Nontrivial Topological Structures Research Articles

Electrically engineering synthetic magnetic fields for polarized photons

Polarized photons are, in essence, neutral particles and therefore do not couple directly to external fields, thus hampering the effective interaction of photons with external fields. Here, we theoretically identify an equivalent spin-1/2 model for polarized photons and synthesize a magnetization vector for coupling differently polarized photons in an engineered anisotropic medium. The synthetic magnetic field can be electrically engineered to manipulate the magnetic moments of the pseudo-spin-1/2 photons, leading to observation of the Lorentz force and analogous Stern–Gerlach effect. We experimentally demonstrate these fundamental effects by using different spins, including purely single-polarization spins and mutually two-polarization mixing spins. We also demonstrate the higher-order Stern–Gerlach effect by using spins having nontrivial topological structures. Our findings could enable polarization-based elements with potential applications in polarization selection and conversion, benefiting classical and quantum information processing.

Emergence of Complex Network Topologies from Flow-Weighted Optimization of Network Efficiency

Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral branches, which can appear both in natural and manmade systems, such as subway and railway networks. In this study, we investigate the conditions for the emergence of these nontrivial topological structures in the context of human transportation in cities. We propose a simple model for spatial networks generation, where a network lattice acts as a planar substrate and edge speeds define an effective temporal distance which we aim to optimize and quantifies the efficiency in exploring the urban space. Complex network topologies can be recovered from the optimization of edges’ speeds and we study how the interplay between a flow probability between two nodes in space and the associated travel cost influences the resulting optimal network. In the perspective of urban transportation we simulate these flows by means of human mobility models to obtain origin-destination matrices. We find that when using simple lattices, the obtained optimal topologies transition from treelike structures to more regular networks, depending on the spatial range of flows. Remarkably, we find that branches paired to large loops structures appear as optimal structures when the network is optimized for an interplay between heterogeneous mobility patterns of small range travels and longer-range ones typical of commuting. Moreover, when congestion dynamics in traffic routing is considered, we study the emergence of additional edges from the tree structure to mitigate temporal delays. Finally, we show that our framework is able to recover the statistical spatial properties of the Greater London area subway network. Published by the American Physical Society 2024

Atomic-Scale Tracking Topological Phase Transition Dynamics of Polar Vortex-Antivortex Pairs.

Non-trivial topological structures, such as vortex-antivortex (V-AV) pairs, have garnered significant attention in the field of condensed matter physics. However, the detailed topological phase transition dynamics of V-AV pairs, encompassing behaviors like self-annihilation, motion, and dissociation, have remained elusive in real space. Here, polar V-AV pairs are employed as a model system, and their transition pathways are tracked with atomic-scale resolution, facilitated by in situ (scanning) transmission electron microscopy and phase field simulations. This investigation reveals that polar vortices and antivortices can stably coexist as bound pairs at room temperature, and their polarization decreases with heating. No dissociation behavior is observed between the V-AV phase at room temperature and the paraelectric phase at high temperature. However, the application of electric fields can promote the approach of vortex and antivortex cores, ultimately leading to their annihilation near the interface. Revealing the transition process mediated by polar V-AV pairs at the atomic scale, particularly the role of polar antivortex, provides new insights into understanding the topological phases of matter and their topological phase transitions. Moreover, the detailed exploration of the dynamics of polar V-AV pairs under thermal and electrical fields lays a solid foundation for their potential applications in electronic devices.

Ferroelectric behavior arising from polar topologies in epitaxially strained SrTiO3-δ ultrathin films

In this work, we show that epitaxially strained SrTiO3-δ thin films, grown by ion-beam sputtering onto (001)Nb:SrTiO3 substrates, exhibit a ferroelectric behavior. At the atomic-scale, through high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images, it was possible to identify the presence of polar nanoregions with non-trivial polar topological structures in the SrTiO3-δ film, which are induced through oxygen vacancies. To further confirm the presence of strained regions with a polar structure, Raman spectroscopy and high-resolution X-ray diffraction were employed and it was possible to confirm the presence of a tetragonal structure in the SrTiO3-δ film, with a tetragonality ratio (c/a) of 1.005. Scanning probe microscopy and macroscopic polarization-electric field hysteresis loops show ferroelectric behavior with maximum polarization of ∼1.5 μC/cm2, remnant polarization of ∼0.4 μC/cm2 and coercive field of ∼0.3 MV/cm. This work opens a window for exploring novel polar topological effects in sub-10 nm thin film materials for non-volatile memory application.

Thickness-dependent topological domain textures of layered ferroelectric Bi2WO6 thin films

Topological polar structures are attracting attention as potential applications of next-generation high-density memories. We investigate how the ferroelectric domain evolves with film thickness in c-axis oriented epitaxial Bi2WO6 thin films grown on (LaAlO3)0.3(Sr2AlTaO6)0.7 substrates. In addition to the general thickness scaling effect on domain size, we find that 3- or 4-variant domains appear in a sample thicker than 120 nm, whereas ⟨100⟩-type domains compete with the ⟨110⟩ ones in thinner samples, resulting in a variety of nontrivial topological structures. By visualizing the spatial distribution of electric polarizations through angle-resolved piezoresponse force microscopy, we provide direct evidence for the spontaneous emergence of nontrivial topological polar structures. These results provide useful insights into the domain behavior of layered ferroelectric thin films.

Topological Structure Realized in Cove-Edged Graphene Nanoribbons via Incorporation of Periodic Pentagon Rings.

Cove-edged zigzag graphene nanoribbons are predicted to show metallic, topological, or trivial semiconducting band structures, which are precisely determined by their cove offset positions at both edges as well as the ribbon width. However, due to the challenge of introducing coves into zigzag-edged graphene nanoribbons, only a few cove-edged graphene nanoribbons with trivial semiconducting bandgaps have been realized experimentally. Here, we report that the topological band structure can be realized in cove-edged graphene nanoribbons by embedding periodic pentagon rings on the cove edges through on-surface synthesis. Upon noncontact atomic force microscopy and scanning tunneling spectroscopy measurements, the chemical and electronic structures of cove-edged graphene nanoribbons with periodic pentagon rings have been characterized for different lengths. Combined with theoretical calculations, we find that upon inducing periodic pentagon rings the cove-edged graphene nanoribbons exhibit nontrivial topological structures. Our results provide insights for the design and understanding of the topological character in cove-edged graphene nanoribbons.

Topological phase transitions of generalized Brillouin zone

It has been known that the bulk-boundary correspondence (BBC) of the non-Hermitian skin effect is characterized by the topology of the complex eigenvalue spectra, while the topology of the wave function gives rise to Hermitian BBC with conventional boundary modes. In this work, we go beyond the known description of the non-Hermitian topological phase and find a different type of BBC that appears in generalized boundary conditions. The generalized Brillouin zone (GBZ) possesses non-trivial topological structures in the intermediate boundary condition between open and periodic boundary conditions. Unlike the conventional BBC, the topological phase transition is characterized by the generalized momentum touching of GBZ, which manifests as exceptional points. As a realization of our proposal, we suggest the non-reciprocal Kuramoto oscillator lattice, where phase slips accompany exceptional points as a signature of such topological phase transition. Our work establishes an understanding of non-Hermitian topological matter by complementing the non-Hermitian BBC as a general foundation of the non-Hermitian topological systems.

Prediction of Magnetic Janus Materials Based on Machine Learning and First-Principles Calculations

Discovering the compact、 stable and easily controllable nanoscale non-trivial topological magnetic structures—magnetic skyrmions,is the key to develop next-generation high-density, high-speed,and lowenergy non-volatile information storage devices.Based on the topological generation mechanism,magnetic skyrmions could be generated through the Dzyaloshinskii–Moriya Interaction (DMI) induced by spacereversal symmetry broken.Two dimensional (2D) non-centrosymmetric Janus could generate vertical builtin electric fields to break spatial inversion symmetry. Therefore, seeking 2D Janus with intrinsic magnetism is fundamental to develop the novel chiral magnetic storage technologies.In this work, we combined detailed machine learning techniques and first-principles calculations to discover the magnetism of the unexplored 2D janus. we first collected 1179 2D hexagonal ABC-type Janus based on the Materials Project database, and used elemental composition as feature descriptors to construct four machine learning models: Random Forest(RF), Gradient Boosting Decision Trees (GBDT), Extreme Gradient Boosting (XGB), and Extra Trees(ET). These algorithms and models were constructed to predict lattice constants, formation energies, and magnetic moment, via hyperparameter optimization and ten-fold cross-validation. GBDT exhibits the highest accuracy and best prediction performance for magnetic moment classification. Subsequently, the collected data of 82,018 yet-undiscovered 2D Janus,were input into the trained models to generate 4,024 high magnetic moment 2D Janus with thermal stability. First-principles calculations were employed to validate random sample of 13 Janus with high magnetic moment. This study provides an effective machine learning framework for magnetic moment classification and high-throughput screening of 2D Janus, accelerating the exploration of magnetic properties in 2D Janus structures.

Topological structures of DNA octahedrons determined by the number of ssDNA strands

How to control the nontrivial topological structures of DNA nanocages by the number of ssDNA strands is a fundamental problem for polyhedra assembly. In this paper, oriented octahedral links have been established as topological structure models to characterize DNA octahedrons with double helix edges assembled from one or more ssDNA strands. Here a program “Octa-links” has been developed in Python language to give all octahedral links and their components (number). There are 1566 types of octahedral links generated by considering all orientations calculated and the allowable tangle types on each edge. Note that all same orientations and links have been excluded by introducing 24 symmetric operations of octahedra. Furthermore, a new algorithm is proposed to give each component of each octahedral link as a series of vertex arcs, obtaining that the component number of all links fills the integer interval [1, 8]. Hence our program designed according to this algorithm paves an effective approach to calculate the component number of polyhedral links, making up the gap in the computer program on this aspect. Also, our work provides a complete list of topological structures with different component number for new DNA octahedrons assembled by adjusting the number of ssDNA strands.

Observation of modes reversion by encircling exceptional points in high-order non-hermitian system

The special properties of non-trivial topological structures usually come from a so-called edge mode which emerges in the band gap after the band inversion. The topological winding number of exceptional points (EPs) in non-Hermitian physical systems can be regarded as another type of topology. In photonics, the topological properties of EPs have been observed widely both in adiabatic and non-adiabatic second-order non-Hermitian systems. Here, we construct a higher-order non-Hermitian system with meta-atoms, including two independent second-order EPs. By circling EPs in different paths in the Riemann parameter surface, we observe extraordinary modes of reversion and repulsion, which is quite different from the conventional second-order EP systems. We propose a theoretical model of three-resonance non-Hermitian system and verify experimentally the mode reversion by encircling exceptional points in the microwave band, which may pave a new way for studying the topological physical mechanism of non-Hermitian systems, and provide a practical experimental system for its application.

Many-body Aharonov-Bohm caging in a lattice of rings

We study a system of a few ultracold bosons loaded into the states with orbital angular momentum $l=1$ of a one-dimensional staggered lattice of rings. Local eigenstates with winding numbers $+l$ and $-l$ form a Creutz ladder with a real dimension and a synthetic one. States with opposite winding numbers in adjacent rings are coupled through complex tunnelings, which can be tuned by modifying the central angle $\phi$ of the lattice. We analyze both the single-particle case and the few boson bound-state subspaces for the regime of strong interactions using perturbation theory, showing how the geometry of the system can be engineered to produce an effective $\pi$-flux through the plaquettes. We find non-trivial topological band structures and many-body Aharonov-Bohm caging in the $N$-particle subspaces even in the presence of a dispersive single-particle spectrum. Additionally, we study the family of models where the angle $\phi$ is introduced at an arbitrary lattice periodicity $\Gamma$. For $\Gamma>2$, the $\pi$-flux becomes non-uniform, which enlarges the spatial extent of the Aharonov-Bohm caging as the number of flat bands in the spectrum increases. All the analytical results are benchmarked through exact diagonalization.

Mapping between Spin-Glass Three-Dimensional (3D) Ising Model and Boolean Satisfiability Problem

The common feature for a nontrivial hard problem is the existence of nontrivial topological structures, non-planarity graphs, nonlocalities, or long-range spin entanglements in a model system with randomness. For instance, the Boolean satisfiability (K-SAT) problems for K ≥ 3 MSATK≥3 are nontrivial, due to the existence of non-planarity graphs, nonlocalities, and the randomness. In this work, the relation between a spin-glass three-dimensional (3D) Ising model MSGI3D with the lattice size N = mnl and the K-SAT problems is investigated in detail. With the Clifford algebra representation, it is easy to reveal the existence of the long-range entanglements between Ising spins in the spin-glass 3D Ising lattice. The internal factors in the transfer matrices of the spin-glass 3D Ising model lead to the nontrivial topological structures and the nonlocalities. At first, we prove that the absolute minimum core (AMC) model MAMC3D exists in the spin-glass 3D Ising model, which is defined as a spin-glass 2D Ising model interacting with its nearest neighboring plane. Any algorithms, which use any approximations and/or break the long-range spin entanglements of the AMC model, cannot result in the exact solution of the spin-glass 3D Ising model. Second, we prove that the dual transformation between the spin-glass 3D Ising model and the spin-glass 3D Z2 lattice gauge model shows that it can be mapped to a K-SAT problem for K ≥ 4 also in the consideration of random interactions and frustrations. Third, we prove that the AMC model is equivalent to the K-SAT problem for K = 3. Because the lower bound of the computational complexity of the spin-glass 3D Ising model CLMSGI3D is the computational complexity by brute force search of the AMC model CUMAMC3D, the lower bound of the computational complexity of the K-SAT problem for K ≥ 4 CLMSATK≥4 is the computational complexity by brute force search of the K-SAT problem for K = 3 CUMSATK=3. Namely, CLMSATK≥4=CLMSGI3D≥CUMAMC3D=CUMSATK=3. All of them are in subexponential and superpolynomial. Therefore, the computational complexity of the K-SAT problem for K ≥ 4 cannot be reduced to that of the K-SAT problem for K < 3.

Topological phase transitions in Tl<sub>2</sub>Ta<sub>2</sub>O<sub>7 </sub> under strain regulation

Topological electronic materials exhibit many novel physical properties, such as low dissipation transport and high carrier mobility. These extraordinary properties originate from their non-trivial topological electronic structures in momentum space. In recent years, topological phase transitions based on topological electronic materials have gradually become one of the hot topics in condensed matter physics. Using first-principles calculations, we explore the topological phase transitions driven by in-plane strain in ternary pyrochlore oxide Tl<sub>2</sub>Ta<sub>2</sub>O<sub>7</sub>. Firstly, we analyze the atomic-orbital-resolved band structure and find that the O (p<sub><i>x</i></sub>+p<sub><i>y</i></sub>) and p<sub><i>z</i></sub> orbitals of the system near the Fermi level have band inversion, indicating the emergence of topological phase transitions in the system. Then the tight-binding models are constructed to calculate the <i>Z</i><sub>2</sub> topological invariants, which can determine the topologically non-trivial feature of the system. Finally, topological properties such as surface states and a three-dimensional Dirac cone are studied. It is found that Tl<sub>2</sub>Ta<sub>2</sub>O<sub>7</sub> without strain is a semimetal with a quadratic band touching point at Fermi level, while the in-plane strain can drive the topological phase transition via breaking crystalline symmetries. When the system is under the –1% in-plane compression strain and without considering the spin orbit coupling (SOC), the application of strain results in two triply degenerate nodal points formed in the –<i>Z</i> to <i>Γ</i> direction and <i>Γ</i> to <i>Z</i> direction, respectively. When the SOC is included, there are two fourfold degenerate Dirac points on the –<i>Z</i> to <i>Γ</i> path and <i>Γ</i> to <i>Z</i> path<i>,</i> respectively. Thus, the –1% in-plane compression strain makes the system transit from the quadratic contact point semimetal to a Dirac semimetal. When 1% in-plane expansion strain is applied and the SOC is neglected, there exists one band intersection along <i>Y→</i><i>Γ</i>. When the SOC is taken into consideration, the gap is opened. Therefore, the 1% in-plane expansion strain drives Tl<sub>2</sub>Ta<sub>2</sub>O<sub>7</sub> into a strong topological insulator. In addition, the system is also expected to have strong correlation effect and superconductivity due to the possible flat band. This work can guide the study of topological phase transitions in three-dimensional materials and provide a good material platform for the design of low-dissipation electronic devices.

Surface-independent CO2 and CO reduction on two-dimensional kagome metal KV3Sb5.

Two-dimensional kagome metals possess rich band structure characteristics, including Dirac points, flat bands, and van Hove singularities, because of their special geometric structures. Furthermore, kagome metals AV3Sb5 (A = K, Rb, and Cs) have garnered significant attention due to their nontrivial topological electronic structures. In this study, we theoretically demonstrate that the KV3Sb5 (001) surface is conducive to CO2 and CO reduction. The thermodynamic stability and electrochemical states of various surface types are investigated. The reaction paths reveal that the product is identical on different surfaces, and the free energy profiles exhibit low onset potentials. This paper elucidates the effect of two-dimensional topological kagome metals on CO2 and CO reduction.

Synthetic Topological Vacua of Yang-Mills Fields in Bose-Einstein Condensates.

Topological vacua are a family of degenerate ground states of Yang-Mills fields with zero field strength but nontrivial topological structures. They play a fundamental role in particle physics and quantum field theory, but have not yet been experimentally observed. Here we report the first theoretical proposal and experimental realization of synthetic topological vacua with a cloud of atomic Bose-Einstein condensates. Our setup provides a promising platform to demonstrate the fundamental concept that a vacuum, rather than being empty, has rich spatial structures. The Hamiltonian for the vacuum of topological number n=1 is synthesized and the related Hopf index is measured. The vacuum of topological number n=2 is also realized, and we find that vacua with different topological numbers have distinctive spin textures and Hopf links. Our Letter opens up opportunities for exploring topological vacua and related long-sought-after instantons in tabletop experiments.

Superconductivity in clathrate LiLaB8 with nontrivial band topology

Materials that exhibit both superconductivity and nontrivial topological electronic structures have attracted considerable attention due to the potential for the realization of novel quantum states. Here, using swarm-intelligence structure prediction methodology and first-principles calculations, we have predicted a ternary double-metal boron clathrate superconductor LiLaB8 with topologically protected surface states. B atoms in LiLaB8 polymerize into two kinds of caged structures, i.e. B12 and B24 cages, enclosing Li and La atoms, respectively. LiLaB8 can be possibly synthesized at the pressure above 75 GPa and recovered to ambient conditions with B cages well preserved. Electron-phonon coupling calculations show that LiLaB8 is a potential superconductor with an estimated Tc of 2.4 K at 100 GPa, which increases to 9.5 K at ambient pressure. The enhanced superconductivity is considered to originate from softened mode related to the vibrations of La and B atoms. Electronic band structure calculations showcase the apparent “band inversion” of La 5d and B 2p orbitals. Z2 invariant and topologically protected surface states demonstrate that LiLaB8 is indeed a nontrivial-topological material. These results indicate LiLaB8 is a superconductor with nontrivial band topology that helps in the study of fascinating phenomena arising from the interplay of and superconductivity and band topology.

3D-Printed Möbius Microring Lasers: Topology Engineering in Photonic Microstructures.

Manipulating photons in artificially structured materials is highly desired in modern photonic technology. Nontrivial topological structures are rapidly emerging as a state-of-art platform for achieving unprecedented fascinating phenomena of photon manipulation. However, the current studies mainly focus on planar structures, and the fabrication of photonic microstructures with specific topological geometric features still remains a great challenge. Extending the topological photonics to 3Dmicroarchitectures is expected to enrich the photon manipulation capabilities and further advance the topological photonic devices. Here, a femtosecond laser direct writing technique is employed to fabricate 3D topological Möbius microring resonators from dye-doped polymer. The high-quality-factor Möbius microring resonator supports a unique spin-orbit coupled lasing at very low threshold. Due to the spin-orbit coupling induced geometric/Berry phase, the Möbius microrings, in striking contrast with ordinary microrings, output laser signals with all polarization states. The manipulation of miniaturized coherent light sources in the fabricated Möbius microrings represents a significant step forward toward 3D topological photonics that offers a novel design philosophy for functional photonic and optoelectronic devices.

Subwavelength Su-Schrieffer-Heeger topological modes in acoustic waveguides.

Topological systems furnish a powerful way of localizing wave energy at edges of a structured material. Usually, this relies on Bragg scattering to obtain bandgaps with nontrivial topological structures. However, this limits their applicability to low frequencies because that would require very large structures. A standard approach to address the problem is to add resonating elements inside the material to open gaps in the subwavelength regime. Unfortunately, generally, one has no precise control on the properties of the obtained topological modes, such as their frequency or localization length. In this work, a unique construction is proposed to couple acoustic resonators such that acoustic modes are mapped exactly to the eigenmodes of the Su-Schrieffer-Heeger (SSH) model. The relation between energy in the lattice model and the acoustic frequency is controlled by the characteristics of the resonators. In this way, SSH topological modes are obtained at any given frequency, for instance, in the subwavelength regime. The construction is also generalized to obtain well-controlled topological edge modes in alternative tunable configurations.

A Method of the Riemann–Hilbert Problem for Zhang’s Conjecture 2 in a Ferromagnetic 3D Ising Model: Topological Phases

A method of the Riemann–Hilbert problem is employed for Zhang’s conjecture 2 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in a zero external magnetic field. In this work, we first prove that the 3D Ising model in the zero external magnetic field can be mapped to either a (3 + 1)-dimensional ((3 + 1)D) Ising spin lattice or a trivialized topological structure in the (3 + 1)D or four-dimensional (4D) space (Theorem 1). Following the procedures of realizing the representation of knots on the Riemann surface and formulating the Riemann–Hilbert problem in our preceding paper [O. Suzuki and Z.D. Zhang, Mathematics 9 (2021) 776], we introduce vertex operators of knot types and a flat vector bundle for the ferromagnetic 3D Ising model (Theorems 2 and 3). By applying the monoidal transforms to trivialize the knots/links in a 4D Riemann manifold and obtain new trivial knots, we proceed to renormalize the ferromagnetic 3D Ising model in the zero external magnetic field by use of the derivation of Gauss–Bonnet–Chern formula (Theorem 4). The ferromagnetic 3D Ising model with nontrivial topological structures can be realized as a trivial model on a nontrivial topological manifold. The topological phases generalized on wavevectors are determined by the Gauss–Bonnet–Chern formula, in consideration of the mathematical structure of the 3D Ising model. Hence we prove the Zhang’s conjecture 2 (main theorem). Finally, we utilize the ferromagnetic 3D Ising model as a platform for describing a sensible interplay between the physical properties of many-body interacting systems, algebra, topology, and geometry.

Quantum Transport Evidence of Topological Band Structures of Kagome Superconductor CsV3Sb5

We report the transport properties of kagome superconductor CsV_{3}Sb_{5} single crystals at magnetic field up to 32 T. The Shubnikov-de Haas oscillations emerge at low temperature and four frequencies of F_{α}=27 T, F_{β}=73 T, F_{ε}=727 T, and F_{η}=786 T with relatively small cyclotron masses are observed. For F_{β} and F_{ε}, the Berry phases are close to π, providing clear evidence of nontrivial topological band structures of CsV_{3}Sb_{5}. Furthermore, the consistence between theoretical calculations and experimental results implies that these frequencies can be assigned to the Fermi surfaces locating near the boundary of Brillouin zone and confirms that the structure with an inverse Star of David distortion could be the most stable structure at charge density wave state. These results will shed light on the nature of correlated topological physics in kagome material CsV_{3}Sb_{5}.