Polar Lattices Research Articles

Breakdown of Volterra's Elasticity Theory of Dislocations in Polar Skyrmion Lattices.

Emerging polar skyrmion crystals (SkX) have raised much interest for technological applications owing to their nontrivial topologies of electric dipoles, quasiparticle-like behaviors, and unique electrical responses. Understanding SkX defects, especially dislocations, is crucial for their unique lattice dynamics and responses; however, it still remains elusive. Here, we have not only demonstrated that a SkX dislocation exhibits an anomalously deformed core structure with over 50% elongation of skyrmions but also discovered that Volterra's elasticity theory of dislocation is broken down in SkX. Our phase-field simulation reveals that these distinct features of SkX dislocation arise from a rigid to soft quasiparticle transition of skyrmions depending on the electric field and temperature. In SkX, there exist inherent mechanics that mitigate the mismatch by both migration and deformation of skyrmions. This work provides novel insights into a new class of lattice mechanics and related functionality arising from the unique properties of quasi-particle SkX.

Emergence and transformation of polar skyrmion lattices via flexoelectricity

As analogies to magnetic skyrmions, polar skyrmions in ferroelectric superlattices and multilayers have garnered widespread attention for their non-trivial topology and novel properties like negative capacitance and nonlinear optical effect. So far, they have only been theoretically predicted to be able to assemble ordered hexagonal skyrmion lattices (SkLs) in ferroelectric thin films. Here, based on phase-field simulations, we report the critical roles of flexoelectricity playing in the stabilization and transformation of polar SkLs. Different polar SkL patterns can emerge in the ferroelectric thin films, including tetragonal-SkL, and hexagonal-SkLs with diverse orientations, as summarized by phase diagrams. These emergent SkL states are attributed to the material anisotropy modified by the flexoelectric effect. Interestingly, we further found that the hexagonal-SkLs can be rotated by applying strain gradient or in-plane electric field to the films. Moreover, a nonreciprocal bending response of tetragonal-SkL is also induced by the flexoelectric effect. Our results provide useful guidelines for the implementation of polar skyrmion lattices in experiments.

Optical vortex-antivortex crystallization in free space

Stable vortex lattices are basic dynamical patterns which have been demonstrated in physical systems including superconductor physics, Bose-Einstein condensates, hydrodynamics and optics. Vortex-antivortex (VAV) ensembles can be produced, self-organizing into the respective polar lattices. However, these structures are in general highly unstable due to the strong VAV attraction. Here, we demonstrate that multiple optical VAV clusters nested in the propagating coherent field can crystallize into patterns which preserve their lattice structures over distance up to several Rayleigh lengths. To explain this phenomenon, we present a model for effective interactions between the vortices and antivortices at different lattice sites. The observed VAV crystallization is a consequence of the globally balanced VAV couplings. As the crystallization does not require the presence of nonlinearities and appears in free space, it may find applications to high-capacity optical communications and multiparticle manipulations. Our findings suggest possibilities for constructing VAV complexes through the orbit-orbit couplings, which differs from the extensively studied spin-orbit couplings.

Insights into Strain Engineering: From Ferroelectrics to Related Functional Materials and Beyond.

Ferroelectrics have become indispensable components in various application fields, including information processing, energy harvesting, and electromechanical conversion, owing to their unique ability to exhibit electrically or mechanically switchable polarization. The distinct polar noncentrosymmetric lattices of ferroelectrics make them highly responsive to specific crystal structures. Even slight changes in the lattice can alter the polarization configuration and response to external fields. In this regard, strain engineering has emerged as a prevalent regulation approach that not only offers a versatile platform for structural and performance optimization within ferroelectrics but also unlocks boundless potential in various functional materials. In this review, we systematically summarize the breakthroughs in ferroelectric-based functional materials achieved through strain engineering and progress in method development. We cover research activities ranging from fundamental attributes to wide-ranging applications and novel functionalities ranging from electromechanical transformation in sensors and actuators to tunable dielectric materials and information technologies, such as transistors and nonvolatile memories. Building upon these achievements, we also explore the endeavors to uncover the unprecedented properties through strain engineering in related chemical functionalities, such as ferromagnetism, multiferroicity, and photoelectricity. Finally, through discussions on the prospects and challenges associated with strain engineering in the materials, this review aims to stimulate the development of new methods for strain regulation and performance boosting in functional materials, transcending the boundaries of ferroelectrics.

Quantum criticality at cryogenic melting of polar bubble lattices

Quantum fluctuations (QFs) caused by zero-point phonon vibrations (ZPPVs) are known to prevent the occurrence of polar phases in bulk incipient ferroelectrics down to 0 K. On the other hand, little is known about the effects of QFs on the recently discovered topological patterns in ferroelectric nanostructures. Here, by using an atomistic effective Hamiltonian within classical Monte Carlo (CMC) and path integral quantum Monte Carlo (PI-QMC), we unveil how QFs affect the topology of several dipolar phases in ultrathin Pb(Zr0.4Ti0.6)O3 (PZT) films. In particular, our PI-QMC simulations show that the ZPPVs do not suppress polar patterns but rather stabilize the labyrinth, bimeron and bubble phases within a wider range of bias field magnitudes. Moreover, we reveal that quantum fluctuations induce a quantum critical point (QCP) separating a hexagonal bubble lattice from a liquid-like state characterized by spontaneous motion, creation and annihilation of polar bubbles at cryogenic temperatures. Finally, we show that the discovered quantum melting is associated with anomalous physical response, as, e.g., demonstrated by a negative longitudinal piezoelectric coefficient.

Strong Coupling of Self‐Trapped Excitons to Acoustic Phonons in Bismuth Perovskite Cs3Bi2I9

AbstractTo assess the potential optoelectronic applications of metal‐halide perovskites, it is critical to have a detailed understanding of the nature and dynamics of interactions between carriers and the polar lattices. Here, the electronic and structural dynamics of bismuth‐based perovskite Cs3Bi2I9 are revealed by transient reflectivity and ultrafast electron diffraction. A cross‐examination of these results combined with theoretical analyses allows the identification of the major carrier–phonon coupling mechanism and the associated time scales. It is found that carriers photoinjected into Cs3Bi2I9 form self‐trapped excitons on an ultrafast time scale. However, they retain most of their energy, and their coupling to Fröhlich‐type optical phonons is limited at early times. Instead, the long‐lived excitons exert an electronic stress via deformation potential and develop a prominent, sustaining strain field as coherent acoustic phonons in 10 ps. From sub‐ps to ns and beyond, a similar extent of the atomic displacements is found throughout the different stages of structural distortions, from limited local modulations to a coherent strain field to the Debye–Waller random atomic motions on longer times. The current results suggest the potential use of bismuth‐based perovskites for applications other than photovoltaics to take advantage of the carriers’ stronger self‐trapping and long lifetimes.

Universal Gaussian Quantization With Side-Information Using Polar Lattices

We consider universal quantization with side information for Gaussian observations, where the side information is a noisy version of the sender’s observation with noise variance unknown to the sender. In this paper, we propose a universally rate optimal and practical quantization scheme for all values of unknown noise variance. Our scheme uses Polar lattices from prior work, and proceeds based on a structural decomposition of the underlying auxiliaries so that even when recovery fails in a round, the parties agree on a common “reference point” that is closer than the previous one. We also present the finite blocklength analysis showing an sub-exponential convergence for distortion and exponential convergence for rate. The overall complexity of our scheme is O(N2log2N) for any target distortion and fixed rate larger than the rate-distortion bound.

Morphology-Dependent One- and Two-Photon Absorption Properties in Blue Emitting CsPbBr3 Nanocrystals.

The linear and nonlinear optical parameters and morphologic dependence of CsPbBr3 nanocrystals (NCs) are crucial for device engineering. In particular, such information in asymmetric nanocrystals is still insufficient. We characterized the OPLA (σ1) and TPA cross sections (σ2) of a series CsPbBr3 nanocrystals with various aspect ratios (AR) using femtosecond transient absorption spectroscopy (TAS). The σ1 presents a linear volume dependence of all the samples, which agrees with the previous behavior in CsPbBr3 QDs. However, the σ2 values do not exhibit conventional power dependency of the crystal volume but are also modulated by the shape-dependent local field factors. In addition, the local field effect in CsPbBr3 NCs is contributed by their asymmetric morphologies and polar ionic lattices, which is more pronounced than in conventional semiconductor NCs. Finally, we revealed that the lifetimes of photogenerated multiexcitonic species of those nanocrystals feature identical morphology independence in both OPLA and TPA.

Polar Lattices for Lossy Compression

In this work, we propose a new construction of polar lattices to achieve the rate-distortion bound of a memoryless Gaussian source. The structure of the proposed polar lattices allows to integrate entropy coding into the lattice quantizer, which greatly simplifies the compression process. The overall complexity of encoding and decoding is O(N log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> N) for any target distortion and fixed rate larger than the rate-distortion bound. Moreover, the nesting structure of polar lattices provides solutions to various multi-terminal coding problems. The Wyner-Ziv coding problem for a Gaussian source can be solved by using a capacity-achieving polar lattice for the Gaussian channel, nested with a rate-distortion bound achieving lattice, while the Gelfand-Pinsker problem can be solved in a reversed manner. The polar lattice quantizer is further extended to extract Wyner's common information of a pair of Gaussian sources or multiple Gaussian sources.

Azimuthal jittered sampling of bandlimited functions in the two-dimensional Fourier transform and the Hankel transform domains

Stark’s sampling theorems in polar coordinates have important significance in the field of medical imaging. However, the direct use of Stark’s results may mislead as in most real-world scenarios the jitter occurs in azimuth due to uncertainty of sampling at the medical imaging system transmitter end. On the basis of the classical Stark’s interpolation formulae, this paper addresses the image reconstruction problem when the sample data are collected on nonuniform polar radius and polar azimuth lattices, where the sample points are normalized zeros of Bessel functions in radius while random jittered ones in azimuth that are clustered around uniform points with a given probability distribution. By using the existing basis functions found in Stark’s formulae, it follows a biased estimate of the original angularly periodic images that are bandlimited both to the highest frequency and in the Fourier transform or the Hankel transform domain. With the newly designed angular generating functions, there are a kind of unbiased estimators whose variance approaches zero as the jitter becomes less and less pronounced.

Electronic structure variations of polar and nonpolar ZnO lattices with nitrogen-ion bombardment using synchrotron-based in situ photoemission and X-ray absorption spectroscopy.

Surface polarity with different crystal orientations has been demonstrated as a crucial parameter in determining the physical properties and device applications in many transition metal oxide and semiconductor compound systems. The influences of surface polarity on electronic structures in nitrogen-incorporated ZnO lattices have been investigated in the present work. The successful doping of nitrogen atoms in ZnO lattices is suggested by the existence of N-related chemical bonds obtained from X-ray photoelectron spectroscopy analysis where a pronounced N-Zn peak intensity has been observed in the (000\bar 1)-terminated polar ZnO compound compared with the (10\bar 10)-terminated nonpolar ZnO compound. An energy shift of the valence band maximum towards the Fermi level has been resolved for both polar and nonpolar ZnO lattices, whereas a charge redistribution of the O 2p hybridized states is only resolved for o-plane ZnO with a polar surface. Angular-dependent X-ray absorption analyses at the O K-edge reveal enhanced surface-state contributions and asymmetric O 2p orbital occupations in the (000\bar 1)-terminated o-plane ZnO compound. The results shed light on the efficient nitrogen doping in ZnO lattices with polar surfaces. The comprehensive electronic structure investigations of correlations between impurity doping and surface polarity in ZnO lattices may also offer guidance for the material design in other transition metal oxide and semiconductor systems.

Multilevel LDPC Lattices With Efficient Encoding and Decoding and a Generalization of Construction $\text{D}'$

Lattice codes are elegant and powerful structures that not only can achieve the capacity of the AWGN channel but are also a key ingredient to many multiterminal schemes that exploit linearity properties. However, constructing lattice codes that can realize these benefits with low complexity is still a challenging problem. In this paper, efficient encoding and decoding algorithms are proposed for multilevel binary LDPC lattices constructed via Construction D' whose complexity is linear in the total number of coded bits. Moreover, a generalization of Construction D' is proposed that relaxes some of the nesting constraints on the parity-check matrices of the component codes, leading to a simpler and improved design. Based on this construction, low-complexity multilevel LDPC lattices are designed whose performance under multistage decoding is comparable to that of polar lattices and close to that of low-density lattice codes (LDLC) on the power-unconstrained AWGN channel.

Construction of Capacity-Achieving Lattice Codes: Polar Lattices

In this paper, we propose a new class of lattices constructed from polar codes, namely polar lattices, to achieve the capacity (1/2) log(1+SNR) of the additive white Gaussiannoise (AWGN) channel. Our construction follows the multilevel approach of Forney et al., where we construct a capacity-achieving polar code on each level. The component polar codes are shown to be naturally nested, thereby, fulfilling the requirement of the multilevel lattice construction. We prove that the polar lattices are AWGN-good. Furthermore, using the technique of source polarization, we propose discrete Gaussian shaping over the polar lattice to satisfy the power constraint. Both the construction and shaping are explicit, and the overall complexity of encoding and decoding is O(N log N) for any fixed target error probability.

Polar Codes and Polar Lattices for the Heegard–Berger Problem

Explicit coding schemes are proposed to achieve the rate-distortion function of the Heegard–Berger problem using polar codes. Specifically, a nested polar code construction is employed to achieve the rate-distortion function for doubly symmetric binary sources when the side information may be absent. The nested structure contains two optimal polar codes for lossy source coding and channel coding, respectively. Moreover, a similar nested polar lattice construction is employed when the source and the side information are jointly Gaussian. The proposed polar lattice is constructed by nesting a quantization polar lattice and a capacity-achieving polar lattice for the additive white Gaussian noise channel.

Achieving Secrecy Capacity of the Gaussian Wiretap Channel With Polar Lattices

In this paper, an explicit scheme of wiretap coding based on polar lattices is proposed to achieve the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel. First, polar lattices are used to construct secrecy-good lattices for the mod- $\Lambda _{s}$ Gaussian wiretap channel (GWC). Then, we propose an explicit shaping scheme to remove this mod- $\Lambda _{s}$ front end and extend polar lattices to the genuine GWC. The shaping technique is based on the lattice Gaussian distribution, which leads to a binary asymmetric channel at each level for the multilevel lattice codes. By employing the asymmetric polar coding technique, we construct an AWGN-good lattice and a secrecy-good lattice with optimal shaping simultaneously. As a result, the encoding complexity for the sender and the decoding complexity for the legitimate receiver are both $O(N\log N\log (\log N))$ . The proposed scheme is proven to be semantically secure.

Polar Codes and Polar Lattices for Independent Fading Channels

In this paper, we design polar codes and polar lattices for i.i.d. fading channels when the channel state information is only available to the receiver. For the binary input case, we propose a new design of polar codes through single-stage polarization to achieve the ergodic capacity. For the non-binary input case, polar codes are further extended to polar lattices to achieve the egodic Poltyrev capacity, i.e., the capacity without power limit. When the power constraint is taken into consideration, we show that polar lattices with lattice Gaussian shaping achieve the egodic capacity of fading channels. The coding and shaping are both explicit, and the overall complexity of encoding and decoding is $O(N \log^2 N)$.

Low-loss, infrared and terahertz nanophotonics using surface phonon polaritons

AbstractThe excitation of surface-phonon-polariton (SPhP) modes in polar dielectric crystals and the associated new developments in the field of SPhPs are reviewed. The emphasis of this work is on providing an understanding of the general phenomenon, including the origin of the Reststrahlen band, the role that optical phonons in polar dielectric lattices play in supporting sub-diffraction-limited modes and how the relatively long optical phonon lifetimes can lead to the low optical losses observed within these materials. Based on this overview, the achievements attained to date and the potential technological advantages of these materials are discussed for localized modes in nanostructures, propagating modes on surfaces and in waveguides and novel metamaterial designs, with the goal of realizing low-loss nanophotonics and metamaterials in the mid-infrared to terahertz spectral ranges.

On successive minima and the Absolute Siegel's Lemma

We prove a new bound on the product of the nth successive minimum of an automorphism of GL ( N , k A ) and the ( N − n + 1 ) th successive minimum of its dual, extending a classical inequality of K. Mahler for polar lattices to the geometry of numbers over the adèles. As a corollary we derive the Absolute Siegel's Lemma in Q ¯ as stated by D. Roy and J.L. Thunder.

Structure and lattice dynamics of binary lead silicate glasses investigated by infrared spectroscopy

The polar lattices dynamics of seven binary lead silicate glasses have been studied by infrared spectroscopy. The analysis of the reflectivity spectra with a dielectric function model, based on a modified Gaussian profile, allows a quantitative evaluation of the presence of lead cations within different structural sites. From the role of the lead cations versus the degree of polymerization of the silicate network and the comparison with literature results, we may to give a scenario for explaining the observed structural evolution of the glass matrix and more particularly the drastic change occurring around 45% of lead content. Below this threshold, lead cations act only as modifiers of the silicate network. Above, the glass structure is deeply modified; a lead network involving around 10% of the lead content appears in glasses whose composition is just above the threshold and progressively grows at the expense of the silicate network with the increase of lead content. For high lead content, lead cations can act as modifiers of the silicate network or as network formers. Results also show that the analysis of far infrared measurements combined with the knowledge of the UV edge optical response is very promising to characterize the local disorder around cations in glasses.

The Coulomb effects in the dynamics of polar lattices

Zone-center phonon frequencies of polar lattices are calculated for uniaxial crystals from the symmetry arguments. Long-range Coulomb forces and crystal anisotropy are explicitly taken into account. Free-carrier contributions into a dielectric constant are included. The angular dispersion of optical-phonon modes is compared with data for hexagonal 6H-SiC politype.