Resonators are a key component in modern communications and computing. As demand and technological advances push component requirements into the terahertz regime, there is significant research devoted to the search for resonances at these frequencies. While uniform solid-state materials usually do not intrinsically feature resonances in this frequency range, self-assembled periodic arrays of ferroelectric nanodomains may provide an engineering route to design millimeter-wave properties. Here, we utilize prototypical dielectric-ferroelectric SrTiO3/PbTiO3 superlattices to robustly design periodic ferroelectric nano-scale domains. Phase field simulations predict an emergent domain breathing mode in complex polar textures and state-of-the-art millimeter-wave characterization shows evidence for such emergent resonances up to hundreds of GHz. Complex polar textures in these superlattices lead to emergent piezoelectric properties that also result in millimeter-wave resonances, which are predicted by second principles methods and confirmed by direct measurement. The principles investigated in this work suggest a new modality for ferroelectrics in the design of millimeter-wave electronics.

CrSBr, a layered anisotropic van der Waals antiferromagnet, has recently emerged as a versatile platform where strong coupling between optical excitations and magnetic order enables magneto-optical control at low dimensions. While experiments have progressed rapidly, predictive and reliable ab initio descriptions remain limited to self-consistent, many-body perturbation theory, which is computationally expensive and technically challenging. Here, we present an alternative approach that accurately predicts the electronic and optical properties of CrSBr at substantially lower computational cost, while retaining quantitative accuracy in the coupling between excitons and magnetic order. Using a tuned hybrid density functional with on-site corrections, we reproduce fundamental and optical gaps and quantitatively capture the interaction between excitonic transitions and magnetic order. We then employ this functional to investigate excitonic shifts induced by spin canting that would result from applying an external magnetic field. Our results establish an efficient framework for modeling excitonic and magneto-optical phenomena in layered magnetic semiconductors.

Ferroelectric materials exhibit a spontaneous electric polarization that can be reversed byan electric field 1 , a property central to non-volatile memories 2,3 , sensors 4 and actuators 5,6 . In most conventional ferroelectric oxides, the polarization originates from a softening of a polar mode 7 . The amplitude of the mode along a given direction couples with the applied field along the same direction 8 . A long-standing challenge has been to achieve controlled switching of the in-plane polarization component using an out-of-plane electric field. We have discovered that a trilinear coupling between the in-plane and out-of-plane polarization, mediated via the octahedral tilts and rotations in the layered ferroelectric Bi 4 Ti 3 O 12 naturally fulfills these requirements and enables trans-switching of the polarization state. In its monoclinic phase, this material hosts a large in-plane polarization (∼ 50 μC cm -2 ) driven by a proper ferroelectric instability, together with smaller out-of-plane polarization (∼ 5 μC cm -2 ) of improper origin, induced by oxygen-octahedral distortions. We demonstrate that in c-axis-oriented epitaxial films the in-plane polarization switches deterministically under an out-of-plane electric field. This cross-coupling between orthogonal polarization components provides a route to transverse manipulation of ferroic order parameters and establishes layered ferroelectrics as a platform for capacitive computing concepts, analogous to the transconductance of modern CMOS electronics.

Ferroelectric materials exhibit a spontaneous electric polarization that can be reversed by an electric field1, a property central to non-volatile memories2,3, sensors4 and actuators5,6. In most conventional ferroelectrics, the polarization originates from a softening of a polar mode7. The amplitude of the mode along a given direction couples with the applied field along the same direction8. Ferroelectrics with a predominant in-plane polarization are harder to use in standard device geometries and therefore the field has mostly focused on out-of-plane ferroelectrics. Developing approaches that enable manipulation of the in-plane polarization component with an out-of-plane field would therefore provide new opportunities for device design and functionality. Here we have discovered that a trilinear coupling between the in-plane and out-of-plane polarization, mediated by means of the octahedral tilts and rotations in the layered ferroelectric Bi4Ti3O12, naturally fulfils this challenge and enables perpendicular switching of the polarization state. In its bulk monoclinic phase, this material hosts a large in-plane polarization (about 50 μC cm-2) driven by a proper ferroelectric instability, together with smaller out-of-plane polarization (about 5 μC cm-2) of improper origin, induced by oxygen octahedral distortions. We demonstrate that, in c-axis-oriented epitaxial films, the in-plane polarization switches deterministically under an out-of-plane electric field. This cross-coupling between orthogonal polarization components provides a route to transverse manipulation of ferroic order parameters and establishes layered ferroelectrics as a platform for capacitive computing concepts.

We present a comprehensive analysis of the electronic structure of the PF6− anion, a prototypical octahedral molecular system with high Oh symmetry. Using symmetry-adapted linear combinations of atomic orbitals and group theoretical techniques, we construct molecular orbitals and provide a systematic classification according to irreducible representations of the Oh point group. The role of the P-centered 3s, 3p, and 3d orbitals, together with the symmetry-adapted 2s and 2p orbitals of the six surrounding fluorine atoms, is explicitly analyzed. The electronic structure is described both within the theory of molecular orbitals and with the picture based on sp3d2 hybridization. Maximally localized Wannier functions derived from first-principles density functional theory calculations using the siesta and wannier90 codes are computed. The constructed Wannier functions accurately reflect the expected molecular symmetries and provide a natural minimal basis for tight-binding and second-principles modeling. A detailed comparison is made between bonding, nonbonding, and antibonding orbitals, as well as their energetic ordering. Our results demonstrate the interplay between symmetry, bonding, and electronic structure in molecular systems with high cubic symmetry and set the stage for the development of accurate minimal models for such systems.

Magnetic skyrmions and related topological spin textures have emerged as a central topic in condensed-matter physics, combining fundamental significance with potential for transformative applications in spintronics, magnonics, and beyond. Over the past decade, advances in material platforms, imaging techniques, theoretical modeling, and device concepts have established skyrmionics as a rapidly expanding field. At the same time, challenges remain in stabilizing, controlling, and integrating such textures into functional architectures, while novel phenomena such as antiskyrmions, higher-order skyrmions, hopfions, and antiferromagnetic textures arise. The 2026 Skyrmionics Roadmap represents a collective effort of many authors, providing a comprehensive perspective on the current state-of-the-art and the outlook for the coming years. In 33 focused sections, each co-authored by two researchers, we chart progress in theory and modeling, material systems, skyrmion dynamics, and skyrmion technologies. By offering a consolidated vision, this Roadmap aims to guide both fundamental research and application-driven efforts, accelerating the transition of skyrmionics from conceptual breakthroughs toward practical technologies.

We present an efficient and accurate implementation of hybrid exchange-correlation (XC) functionals in the siesta code, enabling large-scale simulations based on Hartree-Fock-type exact exchange combined with strictly localized numerical atomic orbitals (NAOs). Our approach exploits a fitted representation of the NAOs in terms of Gaussian-type orbitals (GTOs), which allows for the analytical evaluation of four-center electron repulsion integrals (ERIs) via the libint library. This framework is seamlessly integrated with siesta’s real-space grid and sparse-matrix infrastructure, and is combined with multiple screening techniques to control the computational complexity. We also introduce a fully analytical formulation of hybrid-functional forces and a dynamic parallel distribution scheme that ensures excellent scalability. We validate our implementation through benchmark calculations on a broad set of systems (including semiconductors, insulators, and two-dimensional materials) and demonstrate that the HSE06 functional significantly improves the prediction of band gaps compared to PBE, in close agreement with G0W0 and experimental data. We analyze in detail the trade-offs between accuracy and computational efficiency as a function of the number of Gaussians, basis set range, and integral screening thresholds. Our results confirm that hybrid functional calculations in siesta are now feasible for large extended systems, making accurate first-principles predictions of electronic and structural properties accessible at scale.

We report the emergence of a transverse dielectric response in PbTiO_3/SrTiO_3 superlattices hosting polar vortex structures. Using second-principles simulations, we find that an electric field applied along one direction induces significant local polarization responses along orthogonal directions, with magnitudes approaching half that of the diagonal susceptibility components. These off-diagonal responses are strongly dependent on the topology of the vortex structure and can be deterministically tuned or even reversed via homogeneous electric fields or epitaxial strain. Notably, the transverse susceptibilities become comparable to the diagonal components during a field- or strain-induced transition to a polarization wave state. This discovery opens avenues for engineering reconfigurable nanoscale dielectric responses in topologically textured ferroelectric systems.

We present an extension of the second-principles density functional theory (SPDFT) method to perform time-dependent simulations. Our approach, which calculates the evolution of the density matrix in real time and real space using the Liouville-von Neumann equation of motion, allows determining optical and transport properties for very large systems, involving tens of thousands of atoms, using very modest computational platforms. In contrast with other methods, we show that SPDFT can be applied to a wide variety of materials including both metals and insulators. In particular, we illustrate its capabilities by obtaining the spectra of SrTiO_3, diamond and metallic lithium. We find that, while SPDFT results in SrTiO_3 are quite similar to those obtained from DFT using linear perturbation theory, we observe significant improvements over this method in both diamond and metallic lithium. The inclusion of electron-electron interactions during the evolution of the density matrix in diamond allows the spectra to more closely resemble those obtained with the Bethe-Salpeter equation than from perturbation theory. In lithium time-dependent SPDFT not only predicts interband transitions but also the Drude peak, opening the possibility of detailed ab initio studies of transport properties beyond many of the usual approximations.

We investigate the emergence of Bloch-type polarization components in 180° ferroelectric domain walls in bulk PbTiO3 under varying mechanical boundary conditions, using first-principles simulations based on density functional theory. A spontaneous Bloch component—primarily associated with Pb displacements confined within the PbO domain wall plane—can condense under realistic strain conditions on top of the Ising-type domain walls. The amplitude and energetic stabilization of this component are highly sensitive to the in-plane lattice parameters. In particular, tensile strains akin to those imposed by DyScO3 substrates enhance the Bloch component and lead to energy reductions as large as 10.7 mJ/m2 (10.6 meV/□, where □ stands for “per domain wall unit cell”) with respect to the most stable structure including only Ising and Néel components. We identify a relatively flat energy landscape for the Bloch polarization, highlighting the tunability of chiral textures through strain engineering. Our results offer a predictive framework for estimating the strain-dependent onset temperature of Bloch-type domain wall components and provide insight into the design of topologically nontrivial and chiral polar structures in ferroelectrics.

Fluorescent semiconducting single-walled carbon nanotubes (SWCNTs) hold considerable promise for photonics. Furthermore, the optical characteristics of the material can be significantly improved by covalent modification, which generates new spectral features in the near-infrared region and enhances its photoluminescence quantum yield. However, despite the dynamic development of this research domain, the importance of the solvent environment in which the SWCNT functionalization is conducted remains relatively unexplored. In this work, the complex relationships between solvent, dispersant, and SWCNTs were untangled to unravel the underlying phenomena. Through a systematic investigation of SWCNT reactivity in a broad spectrum of solvents, supported by multi-scale modeling enabled by our new implementation of a hybrid functional within SIESTA, we discovered that both the solvent medium and the dispersant enabling SWCNT solubilization affect not only the kinetics but also the course of the covalent modification of SWCNTs. Polar solvents proved to induce significant structural reorganization of polymer molecules on the SWCNT surface and enhance charge redistribution at the polymer-SWCNT interface. Consequently, we achieved a high degree of control over the optical properties of SWCNTs, and the tailored SWCNTs enabled facile optical detection of cholesterol, a significant risk factor for cardiovascular diseases.

We present a systematic, quasi-automated methodology for generating electronic models in the framework of second-principles density functional theory (SPDFT). This approach enables the construction of accurate and computationally efficient models by deriving all necessary parameters from first-principles calculations on a carefully designed training set. A key feature of our method is the enforcement of space group symmetries, which reduces both the number of independent parameters and the required computational effort. The formalism includes improved treatments of one-electron Hamiltonians, electron-lattice coupling-through both linear and quadratic terms-and electron-electron interactions, enabling accurate modeling of structural and electronic responses. We apply the methodology to SrTiO_3 and LiF, materials representative of transition-metal perovskites and wide-band-gap insulators, respectively. In both cases, the resulting models reproduce DFT reference data with high fidelity across various atomic configurations and charge states. Our results validate the robustness of the approach and highlight its potential for simulating complex phenomena such as polarons and excitons. This work lays the foundation for extending SPDFT to real-time simulations of optoelectronic properties and further integration with machine-learning methods.

First-principles density functional theory (DFT) codes which employ a localized basis offer advantages over those which use plane-wave bases, such as better scaling with system size and better suitability to low-dimensional systems. The trade-off is that care must be taken in order to generate a good localized basis set which is efficient and accurate in a variety of environments. Here we develop and make freely available optimized local basis sets for two common two-dimensional materials, graphene and hexagonal boron nitride, for the SIESTA DFT code. Each basis set is benchmarked against the ABINIT plane-wave code, using the same pseudopotentials and exchange-correlation functionals. We find that a significant improvement is obtained by including the l + 2 polarization orbitals (4 f ) in the basis set, which greatly improves angular flexibility. The optimized basis sets yield much better agreement with plane-wave calculations for key features of the physical system, including total energy, lattice constant, and cohesive energy. The optimized basis sets also result in a speedup of the calculations with respect to the nonoptimized, native choices.

The development of advanced materials with high specific energy is crucial for enabling sustainable energy storage solutions, particularly in applications such as lithium-air batteries. Lithium peroxide (Li$_{2}$O$_{2}$) is a key discharge product in non-aqueous lithium-air systems, where its structural and electronic properties significantly influence battery performance. In this work, we investigate the atomic structure, electronic band structure, and Wannier functions of bulk Li$_{2}$O$_{2}$ using density functional theory. The performance of different basis sets of numerical atomic orbitals are compared with respect to a converged plane-wave basis results. We analyze the material's ionic characteristics, the formation of molecular orbitals in oxygen dimers, and the band gap discrepancies between various computational approaches. Furthermore, we develop a localized Wannier basis to model electron-vibration interactions and explore their implications for polaron formation. Our findings provide a chemically intuitive framework for understanding electron-lattice coupling and offer a basis for constructing reduced models that accurately describe the dynamics of polarons in Li$_{2}$O$_{2}$. These insights contribute to the broader goal of improving energy storage technologies and advancing the field of materials design.

The recent discovery of polar topological structures has opened the door for exciting physics and emergent properties. There is, however, little methodology to engineer stability and ordering in these systems, properties of interest for engineering emergent functionalities. Notably, when the surface area is extended to arbitrary thicknesses, the topological polar texture becomes unstable. Here we show that this instability of the phase is due to electrical coupling between successive layers. We demonstrate that this electrical coupling is indicative of an effective screening length in the dielectric, similar to the conductor-ferroelectric interface. Controlling the electrostatics of the superlattice interfaces, the system can be tuned between a pure topological vortex state and a mixed classical-topological phase. This coupling also enables engineering coherency among the vortices, not only tuning the bulk phase diagram but also enabling the emergence of a 3D lattice of polar textures.

Nanostructured ferroelectrics display exotic multidomain configurations resulting from the electrostatic and elastic boundary conditions they are subject to. While the ferroelectric domains appear frozen in experimental images, atomistic second-principles studies suggest that they may become spontaneously mobile upon heating, with the polar order melting in a liquidlike fashion. Here, we run molecular dynamics simulations of model systems (PbTiO_{3}/SrTiO_{3} superlattices) to study the unique features of this transformation. Most notably, we find that the multidomain state loses its translational and orientational orders at different temperatures, resembling the behavior of liquid crystals and yielding an intermediate hexaticlike phase. Our simulations reveal the mechanism responsible for the melting and allow us to characterize the stochastic dynamics in the hexaticlike phase: we find evidence that it is thermally activated, with domain reorientation rates that grow from tens of gigahertzs to terahertzs in a narrow temperature window.

Polymorphism is gaining attention among van der Waals layered materials. In the case of gallium monosulfide, a hexagonal phase has predominantly been reported. Here the successful growth of rhombohedral gallium sulfide (GaS) with R (3) over barm space group on sapphire substrates using chemical vapor deposition (CVD) is presented. Crystallographic analysis reveals that the CVD GaS R (3) over barm has preferred..-axis orientation, low microstrain and moderate mosaicity. A combined approach of X-ray diffraction, Raman spectroscopy and photoluminescence measurements with first principles calculations is used to determine phononic and photonic properties of the rhombohedral GaS with direct band gap of 2.55 eV and near-blue light emission at room temperature. These results pave the way to novel applications in optoelectronics and photonics, particularly for development of efficient light-emitting devices such as LEDs or lasers, quantum dots, photodetectors, and integrated photonic circuits.

We report second-principles simulations on the structural and energetic properties of domains in (PbTiO$_{3}$)$_{n}$/(SrTiO$_{3}$)$_{n}$ superlattices. For the explored layer thickness ($n$ ranging between 8 and 16 unit cells) and lateral sizes of the domains, the most stable configuration corresponds to polar domains separated by a sequence of counter-rotating vortices (clockwise/counterclockwise) perpendicular to the stacking direction and acting as domain walls. The balance between the domain wall energy and the electrostatic energy yields to an optimal domain period $ω$ that is proportional to the square-root of the thickness of the PbTiO$_{3}$ layer, following the Kittel law. For a given lateral size of the simulation box, suboptimal domain structures (with a width larger than the one predicted by the Kittel law) can be obtained in a metastable form. However, at finite temperature, molecular dynamics simulations show the spontaneous change of periodicity, which implies the formation of new domains whose generation is initiated by the nucleation of vortices and antivortices at the interface between the SrTiO$_{3}$ and the PbTiO$_{3}$ layers. The vortices progressively elongate and eventually annihilate with the antivortices yielding the formation of new domains to comply the Kittel law via a topological phase transition.

Chirality or handedness of a material can be used as an order parameter to uncover the emergent electronic properties for quantum information science. Conventionally, chirality is found in naturally occurring biomolecules and magnetic materials. Chirality can be engineered in a topological polar vortex ferroelectric/dielectric system via atomic-scale symmetry-breaking operations. We use four-dimensional scanning transmission electron microscopy (4D-STEM) to map out the topology-driven three-dimensional domain walls, where the handedness of two neighbor topological domains change or remain the same. The nature of the domain walls is governed by the interplay of the local perpendicular (lateral) and parallel (axial) polarization with respect to the tubular vortex structures. Unique symmetry-breaking operations and the finite nature of domain walls result in a triple point formation at the junction of chiral and achiral domain walls. The unconventional nature of the domain walls with triple point pairs may result in unique electrostatic and magnetic properties potentially useful for quantum sensing applications.

Polar skyrmions are predicted to emerge from the interplay of elastic, electrostatic and gradient energies, in contrast to the key role of the anti-symmetric Dzyalozhinskii-Moriya interaction in magnetic skyrmions. Here, we explore the reversible transition from a skyrmion state (topological charge of −1) to a two-dimensional, tetratic lattice of merons (with topological charge of −1/2) upon varying the temperature and elastic boundary conditions in [(PbTiO 3 ) 16 /(SrTiO 3 ) 16 ] 8 membranes. This topological phase transition is accompanied by a change in chirality, from zero-net chirality (in meronic phase) to net-handedness (in skyrmionic phase). We show how scanning electron diffraction provides a robust measure of the local polarization simultaneously with the strain state at sub-nm resolution, while also directly mapping the chirality of each skyrmion. Using this, we demonstrate strain as a crucial order parameter to drive isotropic-to-anisotropic structural transitions of chiral polar skyrmions to non-chiral merons, validated with X-ray reciprocal space mapping and phase-field simulations.