Boundary States Research Articles

Synthesizing spin–orbit couplings and symmetry-protected topological phase in acoustic metamaterials

Spin–orbit couplings (SOCs) underlie several key concepts of topological matter. However, acoustic waves lack intrinsic spin and SOCs, which makes some topological phases impossible. We develop in the present work a realistic scheme to synthesize simultaneously the intrinsic and Rashba–Dresselhaus SOCs in acoustic systems and explore the symmetry-protected topological phase induced by the SOCs. To be precise, we construct a two-leg ladder composed of acoustic resonators and linking tubes. Utilizing the concept of pseudospin, the spin-1/2 is encoded by the leg degree of freedom of the ladder, and meanwhile, the SOCs are achieved by engineering the couplings between resonators. We further highlight the emergence of the symmetry-protected topological phase respecting the chiral unitary (AIII) symmetry in such acoustic SOC lattices. This scheme is confirmed by the full-wave simulations. Our acoustic structure is within immediate experimental reach and enables the direct visualization of symmetry-protected topological boundary states, not yet been observed experimentally. Our results represent a route to synthesize the SOCs and will benefit an in-depth study of the spin–orbit physics in acoustics.

Adaptive iterative learning control for 2-D nonlinear discrete systems with iteration-dependent uncertainties

In the existing high-order internal model (HOIM)-based iterative learning control (ILC) results, they are primarily concerned with 1-D systems with fixed orders and coefficients. This paper first investigates the iteration-dependent HOIM-based adaptive ILC problem for 2-D nonlinear discrete systems with unknown input gain and multiple unknown iteration-dependent parameters, which can be generated by multiple HOIMs with iteration-dependent orders and coefficients. The adaptive control law with parameter learning law is designed by using the recursive least squares algorithm. Under iteration-dependent boundary states and reference trajectory, the proposed adaptive ILC algorithm is capable to drive the ILC tracking error to be zero asymptotically. In addition, the established adaptive ILC results can be extended to 2-D nonlinear discrete systems with multiple iteration-dependent HOIM-based boundary states, reference trajectory, and external disturbances. Finally, an illustrative example on practical dynamical processes is provided to demonstrate the validity and feasibility of the designed method.

Magnetic and Electric Properties of a Grain Boundary in Single‐Layer CrI3

Single‐layer CrI3 has attracted considerable interest because of its 2D magnetism. However, the properties of defects in single‐layer CrI3 have not been thoroughly studied yet. In this study, a line defect in the CrI3 single layer, which is a grain boundary caused by the position flipping of iodine atoms, is theoretically investigated. Using first‐principles calculations, the structural and electronic properties of this grain boundary in both zigzag and armchair directions are explored. The grain boundary exhibits ferromagnetic exchange interaction between the two grains. The conduction band minimum and valence band maximum of the grain boundary states are in the energy gap of perfect CrI3 single layer and form a direct gap, indicating an enhancement in photoelectronic properties. Moreover, the partial charge density in real space reveals that the doped electrons or holes predominantly distribute at the grain boundary. This can support a purely spin‐polarized current along the grain boundary. Findings suggest that the grain boundary exhibits unique electronic and magnetic properties, potentially offering valuable insights for spintronics applications.

Observation of momentum-gap topology of light at temporal interfaces in a time-synthetic lattice

Topological phases have prevailed across diverse disciplines, spanning electronics, photonics, and acoustics. Hitherto, the understanding of these phases has centred on energy (frequency) bandstructures, showcasing topological boundary states at spatial interfaces. Recent strides have uncovered a unique category of bandstructures characterised by gaps in momentum, referred to as momentum bandgaps or k gaps, notably driven by breakthroughs in photonic time crystals. This discovery hints at abundant topological phases defined within momentum bands, alongside a wealth of topological boundary states in the time domain. Here, we report the experimental observation of k-gap topology in a large-scale optical temporal synthetic lattice, manifesting as temporal topological boundary states. These boundary states are uniquely situated at temporal interfaces between two subsystems with distinct k-gap topology. Counterintuitively, despite the exponential amplification of k-gap modes within both subsystems, these topological boundary states exhibit decay in both temporal directions [i.e., with energy growing (decaying) before (after) the temporal interfaces]. Our findings mark a significant pathway for delving into k gaps, temporal topological states, and time-varying physics.

Approaches for aggregating data from the regional to the global level: importance for conclusions on Earth system state

Abstract A number of initiatives attempt to delimit the safe operating space (SOS) for human pressures on the Earth system, including the Planetary Boundaries framework. In some cases, data describing regional status are spatially aggregated to provide a global assessment. Several aggregation approaches can be observed, and the chosen approach may impact the conclusions. This study systematically reviews approaches of aggregating regional environmental boundaries and their state to the global level and uses a case study to compare them, aiming to highlight assumptions and implications and show how inconsistent approaches affect the accuracy and comparability of global boundary state. In the comprehensive literature review, 25 studies dealing with spatial aggregation of regional occupation of SOS and 43 associated regional boundary records were identified and categorized according to five spatial aggregation approaches and five types of adjustments that apply across approaches. These approaches were further classified as high- and low-risk approaches based on their assumptions and value judgements regarding precautionary levels and accepted regional transgressions. Notably, key publications dealing with multiple environmental boundaries use different aggregation approaches across the boundaries, potentially introducing biases. The application of these approaches to a case study revealed that the choice can influence the resulting aggregated occupation of SOS substantially, impacting conclusions as to whether or not a boundary is exceeded. To mitigate biases and inconsistencies, future estimates of spatially aggregated regional SOS should transparently communicate assumptions underlying the chosen aggregation approach, address potential inconsistencies across boundaries, and advance understanding of spatial propagation mechanisms.

Effect of Severe Plastic Deformation on the Structure and State of Grain Boundaries in Niobium

Effect of Severe Plastic Deformation on the Structure and State of Grain Boundaries in Niobium

Gigahertz Surface Acoustic Wave Topological Rainbow in Nanoscale Phononic Crystals.

Precisely engineered gigahertz surface acoustic wave (SAW) trapping enables diverse and controllable interconnections with various quantum systems, which are crucial to unlocking the full potential of phonons. The topological rainbow based on synthetic dimension presents a promising avenue for facile and precise localization of SAWs. In this study, we successfully developed a monolithic gigahertz SAW topological rainbow by utilizing a nanoscale translational deformation as a synthetic dimension. We observed a gapless topological boundary state, which originates from a 2π phase winding in the Zak phase during translation. These boundary states enable on-chip single-mode rainbowlike filters with an extensive range of adjustable operating frequencies. Furthermore, we construct nanoscale wedge-shaped grooves, realizing the Born-von-Karman interface. The interface generates topological rainbow resonators with high quality and small mode volume, which can trap topological phononic states of different frequencies into different positions. This study underscores the immense potential of topological acoustics in synthetic dimensions for microwave acoustics, providing a robust design framework for the precise manipulation of SAWs.

Progress and Prospects of Novel Topological Phases of Materials

The field of topological phases has captivated the condensed matter physics (CMP) community with its unique blend of theoretical elegance and practical relevance. The defining characteristic of the most celebrated topological insulator (TI) phase is their insulating bulk paired with a conductive surface; a property stemming from the non-trivial topology of their wavefunctions (Hasan et al 2023). In general, a d-dimensional system is classified as a TI if it has an insulating bulk and features boundary states that remain gapless, unaffected by local boundary perturbations unless the symmetry is broken. The TIs are characterized by the non-zero Z2 invariant which signifies odd number of gapless spinhelical topological surface states (TSS) protected by time-reversal symmetry (TRS). Thus, this provides a solid framework that the scientific community continues to build upon for the potential applications of TIs in spintronics, quantum computing and nano-electronics. The adoption of topological classification in the last decade has unveiled various quantum materials, from insulators and superconductors to Dirac, Weyl semimetals, and fragile topological phases (Chen et al 2023). This letter to the editor outlines the recent advancements in TIs which pave the way for investigation of TIs and multifunctional quantum materials. The non-trivial band topology is intricately embedded within the band structure of an insulator through band inversion. Intrinsic spin-orbit coupling (SOC) present in the system is a key factor in realizing the bulk band inversion or parity exchanges in most of the known TI genome. Numerous SOC induced TIs were theoretically and experimentally investigated ranging from HgTe/CdTe quantum wells, quintuple layered V2VI3 binary compounds, half-Heusler compounds, ternary noncentrosymmetric compounds etc (Patel et al 2024, Hsieh et al 2008, Dhori et al 2022, Dhori et al 2024, Sattigeri et al 2021). Despite theoretical predictions, the practical applications of TIs remain elusive largely due to the interference from the conduction contribution from the bulk in small bandgap semiconductor, precise control over material purity and challenging control over spin-momentum locking at elevated temperatures. Thus, in recent years, there has been a renewed interest in discovering materials that could bridge the gaps

Non-Hermitian Topology in Hermitian Topological Matter.

Non-Hermiticity gives rise to distinctive topological phenomena absent in Hermitian systems. However, connection between such intrinsic non-Hermitian topology and Hermitian topology has remained largely elusive. Here, considering the bulk and boundary as an environment and system, respectively, we demonstrate that anomalous boundary states in Hermitian topological insulators exhibit non-Hermitian topology. We study the self-energy capturing the particle exchange between the bulk and boundary, and show that it detects Hermitian topology in the bulk and induces non-Hermitian topology at the boundary. As an illustrative example, we reveal non-Hermitian topology and concomitant skin effect inherently embedded within chiral edge states of Chern insulators. We also identify the emergence of hinge states within effective non-Hermitian Hamiltonians at surfaces of three-dimensional topological insulators. Furthermore, we comprehensively classify our correspondence across all the tenfold symmetry classes of topological insulators and superconductors. Our Letter uncovers hidden connection between Hermitian and non-Hermitian topology, and provides an approach to identifying non-Hermitian topology in quantum matter.

Native Defect-Dependent Ultrafast Carrier Dynamics in p-Type Dopable Wide-Bandgap NiO.

NiO is a wide-bandgap p-type metal oxide that has extensive applications in optoelectronics and photocatalysts. Understanding the carrier dynamics in p-type NiO is pivotal for optimizing device performance, yet they remain largely unexplored. In this study, we employed femtosecond transient absorption spectroscopy to delve into the dynamics of photogenerated carriers in NiO films containing distinct prominent native defects: undoped NiO with oxygen vacancies (VO) and O-rich NiO (denoted as NiO1+δ) with nickel vacancies (VNi). Our findings unveil significant disparities between the two types of NiO thin films. The undoped NiO film exhibits a broad photoinduced absorption signal spanning the spectral range of 360-600 nm, whereas a photobleaching signal within the spectral range of 400-600 nm is observed in the O-rich NiO1+δ film, which can be attributed to their unique native defects. We ascertain that the fast formation of small electron polarons (SEPs) occurs within a delay time of approximately 200 fs. Subsequently, the photogenerated carriers undergo rapid trapping by localized states (e.g., grain boundary states) in undoped NiO and O-rich NiO1+δ within time scales of around 1-8 and 5-7 ps, respectively, followed by relatively slow trapping and recombination processes via native defects VO and VNi within time scales of approximately 200 ps and ∼2 ns, respectively. These findings illuminate the fundamental processes governing carrier dynamics in NiO thin films with different native defects, offering crucial insights for the advancement of NiO-based devices.

Thermalization and non-monotonic entanglement growth in an exactly solvable model

We study quantum quenches and subsequent non-equilibrium dynamics of free Dirac fermions in 1 + 1 spacetime dimensions using time dependent mass. The final state is a normalized boundary state which is called generalized Calabrese-Cardy (gCC) state and the system thermalizes to a generalized Gibb’s Ensemble(GGE). We can also tune the initial states so that the final states are exact Calabrese-Cardy (CC) state and special gCC states. The system in the CC state thermalizes to a Gibb’s ensemble. We derive closed-form analytic expressions for the growth of entanglement entropy of subsystems consisting of arbitrary number of disjoint intervals in CC state. We show that the entanglement entropy of a single interval grows monotonically before saturation. In case of certain gCC states, for particular charges, the entanglement entropy of a single interval grows non-monotonically when the effective chemical potential is increased beyond a critical value. We argue that the non-monotonic growth of entanglement entropy is a boundary effect which arises due to increase in long range correlation and decrease in short range correlation at early times.

Iterative learning consensus control for switched discrete-time multi-agent systems based on the 2-D linear discrete model

In this article, a class of switched nonlinear discrete-time heterogeneous (NDTH) multi-agent systems (MASs) with switching signals in both agent dynamics and communication topologies are considered, and a distributed iterative learning control (ILC) law is proposed for the output consensus of the switched NDTH MAS so that the outputs of all follower agents can well track the leader agent. With the proposed ILC controller, the iterative learning dynamic process of the switched NDTH MAS is firstly formulated as a two-dimensional (2-D) linear discrete Roesser model with specified boundary states at each switching sub-interval. Afterwards, according to the exploited properties on solution of the 2-D linear discrete Roesser model, a sufficient convergence theorem for the presented ILC controller is derived. At last, the validity of the ILC-based consensus controller is illustrated through a simulation experiment.

Local and energy-resolved topological invariants for Floquet systems

Periodically driven systems offer a perfect breeding ground for out-of-equilibrium engineering of topological boundary states at zero energy (0 mode), as well as finite energy (π mode), with the latter having no static analog. The Floquet operator and the effective Floquet Hamiltonian, which encapsulate the stroboscopic features of the driven system, capture both spectral and localization properties of the 0 and π modes but sometimes fail to provide complete topological characterization, especially when 0 and π modes coexist. In this work, we utilize the spectral localizer, a powerful local probe that can provide numerically efficient, spatially local, and energy-resolved topological characterization. In particular, we apply the spectral localizer to the effective Floquet Hamiltonian for driven one- and two-dimensional topological systems with no or limited symmetries and are able to assign topological invariants, or local markers, that characterize the 0- and the π-boundary modes individually and unambiguously. Due to the spatial resolution, we also demonstrate that the extracted topological invariants are suitable for studying driven disordered systems and can even capture disorder-induced phase transitions. Published by the American Physical Society 2024

Correlation Between Ultrasound Manifestations and Traditional Chinese Medicine Syndrome Differentiation of Breast Nodules

<i>Background </i>Breast nodules are a health issue that concerns women, and clinical practice entails great concern for accurate diagnosis and appropriate prevention and treatment. This study examined the correlation between ultrasound manifestations and traditional Chinese medicine (TCM) syndrome differentiation of breast nodules. <i>Methods </i>This study included 128 patients with breast nodules based on ultrasound-dependent Breast Imaging-Reporting and Data System (BI-RADS) grading and ultrasound elastography (UE) scoring. This study explored the correlation of syndrome differentiation with age, medical history, nodule size, morphology, boundary status, blood flow signals, BI-RADS grading, and UE score. <i>Results </i>Age and medical history were significantly correlated with TCM syndrome differentiation. Patients with the Chong–Ren imbalance syndrome were older, and those with the phlegm–blood stasis syndrome had the longest disease course. The maximum nodule diameter was not correlated with TCM syndrome differentiation. Furthermore, nodule blood flow signal, BI-RADS grading, and UE scoring were significantly correlated with TCM syndrome differentiation. Patients with the phlegm–blood stasis syndrome had the highest proportion of those with “blood flow signal,” BI-RADS Grade 4, and UE score of four points. Furthermore, the morphology and boundary state of the nodules were not correlated with TCM syndrome differentiation. <i>Conclusio</i>n Age, medical history, ultrasound blood flow signals, BI-RADS grading, and UE scoring were correlated with TCM syndrome differentiation in patients with breast nodules, particularly for BI-RADS Grade 4 and UE 4-point nodules, the prevalence of phlegm–blood stasis syndrome is at its highest. After excluding malignant transformation, patients with breast nodules at risk of cancer can receive preventive TCM treatment.

Probing chiral-symmetric higher-order topological insulators with multipole winding number

The interplay between crystalline symmetry and band topology gives rise to unprecedented lower-dimensional boundary states in higher-order topological insulators (HOTIs). However, the measurement of the topological invariants of HOTIs remains a significant challenge. Here, we define a multipole winding number (MWN) for chiral-symmetric HOTIs by applying a corner twisted boundary condition. The MWN, arising from both bulk and boundary states, accurately captures the bulk-corner correspondence including boundary-obstructed topological phases. To address the measurement challenge, we leverage the perturbative nature of the corner twisted boundary condition and develop a real-space approach for determining the MWN in both two-dimensional and three-dimensional systems. The real-space formula provides an experimentally viable strategy for directly probing the topology of chiral-symmetric HOTIs through dynamical evolution. Our findings not only highlight the twisted boundary condition as a powerful tool for investigating HOTIs, but also establish a paradigm for exploring real-space formulas for the topological invariants of HOTIs.

A CFT dual for evaporating black holes: boundary continuous matrix product states

Tensor network states, especially Matrix Product States (MPS), are crucial tools for studying how particles in large quantum systems are entangled with each other. MPS are particularly effective for modeling systems in one-dimensional space. Their continuous version, known as continuous Matrix Product States (cMPS), extends this approach to more complex quantum field theories that describe systems with an infinite number of interacting particles. This paper introduces a novel extension, boundary continuous Matrix Product States (BCMPS), which incorporate boundary states from conformal field theory (TFD state of two CFTs, let). We construct BCMPS and explore their potential holographic duals, linking them to black hole microstates with end-of-the-world branes in AdS/CFT. This connection hints at a deeper relationship between tensor networks and spacetime geometry, potentially offering new insights into the interplay between quantum information and gravity.

Effective geometry of Bell-network states on a dipole graph

Abstract Bell-network states are a class of entangled states of the geometry that satisfy an area-law for the entanglement entropy in a limit of large spins and are automorphism-invariant, for arbitrary graphs. We present a comprehensive analysis of the effective geometry of Bell-network states on a dipole graph. Our main goal is to provide a detailed characterization of the quantum geometry of a class of diffeomorphism-invariant, area-law states representing homogeneous and isotropic configurations in loop quantum gravity, which may be explored as boundary states for the dynamics of the theory. We found that the average geometry at each node in the dipole graph does not match that of a flat tetrahedron. Instead, the expected values of the geometric observables satisfy relations that are characteristic of spherical tetrahedra. The mean geometry is accompanied by fluctuations with considerable relative dispersion for the dihedral angle, and perfectly correlated for the two nodes.

Topological pumping in an inhomogeneous Aubry-André model

The Aubry-André model is a fundamental theoretical model that exhibits interesting topological features. In this paper, we examine topologically protected boundary states in the inhomogeneous off-diagonal Aubry-André model. In contrast to the homogeneous case, the inhomogeneity triggers boundary states at phase boundaries that separate two distinct non-trivial topological domains. Remarkably, the topological character of the boundary states is predicted through topological pumping, where a boundary state is transferred from one boundary across the bulk region to the other by adiabatically tuning the pump parameter. Moreover, the role of the off-diagonal modulation strength (λ) on the transfer efficiency of the topological pumping is addressed. To support our results, we investigate the time evolution of a continuous-time quantum walk and show that its spread rate and λ are inversely related. Our work provides a new avenue to harness topological features of the Aubry-André model, where topological pumping can be used for robust quantum transport.

Multiple boundary states in bilayer and decorated Su-Schrieffer-Heeger-like models

Multiple boundary states in bilayer and decorated Su-Schrieffer-Heeger-like models

Coupling-Controlled Photonic Topological Ring Array.

Photonic topological insulators with boundary states present a robust solution to mitigate structure imperfections. By alteration of the virtual boundary between trivial and topological insulators, it is possible to bypass such defects. Coupled resonator optical waveguides (CROWs) have demonstrated their utility in realizing photonic topological insulators, as they exhibit distinct topological phases and band structures. With this characteristic, we designed and experimentally validated a CROW array capable of altering its topological phase by adjusting the coupling strength. This array functions partially as a topological insulator and partially as a topologically trivial array, guiding light along the virtuous boundary between these two regions. By altering the shape of the topological insulator, we can effectively control the optical path. This approach promises practical applications, such as optical switches, dynamic light steering, optical sensing, and optical computing.