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Since the discovery of polar topological textures, achieving efficient control and manipulation of them has emerged as a significant challenge for their integration into nanoelectronic devices. In this study, we use second principles molecular dynamic simulations to demonstrate the precise and reversible control of domain arrangements stabilizing diverse polarization textures through the application of various inhomogeneous electric fields. Furthermore, we conduct an in-depth study of ferroelectric domain motion under such fields, revealing features consistent with creep dynamics and establishing an upper limit for their propagation speed. Notably, our findings show that domain walls exhibit an asymmetric inertial response, present at the onset of the dynamics but absent during their cessation. These findings provide valuable insights into the dynamic behavior of polar textures, paving the way for the development of high-speed, low-power nanoelectronic applications.

Skyrmions are stable topological textures that have garnered substantial attention within the ferroelectric community for their exotic functional properties. While previous studies have questioned the feasibility of [001]$_{\text{pc}}$ skyrmion tubes in rhombohedral BaTiO$_3$ due to the high energy cost of 180$^\circ$ domain walls, we demonstrate here their stabilization with topological charges of $\mathcal{Q} = \pm 1$ from density functional theory and second-principles calculations. By enabling extensive vortex and antivortex polarization configurations, the expected prohibitive energetic barriers are overcomed while preserving the topological nature of the structures. Notably, we extend these findings to demonstrate the appearance of skyrmion and antiskyrmion tubes in other related materials, highlighting their broader relevance. Furthermore, our computational experiments indicate that these structures can be directly stabilized and reversibly switched by applied electric fields, establishing a straightforward route for their practical realization and functional control in nanoelectronic devices.

The third quantization (3rd Q) for bosons provides the exact steady-state solution of the Lindblad equation with quadratic Hamiltonians. By decomposing the interaction of the Bose Hubbard model (BHM) according to Hartree approximation, we present a self-consistent formalism for solving the open-system bosonic Lindblad equation with weak interactions in the steady state. The 3rd Q with Hartree approximation takes into account the infinite Fock space of bosons while its demand of resource scales polynomially with the system size. We examine the method by analyzing three examples of the BHM, including the uniform chain, interaction induced diode effect, and Su-Schrieffer-Heeger (SSH) Hubbard model. When compared with the simulations with capped boson numbers for small systems, the 3rd Q with Hartree approximation captures the qualitative behavior and suggests an upper bound of the steady-state value. Finite-size scaling confirms the results from the 3rd Q with Hartree approximation converge towards the thermodynamic limit. Thus, the manageable method allows us to characterize and predict large-system behavior of quantum transport in interacting bosonic systems relevant to cold-atom experiments., Comment: 13 pages, 10 figures

Since the recent discovery of polar topologies, a recurrent question has been in the way to remotely tune them. Many efforts have focused on the pumping of polar optical phonons from optical methods but with limited success, as only switching between specific phases has been achieved so far. Additionally, the correlation between optical pulse characteristics and the resulting phase remains poorly understood. Here, we propose an alternative approach and demonstrate the deterministic and dynamical tailoring of polar topologies using instead acoustic phonon pumping. Our second-principles simulations reveal that by pumping specific longitudinal and transverse acoustic phonons, various topological textures can be induced in materials like BaTiO$_\mathrm{3}$ or PbTiO$_\mathrm{3}$. This method leverages the strong coupling between polarization and strain in these materials, enabling predictable and dynamical control of polar patterns. Our findings open up an alternative possibility for the manipulation of polar textures, inaugurating a promising research direction.

Chirality refers to the asymmetry of objects that cannot be superimposed on their mirror image. It is a concept that exists in various scientific fields and has profound consequences. Although these are perhaps most widely recognized within biology, chemistry, and pharmacology, recent advances in chiral phonons, topological systems, crystal enantiomorphic materials, and magneto-chiral materials have brought this topic to the forefront of condensed matter physics research. Our review discusses the symmetry requirements and the features associated with structural chirality in inorganic materials. This allows us to explore the nature of phase transitions in these systems, the coupling between order parameters, and their impact on the material's physical properties. We highlight essential contributions to the field, particularly recent progress in the study of chiral phonons, altermagnetism, magnetochirality between others. Despite the rarity of naturally occurring inorganic chiral crystals, this review also highlights a significant knowledge gap, presenting challenges and opportunities for structural chirality mostly at the fundamental level, e.g., chiral displacive phase transitions and ferrochirality, possibilities of tuning and switching structural chirality by external means (electric, magnetic, or strain fields), whether chirality could be an independent order parameter, and whether structural chirality could be quantified, etc. Beyond simply summarising this field of research, this review aims to inspire further research in materials science by addressing future challenges, encouraging the exploration of chirality beyond traditional boundaries, and seeking the development of innovative materials with superior or new properties.

We compare the various chirality measures most widely used in the literature to quantify chiral symmetry in extended solids, i.e., the continuous chirality measure, the Hausdorff distance, and the angular momentum. By studying these functions in an algebraically tractable case, we can evaluate their strengths and weaknesses when applied to more complex crystals. Going beyond those classical calculations, we propose a new method to quantify the handedness of a crystal based on a pseudoscalar function, i.e., the helicity. This quantity, borrowed from hydrodynamics, can be computed from the eigenvector carrying the system from the high-symmetry non-chiral phase to the low-symmetry chiral phase. Different model systems like K$_3$NiO$_2$, CsCuCl$_3$ and MgTi$_2$O$_4$ are used as test cases where we show the superior interest of using helicity to quantify chirality together with the handedness distinction.

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 {\sl melting} in a liquid-like 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 looses its translational and orientational orders at different temperatures, resembling the behavior of liquid crystals and yielding an intermediate hexatic-like phase. Our simulations reveal the mechanism responsible for the melting and allow us to characterize the stochastic dynamics in the hexatic-like 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., Comment: 7 pages, 4 figures

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 $\omega$ 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., Comment: 7 pages, 6 Figures

We study the emergence of Berezinskii-Kosterlitz-Thouless (BKT) phases in (PbTiO$_3$)$_3$/(SrTiO$_3$)$_3$ superlattices by means of second-principles simulations. Beyond a threshold tensile epitaxial strain of $\epsilon = 0.25 \%$ the local dipole moments within the superlattices are confined to the film-plane, and thus the polarization can be effectively considered as two-dimensional. The analysis of the decay of the dipole-dipole correlation with the distance, together with the study of the density of defects and its distribution as function of temperature, supports the existence of a BKT phase in a range of temperature mediating the ordered ferroelectric (stable at low $T$), and the disordered paraelectric phase that appears beyond a critical temperature $T_{\rm BKT}$. This BKT phase is characterized by quasi-long-range order (whose signature is a power-law decay of the correlations with the distance), and the emergence of tightly bounded vortex-antivortex pairs whose density is determined by a thermal activation process. The proposed PbTiO$_{3}$/SrTiO$_{3}$ superlattice model and the imposed mechanical boundary conditions are both experimentally feasible, opening the door for the first experimental observation of these new topological phases in ferroelectric materials., Comment: 11 pages, 6 Figures

We study the equilibrium arrangements of polarization vortices in (PbTiO$_3$)$_n$/(SrTiO$_3$)$_n$ superlattices by means of second-principles simulations. We find that, at low temperatures, polarization vortices organize in a regular arrangement in which clockwise and counter-clockwise vortices alternate positions, leading to a crystal-like structure with well defined handedness. This chiral crystal melts at a critical temperature $T_\mathrm{M}$ into a chiral liquid, where long-range order is lost but handedness is preserved. At even higher temperatures, $T_\mathrm{C}$, a second phase transition occurs, at which the chiral liquid of polarization vortices loses its handedness. Both phase transitions can be readily identified by the adequate choices of order parameters., Comment: 7 pages, 4 figures

Order-disorder transitions are widely explored in various vortex structures in condensed matter physics, i.e., in the type-II superconductors and Bose-Einstein condensates. In this study, we have investigated the ordering of the polar vortex phase in the (PZT)n/(STO)n superlattice systems through phase-field simulations. An antiorder state is discovered for short periodicity superlattice on an SSO substrate, owing to the huge interfacial coupling between PZT and STO as well as the giant in-plane polarization in STO layers due to the large tensile strain. Increasing the periodicity leads to the anti-order to disorder transition, resulting from the loss of interfacial coupling and disappearance of the polarization in STO layers. On the other hand, for short periodicity superlattices, order-disorder-antiorder transition can be engineered by mediating the substrate strain, due to the delicate competition between the depoling effect, interfacial coupling, and strain effect. We envision this study to spur further interest towards the understanding of order-disorder transition in ferroelectric topological structures., Comment: 20 Pages 5 figures

Polar textures have attracted significant attention in recent years as a promising analog to spin-based textures in ferromagnets. Here, using optical second harmonic generation based circular dichroism, we demonstrate deterministic and reversible control of chirality over mesoscale regions in ferroelectric vortices using an applied electric field. The microscopic origins of the chirality, the pathway during the switching, and the mechanism for electric-field control are described theoretically via phase-field modeling and second-principles simulations, and experimentally by examination of the microscopic response of the vortices under an applied field. The emergence of chirality from the combination of non-chiral materials and subsequent control of the handedness with an electric field has far-reaching implications for new electronics based on chirality as a field controllable order parameter., Comment: 19 pages, 4 figures Supplement: 27 pages, 13 figures

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. With the discovery of topologically-stable polar skyrmions, it is of both fundamental and practical interest to understand the microscopic nature and the possibility of temperature- and strain-driven phase transitions in ensembles of such polar 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 [(PbTiO3)16/(SrTiO3)16]8 lifted-off 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). To map these changes microscopically required developing new imaging methods. We show how scanning convergent beam 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 theoretical phase-field simulations. These results revealed by our new measurement methods provide the first illustration of systematic control of rich variety of topological dipole textures by altering the mechanical boundary conditions, which may offer a promising way to control their functionalities in ferroelectric nanodevices using the local and spatial distribution of chirality and order., Comment: 39 pages, 5 figures, 14 supporting figures

Orbital angular momentum and torque transfer play central roles in a wide range of magnetic textures and devices including skyrmions and spin-torque electronics(1-4). Analogous topological structures are now also being explored in ferroelectrics, including polarization vortex arrays in ferroelectric/dielectric superlattices(5). Unlike magnetic toroidal order, electric toroidal order does not couple directly to linear external fields. To develop a mechanism that can control switching in polarization vortices, we utilize a high-energy electron beam and show that transverse currents are generated by polar order in the ballistic limit. We find that the presence of an electric toroidal moment in a ferro-rotational phase transfers a measurable torque and orbital angular momentum to the electron beam. Furthermore, we find that the complex polarization patterns, observed in these heterostructures, are microscopically chiral with a non-trivial axial component of the polarization. This chirality opens the door for the coupling of ferroelectric and optical properties.

Whereas a very large number of sensors are available in the automotive field, currently just a few of them, mostly proprioceptive ones, are used in telematics, automotive insurance, and mobility safety research. In this paper, we show that exteroceptive sensors, like microphones or cameras, could replace proprioceptive ones in many fields. Our main motivation is to provide the reader with alternative ideas for the development of telematics applications when proprioceptive sensors are unusable for technological issues, privacy concerns, or lack of availability in commercial devices. We first introduce a taxonomy of sensors in telematics. Then, we review in detail all exteroceptive sensors of some interest for vehicle telematics, highlighting advantages, drawbacks, and availability in off-the-shelf devices. Successively, we present a list of notable telematics services and applications in research and industry like driving profiling or vehicular safety. For each of them, we report the most recent and important works relying on exteroceptive sensors, as long as the available datasets. We conclude showing open challenges using exteroceptive sensors both for industry and research., Comment: 18 pages, 4 figures, 7 tables