances in a monolayer of a transition metal dichalcogenide

Transition metal dichalcogenide (TMD) semiconductors are two-dimensional materials with great potential for the future of nano-optics and nano-optoelectronics as well as the rich and exciting development of basic research. The influence of an external magnetic field on a TMD monolayer raises a new question: to unveil the behavior of the magneto-polaron resonances (MPRs) associated with the phonon symmetry inherent in the system. It is shown that the renormalized Landau energy levels are modified by the interplay of the long-range Pekar–Fröhlich (PF) and short-range deformation potential (DP) interactions. This leads to a new series of MPRs involving the optical phonons at the center of the Brillouin zone. The coupling of the two Landau levels with the LO and A_1 optical phonon modes provokes resonant splittings of double avoided-crossing levels giving rise to three excitation branches. This effect appears as bigger energy gaps at the anticrossing points in the renormalized Landau levels. To explore the interplay between the MPRs, the electron-phonon interactions (PF and DP) and the couplings between adjacent Landau levels, a full Green’s function treatment for the evaluation of the energy and its life-time broadening is developed. A generalization of the two-level approach is performed for the description of the new MPR branches. The obtained results are a guideline for the magneto-optical experiments in TMDs, where three MPR peaks should be observable.

QCD sum rule analysis of heavy quarkonium states in magnetized matter: Effects of magnetic and inverse magnetic catalysis

In-medium masses of the $1S$ and $1P$ states of heavy quarkonia are investigated in the magnetized asymmetric nuclear medium, accounting for the Dirac sea effects, using a combined approach of chiral effective model and QCD sum rule method. Masses are calculated from the in-medium scalar and twist-2 gluon condensates, calculated within the chiral model. The gluon condensate is simulated through the scalar dilaton field, $\ensuremath{\chi}$ introduced in the model through a scale-invariance breaking logarithmic potential. Contribution of the Dirac sea is incorporated through the nucleonic tadpole diagrams. Treating the scalar fields as classical, the dilaton field, $\ensuremath{\chi}$, the isoscalar nonstrange $\ensuremath{\sigma}(\ensuremath{\sim}(⟨\overline{u}u⟩+⟨\overline{d}d⟩))$, strange $\ensuremath{\zeta}(\ensuremath{\sim}⟨\overline{s}s⟩)$ and isovector $\ensuremath{\delta}(\ensuremath{\sim}(⟨\overline{u}u⟩\ensuremath{-}⟨\overline{d}d⟩))$ fields, are obtained by solving their coupled equations of motion as derived from the chiral model Lagrangian. The effects of magnetic field are incorporated through the Dirac sea as well as the Landau energy levels of the protons, and the anomalous magnetic moments of the nucleons. The scalar fields modify appreciably with magnetic field due to the Dirac sea contribution. In-medium masses of the charmonium and bottomonium ground states are observed to have significant modifications with magnetic field due to the effects of (inverse) magnetic catalysis. In presence of an external magnetic field, there is mixing between the longitudinal component of the vector and the pseudoscalar mesons (PV mixing) in both quarkonia sectors, leading to a rise (drop) of the masses of $J/{\ensuremath{\psi}}^{||}({\ensuremath{\eta}}_{c})$ and ${\mathrm{\ensuremath{\Upsilon}}}^{||}(1S)({\ensuremath{\eta}}_{b})$ states. These might show in the experimental observables, e.g., the dilepton spectra in the noncentral, ultrarelativistic heavy ion collision experiments at RHIC and LHC, where the produced magnetic field is huge.

Dirac spectroscopy of strongly correlated phases in twisted trilayer graphene.

Magic-angle twisted trilayer graphene (MATTG) hosts flat electronic bands, and exhibits correlated quantum phases with electrical tunability. In this work, we demonstrate a spectroscopy technique that allows for dissociation of intertwined bands and quantification of the energy gaps and Chern numbers C of the correlated states in MATTG by driving band crossings between Dirac cone Landau levels and energy gaps in the flat bands. We uncover hard correlated gaps with C = 0 at integer moiré unit cell fillings of ν = 2 and 3 and reveal charge density wave states originating from van Hove singularities at fractional fillings ν = 5/3 and 11/3. In addition, we demonstrate displacement-field-driven first-order phase transitions at charge neutrality and ν = 2, which are consistent with a theoretical strong-coupling analysis, implying C2T symmetry breaking. Overall, these properties establish a diverse electrically tunable phase diagram of MATTG and provide an avenue for investigating other related systems hosting both steep and flat bands.

Effect of Disparity in Self Dispersion Interactions on Phase Behaviors of Molten A-b-B Diblock Copolymers.

Phase behaviors of molten A-b-B diblock copolymers with disparity in self dispersion interactions are revisited here. A free energy functional is obtained for the corresponding Gaussian copolymers under the influence of effective interactions originating in the localized excess equation of state. The Landau free energy expansion is then formulated as a series in powers of A and B density fluctuations up to 4th order. An alternative and equivalent Landau energy is also provided through the transformation of the order parameters to the fluctuations in block density difference and free volume fraction. The effective Flory χ is elicited from its quadratic term as the sum of the conventional enthalpic χH and the entropic χS that is related to energetic asymmetry mediated by copolymer bulk modulus. It is shown that the cubic term is balanced with Gaussian cubic vertex coefficients in corporation with energetics to yield a critical point at a composition rich in a component with stronger self interactions. The full phase diagrams with classical mesophases are given for the copolymers exhibiting ordering upon cooling and also for others revealing ordering reversely upon heating. These contrasting temperature responses, along with the skewness of phase boundaries, are discussed in relation to χH and χS. The pressure dependence of their ordering transitions is either barotropic or baroplastic; or anomalously exhibits anomalously both at different stages. These actions are all explained by the opposite responses of χH and χS to pressure.

Open bottom mesons in magnetized matter: Effects of (inverse) magnetic catalysis

In-medium masses of the pseudoscalar and vector open bottom mesons ([Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text]) are studied in the magnetized nuclear matter by considering the effects of Dirac sea, within the chiral effective model. The mass modifications arise due to the interactions of the open bottom mesons with the nucleons and the scalar mesons, calculated in terms of the scalar and number densities of the nucleons and the scalar fields fluctuations, within the chiral model. The effects of the magnetized Dirac sea lead to the considerable changes in the scalar fields with increasing magnetic field, which are related to the condensates of light quark–antiquark pairs. There is observed to be a (reduction) enhancement in the QCD light quark condensates with rising magnetic field, a phenomenon called (inverse) magnetic catalysis. The contribution of the magnetic field on the Fermi sea of nucleons is also taken into account through protons Landau energy levels and anomalous magnetic moments (AMMs) of the nucleons. The additional contribution of the lowest Landau level for the charged mesons is taken into account. In the presence of an external magnetic field, the spin–magnetic field interaction between the longitudinal component of the vector mesons and the pseudoscalar mesons ([Formula: see text], [Formula: see text] and [Formula: see text]) are studied, which lead to level repulsion between their masses with increasing magnetic field. The magnetic fields are observed to have significant contribution on the masses of the open bottom mesons through the Dirac sea effects taking into account the AMMs of nucleons. In vacuum, appreciable medium modifications are obtained due to the magnetized Dirac sea contribution with nonzero nucleonic AMMs.