Papers

Spin inertia has been demonstrated to give rise to high-frequency nutational excitations beyond the conventional low-frequency precessional modes. Here, we demonstrate that the hybridization between precessional and nutational magnons may give rise to topological phenomena in the spin-wave spectrum. This hybridization requires the presence of interactions breaking angular-momentum conservation, such as the pseudodipolar interaction. We show on the example of a honeycomb ferromagnet how topological gaps open between the precessional and nutational bands that host chiral edge states in slab geometries. Our work establishes a theoretical foundation for exploring inertial spin dynamics as a new route to engineer topological phases in magnetic materials.

Nonequilibrium conditions fundamentally change how systems undergo phase separation. In lattice gases with attractive interactions under temperature gradients, particles have been shown to form periodic patterns and steady convective currents; however, a clear theoretical explanation of this convective phase separation is still missing. Here, we present a dynamical mean-field model that describes the mechanism behind this convective phase separation. Using linear stability analysis, we show that the transition from a uniform state to a periodic pattern is driven by the emergence of a dominant unstable mode. Numerical simulations confirm the predicted phase diagram and demonstrate that these convective currents are a robust feature of the steady state, appearing regardless of the initial conditions. These results provide a direct approach for understanding how temperature gradients drive the formation of steady-state convective patterns.

Photoemission orbital tomography (POT) is a powerful tool for investigating the orbitals and electronic band structure of oriented layers of organic molecules. In many cases, POT allows conclusions to be drawn regarding the geometric structure, but so far it has been mainly applied to (sub)monolayers and rarely to bilayers, raising the question of whether POT can also provide structure information for thicker films. Here, we use POT to analyze the band dispersion in up to eight layers of $\alpha$-sexithiophene (6T) adsorbed on Cu(110)-p($2\times1$)O. This linear oligomer turns out to be a textbook example that exemplifies the concepts of intra- and intermolecular band dispersion in molecules. Moreover, the rich band and orbital structure information available from POT for this system enables us to trace subtle changes in the crystal structure as a function of layer thickness. Specifically, we find that the periodicity of an intermolecular band changes with film thickness, revealing an increase of the intralayer distance between the molecules with the number of layers. At the same time, the momentum distribution of photoemission from the highest occupied molecular orbital of 6T discloses a decrease of the molecular tilt angle. Following the evolution of tilt angle and lattice constant with layer thickness, we observe – purely based on electronic structure data – that the surface-templated monolayer structure relaxes into the structure of bulk 6T crystals. The experimental findings agree well with the results of density functional theory calculations.

Tensor networks provide discrete representations of quantum many-body systems, yet their precise connection to continuum field theories remains relatively poorly understood. Invoking a notion of typicality, we develop a continuum description for random ensembles of two-dimensional fermionic matchgate tensor networks with spatially fluctuating parameters. As a diagnostic of the resulting universal physics, we analyze disorder-averaged moments of fermionic two-point functions, both in flat geometry and on a hyperbolic disk, where curvature reshapes their long-distance structure. We show that disorder drives universal long-distance behavior governed by a nonlinear sigma-model of symmetry class D with a topological term, placing random matchgate networks in direct correspondence with the thermal quantum Hall problem. The resulting phase structure includes localized phases, quantum Hall criticality, and a robust thermal metal with diffusive correlations and spontaneous replica-symmetry breaking. Weak non-Gaussian deformations reduce the symmetry to discrete permutations, generate a mass for the Goldstone modes, and suppress long-range correlations. In this way, typicality offers a route from ensembles of discrete tensor networks to continuum quantum field theories.

We study thin films that host coexisting collinear $d$-wave altermagnetic and superconducting orders in the presence of an external magnetic field that fully penetrates the films. We use the Ginzburg-Landau functional to analyze the response of the films to magnetic fields and an in-plane supercurrent. We demonstrate that the interplay between superconductivity and altermagnetism induces characteristic fourfold anisotropies in the critical temperature, parallel critical field, and critical current density of the films. These results establish experimentally accessible signatures of altermagnetism in superconducting films and in superconductor/altermagnetic insulator heterostructures.

We provide a framework to theoretically describe long-range energy transfer in single and twisted two-dimensional hyperbolic slabs. We demonstrate that phonon polaritons (PhPs, quantum superpositions of photons and lattice vibrations in polar dielectrics) can mediate and enhance room-temperature energy transfer at ranges far exceeding those of conventional mid-infrared (MIR) platforms, and with extreme directionality. This is because the dipole-dipole interaction potential energy diverges along the asymptotes of the real-space hyperbolic opening angle. Our findings allow us to extend classical and quantum interactions between dipoles, typically strictly confined to the near-field, beyond several free-space MIR wavelengths. We use $\alpha$-MoO$_3$ as a representative material, but this mechanism is not limited to the MIR: it is general to anisotropic media across the whole electromagnetic spectrum.

Amorphous oxide semiconductors (AOSs) have recently gained attention as a promising channel material of back-end-of-line (BEOL)-compatible transistors for monolithic three-dimensional (3D) integrations. However, the degradation in device performance resulting from the high trap densities in AOS, compared to conventional crystalline channel materials, has remained an intractable issue. We introduce the negative-capacitance (NC) operation into the AOS-based transistors. Negative-capacitance field-effect transistors (NCFETs) have been proposed for low-power devices, enabling sub-60 mV/decade subthreshold swing SS induced by a ferroelectric layer. In this work, we develop an AOS NCFET model to investigate the influence of traps within the channel on the steep-slope operation. It is revealed that as the trap density of the channel increases, SS of the MOSFET increases, while the SS of the NCFET decreases. The physical interpretation for steep SS is attributed to the fact that the trapped charges enhance the negative potential drop of the NC layer, enabling the abrupt device switching. This finding will accelerate the development of BEOL transistors and other applications based on the AOS materials in conjunction with the NC effect.

Thermodynamics establishes that information acquired through measurement can be converted into work, as exemplified by Maxwell's demon and Szilard engines. Most experimental realizations of information engines, however, implicitly assume Markovian environments, in which information exchanged with the surroundings is irreversibly lost. Many physical systems instead exhibit environmental memory, with hidden degrees of freedom retaining correlations with the system's past and giving rise to non Markovian dynamics. Whether and how such concealed memory can be harnessed as a thermodynamic resource has remained an open question. Here we experimentally demonstrate work extraction from environmental memory. Using time resolved measurements on an optically trapped Brownian particle in equilibrium, we implement a time delayed double measurement protocol that retrieves information via backflow from hidden bath degrees of freedom. We show that this information backflow alters relaxation dynamics, can be quantified independently of initial state effects, and when appropriately exploited enhances work extraction. Notably, we identify regimes in which the extracted work exceeds the energy stored in the observable degree of freedom alone. Our results establish environmental memory as an experimentally accessible thermodynamic resource and reveal how non Markovian dynamics can be systematically explored to improve the performance of information engines operating in time-correlated environments.

The figure of merit $\rho \lambda$ the product of resistivity and mean free path (MFP) evaluated from first-principles calculations, is widely adopted to screen promising interconnect metals with high electrical conductivity at ultranarrow dimensions. However, the $\rho \lambda$ has been calculated without addressing the validity of the assumption that the MFP is independent of the wavevector $\mathbf{k}$. Here, we assess the validity of the constant MFP approximation, by estimating the $\mathbf{k}$-dependent MFPs for (an)isotropic elemental metals, with explicit treatment of electron-phonon interactions. Additionally, we verify the validity of the constant relaxation time approximation (CRTA) for resistivity calculations. We show that both the constant MFP approximation and CRTA are reasonable even for highly anisotropic Fermi surfaces. Our results support the practical use of those approximations in transport studies, where explicit electron-phonon calculations are not feasible.

Lattice vibrations carrying angular momentum, known as chiral phonons, have emerged as a promising route to control and understand complex material properties, yet their deterministic manipulation remains largely unexplored. Here we demonstrate electric-field switching of phonon angular momentum in the technologically relevant ferroelectric BaTiO3. Using circularly dichroic resonant inelastic X-ray scattering (CD-RIXS) at the oxygen K edge, we directly probe the phonon angular momentum and compare the measured dichroism with first-principles predictions of phonon-mode chirality. We find excellent agreement, revealing a momentum-dependent circular-dichroism contrast that exhibits a reversible gyroelectric effect, stable for at least 15 hours. Our results establish a robust mechanism for non-volatile control of chiral phonons and point towards new opportunities for phonon-based information and energy technologies.

Predictive coding graphs (PCGs) are a recently introduced generalization to predictive coding networks, a neuroscience-inspired probabilistic latent variable model. Here, we prove how PCGs define a mathematical superset of feedforward artificial neural networks (multilayer perceptrons). This positions PCNs more strongly within contemporary machine learning (ML), and reinforces earlier proposals to study the use of non-hierarchical neural networks for ML tasks, and more generally the notion of topology in neural networks.

The chiral material BeAu was recently identified as a multiband type-I superconductor with a critical temperature of 3.2 K. As a member of the B20 crystal family (space group $P2_13$), its band structure hosts multifold fermions at high-symmetry points, unpaired Weyl points and even nodal surfaces. This renders BeAu an appealing system to investigate the interplay between superconductivity and topology. Here we present a comprehensive first-principles analysis of BeAu's electronic structure focusing on its Fermi surface's topology and the implications for superconductivity. Together with the presence of four- and six-fold fermions at high-symmetry points, we identify several additional isolated Weyl points near the Fermi level. We also determine the associated topological edge states – the surface Fermi arcs. Computing the Chern number associated to different Fermi surface sheets, we show that BeAu harbors a $\nu = 4$ topological superconducting phase in the presence of $s$-wave pairing of alternating sign ($s_\pm$ pairing). Notably, we also identify a Fermi surface with a Chern number of +6; the highest value reported to date. Finally, our analysis reveals strong inhomogeneity in the orbital character of electronic states at the Fermi level, suggesting a link to the observed multigap superconductivity.

We investigate a deformable spin-1/2 Ising chain subjected to either a longitudinal or a transverse magnetic field, which incorporates a magnetoelastic coupling linearly dependent on a lattice distortion parameter. Within the harmonic and static adiabatic approximations, the variational Gibbs free energy is evaluated exactly using transfer-matrix and Jordan-Wigner fermionization techniques and then minimized self-consistently with respect to the lattice distortion parameter. This approach enables a unified description of magnetic and elastic properties including the magnetization, magnetic susceptibility, lattice distortion, inverse compressibility, and relative change in the sound velocity. In a longitudinal magnetic field, the deformable Ising chain displays a line of discontinuous thermal phase transitions terminating at a critical point. The discontinuous transitions are accompanied by metastable states, which give rise to a hysteresis loop at low temperatures. In contrast, the deformable Ising chain in a transverse field undergoes exclusively a continuous quantum phase transition at zero temperature with no indication of thermal phase transitions. The magnetic susceptibility and inverse compressibility exhibit cusp- and dip-like anomalies at discontinuous phase transitions, while a diverging susceptibility and vanishing inverse compressibility characterize the continuous phase transitions. An elastic softening of the deformable chain near thermal and quantum phase transitions manifest itself also through a significant sound attenuation.

We use a direct phase-resolved optical technique to study the coherence of spin waves (SWs) that are driven by surface acoustic waves (SAWs) via resonant magnetoelastic coupling. For this, we employ a piezoelectric lithium tantalate (LiTaO$_{3}$) substrate, equipped with micropatterned interdigital transducers for SAW excitation, which interact with SWs in a 5 nm thin and 20 $\mu$m wide Co$_{40}$Fe$_{40}$B$_{20}$-waveguide. We detect the SAW and the SW using a phase-locked micro-focused optical polarization detection experiment and use the characteristic polarization dependence to separate the SAW and SW signals. Our measurements directly image the resonant and coherent excitation of the SW by the SAW.

Using tools from network theory, we analyze the organization of a MYH9-oriented drug-like library in chemical space using a multi-descriptor framework. The dataset is drawn from ZINC, a publicly available database of commercially accessible compounds curated for virtual screening and drug discovery. Starting from 6004 molecules, preprocessing yields 5000 structurally valid and descriptor-complete compounds. Similarity is defined via Tanimoto distance on Morgan fingerprints and single-descriptor distances for xLogP, HBD, HBA, molecular weight, and rotatable bonds. For each representation, we construct k-nearest-neighbor networks and identify communities using the Louvain-Leiden algorithm. All networks exhibit highly significant modularity (Q=0.91-0.99) relative to degree-preserving null models, demonstrating pronounced nonrandom chemical organization across descriptors. Cross-descriptor robustness is quantified through a co-clustering matrix over 1.25 X 10^7 molecular pairs, measuring how consistently compound pairs co-occur within the same community across descriptor-specific networks. Although most pairs show limited agreement, a sparse high-consensus core emerges, highlighting the complementarity of the descriptors. Minimum spanning trees derived from structural and consensus similarities reveal distinct backbone topologies: a scaffold-driven, sparse structure versus a compact, hub-rich consensus network. Betweenness centrality on these backbones identifies compounds that are both structurally central and descriptor-balanced. These results provide a statistically validated network representation of chemical space and a principled strategy to extract consensus-stable compounds for downstream screening.

We study the periodic dynamics of a spin-one chain driven using a square-pulse protocol with amplitude $Q_0$ and frequency $\omega_D$. The Hamiltonian of the spin chain hosts a thermodynamically large number of $Z_2$-valued conserved quantities $W_{\ell}$ on the links $\ell$. This allows us to study the Floquet dynamics of this chain within a given sector with fixed values of $W_{\ell}$. For the sector with all $W_{\ell}=1$, we find signatures of quantum many-body scar states for $\hbar \omega_D \gg Q_0$; they lead to oscillatory dynamics and fidelity revival for specific initial states. Upon lowering $\omega_D$, we find an ergodic regime exhibiting fast thermalization consistent with the prediction of the (Floquet) eigenstate thermalization hypothesis. In addition, we identify special drive frequencies $\omega_n^{\ast}= Q_0/(2n \hbar)$ (where $n = 1, 2, 3, \cdots$) at which the Floquet Hamiltonian exhibits prethermal strong Hilbert space fragmentation (HSF) with the largest fragment being ergodic; in contrast, a weak HSF is found at $\omega'_n= Q_0/[\hbar(2n+1)]$ (where $n = 0, 1, 2, \cdots$). We also study the sector with $W_{\ell} =\{\cdots 1,1,-1,1,1,-1 \cdots \}$ which shows strong HSF at $\omega_n^{\ast}$ but no fragmentation at $\omega'_n$. Our analysis indicates that the strong HSF in this sector harbors an integrable largest fragment. We provide numerical support for our analytical and perturbative results using exact-diagonalization (ED) studies on finite chains of length $L\le 24$. Our numerical results for entanglement entropy, fidelity, and correlation functions of the driven chain provide definitive signatures of prethermal strong HSF for both sectors.

We investigate stochastic resonance (SR) in an ensemble of coupled overdamped bistable oscillators driven by colored noise. The networks incorporate the weighted contributions of both pairwise coupling and 2-simplex coupling. Our findings show that these higher-order interactions further exacerbate the suppression effect of colored noise on SR, reducing the peak of resonance curves and shifting the optimal noise intensity toward higher values. To clarify the underlying mechanism, we establish a close connection between SR and the four-stage variation in network synchronization level. Specially, the synchronization extremes explain the effect of higher-order coupling and colored noise on SR. Our analysis reveals that higher-order interactions do not reverse, but primarily promote the spatial propagation of suppression effects due to colored noise.

The existence of a pseudogap in unitary Fermi gases has recently been established and measured experimentally [Li et al., Nature 626, 288 (2024)]. This lends strong support for the pairing origin as the mechanism of the pseudogap in Fermi superfluids. Here we present a spectral study of unitary Fermi gases, and show how the data can be understood quantitatively, when compared with theoretically calculated momentum-resolved rf or microwave spectra, and the pseudogap extracted from the spectra. We use an iterative treatment of the fermion self energy and hence the spectral function, beyond previous pseudogap approximation, based on a pairing fluctuation theory that incorporates both particle-particle and particle-hole T matrices, with self-consistent self energy feedback. Our results not only provide a microscopic explanation of the experimental data but also strengthen the support for both the pairing-induced pseudogap physics and the pairing fluctuation theory of Fermi superfluidity.

Identifying two-dimensional heterostructures with exceptional electronic and optical properties remains an active area of research in advanced optoelectronics. Here, we present a comprehensive first-principles investigation of the electronic, optical, and excitonic properties of a MoTe2/CrSBr van der Waals heterostructure using density functional theory combined with fully relativistic GW and Bethe-Salpeter equation calculations. The close lattice matching between the two monolayers enables the formation of stable heterobilayers with two inequivalent interfaces (Te-S and Te-Br) arising from the Janus nature of CrSBr. Both interfaces are dynamically and thermally stable and exhibit type-II band alignment with a direct quasiparticle gap, promoting efficient spatial separation of electrons and holes. The heterostructure hosts interlayer excitons with lifetimes 18-45 ps significantly longer than those of the intralayer excitons in the isolated MoTe2, 3.6 ps, and CrSBr, 8.1 ps, monolayers. Moreover, the optical gap, exciton binding energy, and exciton lifetime of the heterostructure are strongly modulated by the built-in electric field associated with the Janus layer. These results establish the MoTe2/CrSBr heterostructure as a versatile platform for engineering long-lived interlayer excitons and highlight its potential for next-generation optoelectronic and light-harvesting applications.

Neutron and X-ray reflectometry are important methods for studying thin multilayer systems. The Parratt method and the method of characteristic matrices, also referred to as transfer matrices, are used for simulation, evaluation of experimental results, and designing optical systems, like mirrors. The Parratt method had been derived for isotropic systems. The method of characteristic matrices can also handle anisotropic problems, but it is burdened with numerical instabilities, which may arise in the case of thick samples at grazing angle incidence. In this paper, we derive a generalized Parratt method applicable to anisotropic systems. Furthermore, as we show, this is devoid of the numerical instabilities arising in the method of characteristic matrices. We derive formulae for both reflectivity and transmissivity. The stability of the new approach is demonstrated by comparing calculated results obtained via different methods. The problem of rough interfaces is also addressed, and the results gained by different approximations for some systems are compared.

Absolute negative mobility (ANM) is one of the most paradoxical transport phenomena in which a setup moves on average in a direction opposite to the applied force. The simplest system exhibiting this effect in minimal one-dimensional dynamics involves an inertial particle subjected to a constant bias while dwelling in a nonlinear, symmetric periodic potential in a nonequilibrium, nonstationary state generated by external driving. The necessity of inertia poses a significant conceptual barrier in predicting the ANM in a microscopic world of soft and living matter such as biological cells. In this work, we solve a two-decade old puzzle and demonstrate that none of the previously thought factors required for this effect are decisive. We show that the ANM may occur in a system composed of an overdamped particle in a piecewise linear symmetric periodic potential in an equilibrium state, provided that it is additionally driven by active fluctuations in the form of white Poisson shot noise. Our result may help to explain exotic transport behaviour emerging in biological cells where dynamics is typically overdamped and assisted by active fluctuations derived from various metabolic activities. It can also be exploited for effective separation strategies in a microscopic world, thus transforming fluctuations from a nuisance into a functional resource.

Topological insulator field-effect transistors (TIFETs) built on 2-D quantum spin Hall insulators are being considered as advanced logic transistors due to their potentially superior performance originating from the dissipationless edge transport. This paper presents a device modeling based on the tight-binding model and the nonequilibrium Green's function formalism to simulate the current-voltage characteristics of the TIFETs. We then use the device simulator to demonstrate the effect of channel length on device performance. The device modeling will not only enable a direct estimation of TIFET performance but also shed light on the nontraditional switching operation via the topological phase transition.

The strong-interaction functionals $W_\infty[n]$ and ${W'}_\infty[n]$ play an important role in the adiabatic-connection method of Density Functional Theory. The strictly-correlated electron approach can be used to exactly compute these functionals, yet calculations are computationally very expensive even for small electronic systems, and thus semilocal approximations have been proposed. In this work we develop a meta-generalized gradient approximation (meta-GGA) model for the strong-interaction functionals, enhanced point-and-charge (ePC), constructed from exact constraints. In particular, the ePC restores the second-order gradient expansion of the PC model, that is relevant for the equilibrium properties of Wigner crystals, and ensures the non-negativity of ${W'}_\infty[n]$. We assess the ePC model for atoms and various model systems: Hooke's atoms, two-electron exponential densities, s- and p-hydrogenic shells, quasi-two-dimensional infinite barrier model, perturbed uniform electron gas and H$_2$ dissociation. We prove a good overall accuracy of the ePC model, that achieves a broader applicability than any previous semilocal models.

Spectroscopy is a central pillar of materials characterization, providing useful information on properties like structure, composition, or excited state dynamics of a system. However, many spectroscopic techniques present challenges in the development of interpretable, performant, and reliable supervised learning models due to the wide range of possible nonlinear correlations that can exist between the signal and the response variable (target) of interest. Here, we present Spectra-Scope, an open-source AutoML framework for automatic characterization of material properties from spectroscopy data using interpretable machine learning (ML) models. The software is implemented in Python and a no-code web application. It comprises tools for data preprocessing, nonlinear feature extraction, machine learning model training, and feature selection. Users can easily train different types of simple, interpretable ML models on a set of feature transformations quickly and with modest computational resources. In this work, we outline the methods of Spectra-Scope and its effectiveness across diverse datasets, with applications to materials and agricultural spectroscopy data. We show that Spectra-Scope can reproduce performance of comparable models in the literature, and highlight how our emphasis on interpretability can be used to rationalize the behavior of individual models and understand the physical processes behind spectral features.

We propose a dynamical scaling analysis improved by a deep learning approach. While Gaussian process regression has been widely employed for estimating scaling parameters, its computational cost for parameter optimization becomes a limitation in dynamical scaling analysis, where large datasets are involved. In contrast, the present method employs a neural network, which significantly reduces the computational cost and enables the use of the entire dataset that was inaccessible with Gaussian process regression. We applied the method to the 2D Ising model and the 2D 3-state Potts model, achieving higher accuracy and computational efficiency than conventional approaches.

The emergence and decline of democratic systems worldwide raises fundamental questions about the dynamics of political change. Contrary to the idea of a stable endpoint of liberal democracy, recent backsliding towards less democratic regimes highlights the non-stationary nature of regime evolution. Here, we analyse the historical trajectories of countries within a two-dimensional regime space derived from the principal components of the Varieties of Democracy dataset. We observe weakly non-ergodic dynamics unfolding in an effective landscape characterised by sparse and shifting basins of stability. Step sizes and sojourn times characterising this dynamics follow heavy-tailed distributions near the critical regime, in which mean values appear to diverge. These facts point to the intermittent and heterogeneous nature of the regime change dynamics. A continuous time random walk model reproduces the dynamics of the three most recent decades with remarkable accuracy. Together, these results suggest that some aspects of political regime evolution follow universal stochastic principles, while remaining punctuated by unique historical pathways.

We propose a new classification of magnetic textures from the viewpoint of differential geometry. Magnetic textures are conventionally classified into collinear, coplanar, and noncoplanar magnets. These classes are typically characterized by the vector spin chirality (VSC) and the scalar spin chirality (SSC), which indicate noncollinearity and noncoplanarity, respectively. However, this conventional classification is incomplete: in particular, noncoplanar textures cannot be fully characterized by the SSC alone, as exemplified by conical magnets. To refine this classification, we analyze the curves and surfaces traced by spins in real space using differential geometry and introduce two novel scalar spin chiralities that properly characterize noncoplanarity: the geodesic scalar spin chirality and the torsional scalar spin chirality. These quantities are directly connected to differential geometry: the former reflects the geodesic curvature while the latter is related to the torsion. Based on these chiralities, we identify three distinct classes of noncoplanar magnetic textures. Furthermore, analogous to the roles of the VSC and the conventional SSC in emergent electrodynamics, the geodesic SSC gives rise to novel emergent phenomena. By constructing a semiclassical theory including nonadiabatic effects and higher-order spatial gradients of magnetic textures, we demonstrate that the geodesic SSC induces an emergent band asymmetry, leading to nonreciprocal responses as a quantum geometric effect. This mechanism is a purely orbital effect, requiring no spin-orbit coupling, and the resulting discussion runs in parallel with the conventional picture of the topological Hall effect driven by the SSC. The geometric viewpoint developed here will provide broad new insights into classification, quantum geometry, emergent electrodynamics, and a wider variety of emergent phenomena.

We investigate nonlinear magnetoelastic wave dynamics and electrically tunable soliton excitations in hexagonal multiferroic media. By varying the magnetoelastic coupling strength and using a coupled magnetoelastic-ferroelectric continuum model, we found that the system evolves from weakly nonlinear quasiperiodic oscillations to strongly anharmonic yet phase-coherent multimode dynamics. Our results suggest that the dynamics remain bounded and approach distorted limit-cycle behavior rather than chaotic motion despite the enhanced nonlinearity. The excitation spectra and the band dispersion relations reveal that this nonlinear evolution originates from strong magnon-phonon hybridization and coupling-induced renormalization of collective excitation branches, leading to coherent energy exchange among magnetic, elastic, and polarization subsystems. In addition, the coupled dynamics can be reduced to an effective magnetoelastic nonlinear Schrödinger equation and support localized excitations such as bright and dark solitons and Kuznetsov-Ma type breathers. Furthermore, it is found that an external electric field modifies both the effective nonlinear coefficient and the dispersion curvature, enabling continuous control of soliton amplitude, width, and stability. The field also induces a saddle-node bifurcation in the magnetization phase space, defining a critical threshold separating multistable and monostable regimes. Our results establish a theoretical framework for electrically tunable nonlinear spin-lattice excitations and soliton engineering in multiferroic systems.

We present a Ginzburg-Landau theory on statics and dynamics of BaTiO$_3$-type ferroelectrics in the paraelectric phase with the cubic structure, where the order parameter is the polarization $\bi p$. Unique effects are caused by the electrostrictive (ES) coupling between ${\bi p}$ and the elastic displacement $\bi u$. We show that the ES coupling gives rise to a central peak in the Fourier-Laplace transform of the displacement time-correlation function at small wave numbers. It emerges and grows with a narrow width as the transition is approached. Such central peaks have long been observed in a number of scattering experiments in various ferroelectrics, but their origin has not been well understood. From the acoustic part of the displacement dynamic correlation we obtain the frequency-dependent elastic moduli $C_{11}^*(\omega)$, $C_{12}^*(\omega)$, and $C_{44}^*(\omega)$, whose singular parts arise from the ES coupling, We then calculate the singular sound velocity and attenuation. In the central peak and the elastic moduli, the frequency $\omega$ appears in the scaled form $\omega\tau_D$, where $\tau_D$ is the Debye relaxation time in the frequency-dependent dielectric constant. {Keywords}: ferroelectric transition, central peak, acoustic anomaly, electrostrictive coupling

Quantum anomalous Hall insulator-superconductor heterostructures are predicted to host chiral Majorana fermions as edge modes, which is essential for topological quantum computing applications. Although the edge states have been extensively studied at zero chemical potential $\mu = 0$, the practically relevant regime with a shifted chemical potential ($\mu \neq 0$) remains less explored. Here, we present an analytical treatment of the edge states for $\mu \neq 0$, deriving an approximate but highly accurate solution applicable to realistic experimental parameters. Surprisingly, we find that the energy dispersion of the edge band exhibits nonlinearity and transforms into a twisted, braid-like structure within specific parameter ranges. This unique braid-like band leads to non-chirality of the edge modes, allowing propagation in both directions.