Topological Boundary Research Articles

3D Carbon Allotropes: Topological Quantum Materials with Obstructed Atomic Insulating Phases, Multiple Bulk‐Boundary Correspondences, and Real Topology

AbstractThe study of topological phases with unconventional bulk‐boundary correspondences and nontrivial real Chern number has garnered significant attention in the topological states of matter. Using the first‐principle calculations and theoretical analysis, a high‐throughput material screening of the 3D obstructed atomic insulators (OAIs) and 3D real Chern insulators (RCIs) based on the Samara Carbon Allotrope Database (SACADA) are performed. Results show that 422 out of 703 3D carbon allotropes are 3D OAIs with multiple bulk‐boundary correspondences, including 2D obstructed surface states (OSSs) and 1D hinge states, which are in 1D and 2Ds lower than the 3D bulk, respectively. The 2D OSSs in these OAIs can be modified when subjected to appropriate boundaries, which benefits the investigation of surface engineering and the development of efficient topological catalysts. These 422 OAIs, which have 2D and 1D boundary states, are excellent platforms for multi‐dimensional topological boundaries research. Remarkably, 138 of 422 OAIs are also 3D RCIs, which show a nontrivial real topology in the protection of spacetime inversion symmetry. This work not only provides a comprehensive list of 3D carbon‐based OAIs and RCIs, but also guides their application in various aspects based on multiple bulk‐boundary correspondences and real topological phases.

Feature-energy duality of topological boundary states in a multilayer quantum spin Hall insulator

Feature-energy duality of topological boundary states in a multilayer quantum spin Hall insulator

A first-principles study of bilayer 1T'-WTe2/CrI3: a candidate topological spin filter

The ability to manipulate electronic spin channels in 2D materials is crucial for realizing next-generation spintronics. Spin filters are spintronic components that polarize spins using external electromagnetic fields or intrinsic material properties like magnetism. Recently, topological protection from backscattering has emerged as an enticing feature that can be leveraged to enhance the robustness of 2D spin filters. In this work, we propose and then characterize one of the first 2D topological spin filters: bilayer CrI3/1T’-WTe2. To do so, we use a combination of density functional theory, maximally localized Wannier functions, and quantum transport calculations to demonstrate that a terraced bilayer satisfies the principal criteria for being a topological spin filter: namely, that it is gapless, exhibits spin-polarized charge transfer from WTe2 to CrI3 that renders the bilayer metallic, and has a topological boundary which retains the edge conductance of monolayer 1T’-WTe2. In particular, we observe that small negative ferromagnetic moments are induced on the W atoms in the bilayer, and the atomic magnetic moments on the Cr are approximately 3.2 μB/Cr compared to 2.9 μB/Cr in freestanding monolayer CrI3. Subtracting the charge and spin densities of the constituent monolayers from those of the bilayer further reveals spin-orbit coupling-enhanced spin-polarized charge transfer from WTe2 to CrI3. We demonstrate that the bilayer is topologically trivial by showing that its Chern number is zero. Lastly, we show that interfacial scattering at the boundary between the terraced materials does not remove WTe2’s edge conductance. Altogether, this evidence indicates that BL 1T’-WTe2/CrI3 is gapless, magnetic, and topologically trivial, meaning that a terraced WTe2/CrI3 bilayer heterostructure in which only a portion of a WTe2 monolayer is topped with CrI3 is a promising candidate for a 2D topological spin filter. Our results further suggest that 1D chiral edge states may be realized by stacking strongly ferromagnetic monolayers, like CrI3, atop 2D nonmagnetic Weyl semimetals like 1T’-WTe2.

Hybrid plasmonic valley-Hall topological insulators

Abstract The emerging field of photonic topological insulators offers promising platforms for high-performance optical communication, computing, and sensing. However, conventional photonic topological insulator designs typically operate within the diffraction limit due to their dielectric nature. This limitation imposes constraints on device miniaturization, reduces light–matter interaction, and decreases overall device sensitivity. Introducing a new valley-Hall hybrid plasmonic topological insulator, we overcome this limitation by exploiting the coupling of surface plasmon oscillations with the optical modes of a dielectric photonic crystal, allowing for sub-diffraction vertical confinement of light. Deep-subwavelength chiral edge states can, therefore, be generated and robustly guided along disordered Z-shaped topological boundaries with much lower propagation loss compared to purely plasmonic platforms. Such extreme manipulation of light on an integrated chip platform maximizes light–matter interaction and opens the door for truly compact and efficient optical modulators, molecular sensors, and next-generation nanophotonic and quantum devices.

Pseudo-spin switches and Aharonov-Bohm effect for topological boundary modes.

Topological boundary modes in electronic and classical-wave systems exhibit fascinating properties. In photonics, topological nature of boundary modes can make them robust and endows them with an additional internal structure-pseudo-spins. Here, we introduce heterogeneous boundary modes, which are based on mixing two of the most widely used topological photonics platforms-the pseudo-spin-Hall-like and valley-Hall photonic topological insulators. We predict and confirm experimentally that transformation between the two, realized by altering the lattice geometry, enables a continuum of boundary states carrying both pseudo-spin and valley degrees of freedom (DoFs). When applied adiabatically, this leads to conversion between pseudo-spin and valley polarization. We show that such evolution gives rise to a geometrical phase associated with the synthetic gauge fields, which is confirmed via an Aharonov-Bohm type experiment on a silicon chip. Our results unveil a versatile approach to manipulating properties of topological photonic states and envision topological photonics as a powerful platform for devices based on synthetic DoFs.

Ultra‐Low‐Power Tunable Topological Photonic Filter on Hybrid Integrated Lithium Tantalite and Silicon Platform

AbstractIntegrated tunable optical filters are essential components in photonic signal processors, telecom systems, sensors, and quantum optical devices. Two of the most important features of a tunable filter are its dimensions and power consumption. Herein, the design and experimental validation of an on‐chip optical filter composed of a 1D topological photonic crystal cavity based on a hybrid integrated lithium tantalite‐silicon platform is presented. The strong optical confinement of the boundary state allows the fabrication of a tunable filter with an ultra‐compact size of 1.14 × 75 µm2 is demonstrated. Moreover, lithium tantalite has excellent electro‐optic properties and enables ultra‐low‐power wavelength tuning of the topological boundary state. The measured power consumption and tuning efficiency of the device are 0.0218 nW pm−1 and 6.64 pm V−1, respectively. The anisotropy of thin‐film lithium tantalite is verified by evaluating its tuning efficiency at different optical angles. The device can compensate for thermally induced refractive index changes ≈20 °C, exhibiting operational robustness. High‐speed transmission experiments confirm the stability of the developed tunable filter. This optical filter implements a topological structure with a compact size and can potentially be applied in on‐chip quantum optics, nonlinear optics, and optical sensing.

Topological Photonic Crystal in Microwave Region Based on Coupled Superconducting Resonators

Topological photonics has been widely investigated due to its profound physical significance and great number of potential applications. Microwaves have long wavelengths, so it is relatively easy to manufacture large-sized microwave photonic crystals, enabling researchers to observe and measure phenomena such as topological boundary states. Nevertheless, the quality factors (QFs) of most resonators composed of traditional materials in the microwave region are relatively low, leading to topological edge states with high decay rates. In this study, we present a one-dimensional topological photonic crystal in the microwave region based on coupled superconducting resonators. A topological state with a QF as high as 6000 is observed, which proves this to be a new platform for the investigation of topological photonics with low decay rates in the microwave regime.

An Improved Secondary Control Strategy for Dynamic Boundary Microgrids toward Resilient Distribution Systems

In order to achieve the flexible and efficient utilization of distributed energy resources, microgrids (MGs) can enhance the self-healing capability of distribution systems. Conventional primary droop control in microgrids exhibits deviations in voltage and frequency and lacks research on voltage–frequency control during network reconfiguration. Therefore, this paper investigates the control strategy of secondary control for voltage and frequency during the process of reconstructing distribution networks to operate in the form of microgrids after faults. Firstly, the mathematical model of three-phase voltage-source inverters with droop control is analyzed. Then, inspired by the generator’s secondary frequency control strategy, an improved secondary control method based on droop control is proposed, and the effectiveness of the improved droop control strategy is verified. Finally, simulation examples of distribution networks with various dynamic boundary topology changes are designed to simulate a relatively stable control result, validating the proposed strategy.

Realization of a quadrupole topological insulator phase in a gyromagnetic photonic crystal

ABSTRACT The field of topological photonics was initiated with the realization of a Chern insulator phase in a gyromagnetic photonic crystal (PhC) with broken time-reversal symmetry (T), hosting chiral edge states that are topologically protected propagating modes. Along a separate line of research, a quadrupole topological insulator was the first higher-order topological phase supporting localized corner states, but has been so far limited to T-invariant systems, as T is a key ingredient in early models. Here we report the realization of a quadrupole topological insulator phase in a gyromagnetic PhC, as a consequence of topological phase transition from the previously demonstrated Chern insulator phase. The phase transition has been demonstrated with microwave measurements, which characterize the evolution from propagating chiral edge states to localized corner states. We also demonstrate the migration of topological boundary states into the continuum, when the gyromagnetic PhC is magnetically tuned. These results extend the quadrupole topological insulator phase into T-broken systems, and integrate topologically protected propagating and localized modes in a magnetically tunable photonic crystal platform.

Bulk-Boundary Correspondence in Point-Gap Topological Phases.

A striking feature of non-Hermitian systems is the presence of two different types of topology. One generalizes Hermitian topological phases, and the other is intrinsic to non-Hermitian systems, which are called line-gap topology and point-gap topology, respectively. Whereas the bulk-boundary correspondence is a fundamental principle in the former topology, its role in the latter has not been clear yet. This Letter establishes the bulk-boundary correspondence in the point-gap topology in non-Hermitian systems. After revealing the requirement for point-gap topology in the open boundary conditions, we clarify that the bulk point-gap topology in open boundary conditions can be different from that in periodic boundary conditions. On the basis of real space topological invariants and the K theory, we give a complete classification of the open boundary point-gap topology with symmetry and show that the nontrivial open boundary topology results in robust and exotic surface states.

Topology optimization of steady Navier-Stokes flow using moving morphable void method

In order to explicitly and smoothly implement fluid-based topology optimization for improving the performance and manufacturing efficiency of flow systems, the moving morphable void (MMV) method is employed to optimize the steady-state navier-stokes (NS) flow for minimizing the dissipation energy under a volume constraint. To this end, a MMV-based Brinkman term is proposed to penalize the velocity in solid area, which can expand the region controlled by the NS flow equilibrium equation from fluid to whole design domain, and can also establish the relationship between design variables and governing equations. Then, a MMV-based optimization model of NS flow is proposed and the design variables are updated by the method of moving asymptotes according to the sensitivity analysis. In benchmark examples, we can precisely track the topology boundary with detailed geometric information without the intuitive geometric judgement error. Also, by means of contrasting the results of proposed method with previous work, the effectiveness and advantages of the MMV method can be confirmed.

Topological dualities via tensor networks

The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable in as much as it connects systems commonly associated to different areas of physics—that of long-range entangled topological order, (topological) band insulators, and classical statistical mechanics, respectively. Connecting fermionic and bosonic systems, the duality construction is intrinsically nonlocal, a complication that has been addressed in a plethora of different approaches, including dimensional reduction to one dimension, conformal field theory methods, and operator algebra. In this paper, we propose a unified approach to this duality, whose main protagonist is a tensor network (TN) assuming the role of an intermediate translator. Introducing a fourth node into the net of dualities offers several advantages: the formulation is integrative in that all links of the duality are treated on an equal footing, (unlike in field theoretical approaches) it is formulated with lattice precision, a feature that becomes key in the mapping of correlation functions, and their possible numerical implementation. Finally, the passage from bosons to fermions is formulated entirely within the two-dimensional TN framework where it assumes an intuitive and technically convenient form. We illustrate the predictive potential of the formalism by exploring the fate of phase transitions, point and line defects, topological boundary modes, and other structures under the mapping between system classes. Having condensed-matter readerships in mind, we introduce the construction pedagogically in a manner assuming only minimal familiarity with the concept of TNs. Published by the American Physical Society 2024

Hermitian and non-Hermitian topology from photon-mediated interactions

As light can mediate interactions between atoms in a photonic environment, engineering it for endowing the photon-mediated Hamiltonian with desired features, like robustness against disorder, is crucial in quantum research. We provide general theorems on the topology of photon-mediated interactions in terms of both Hermitian and non-Hermitian topological invariants, unveiling the phenomena of topological preservation and reversal, and revealing a system-bath topological correspondence. Depending on the Hermiticity of the environment and the parity of the spatial dimension, the atomic and photonic topological invariants turn out to be equal or opposite. Consequently, the emergence of atomic and photonic topological boundary modes with opposite group velocities in two-dimensional Hermitian topological systems is established. Owing to its general applicability, our results can guide the design of topological systems.

Kdm1a safeguards the topological boundaries of PRC2-repressed genes and prevents aging-related euchromatinization in neurons

Kdm1a is a histone demethylase linked to intellectual disability with essential roles during gastrulation and the terminal differentiation of specialized cell types, including neurons, that remains highly expressed in the adult brain. To explore Kdm1a’s function in adult neurons, we develop inducible and forebrain-restricted Kdm1a knockouts. By applying multi-omic transcriptome, epigenome and chromatin conformation data, combined with super-resolution microscopy, we find that Kdm1a elimination causes the neuronal activation of nonneuronal genes that are silenced by the polycomb repressor complex and interspersed with active genes. Functional assays demonstrate that the N-terminus of Kdm1a contains an intrinsically disordered region that is essential to segregate Kdm1a-repressed genes from the neighboring active chromatin environment. Finally, we show that the segregation of Kdm1a-target genes is weakened in neurons during natural aging, underscoring the role of Kdm1a safeguarding neuronal genome organization and gene silencing throughout life.

Dissection of a CTCF topological boundary uncovers principles of enhancer-oncogene regulation

Enhancer-gene communication is dependent on topologically associating domains (TADs) and boundaries enforced by the CCCTC-binding factor (CTCF) insulator, but the underlying structures and mechanisms remain controversial. Here, we investigate a boundary that typically insulates fibroblast growth factor (FGF) oncogenes but is disrupted by DNA hypermethylation in gastrointestinal stromal tumors (GISTs). The boundary contains an array of CTCF sites that enforce adjacent TADs, one containing FGF genes and the other containing ANO1 and its putative enhancers, which are specifically active in GIST and its likely cell of origin. We show that coordinate disruption of four CTCF motifs in the boundary fuses the adjacent TADs, allows the ANO1 enhancer to contact FGF3, and causes its robust induction. High-resolution micro-C maps reveal specific contact between transcription initiation sites in the ANO1 enhancer and FGF3 promoter that quantitatively scales with FGF3 induction such that modest changes in contact frequency result in strong changes in expression, consistent with a causal relationship.

Sub-wavelength topological boundary states and rainbow trapping of local-resonance phononic crystal plate

Based on the analogy of the quantum valley Hall effect, a ligament-type phononic crystal plate with local resonators is designed in this study to facilitate the valley state transport of low-frequency elastic waves. We analyze the key factors affecting the local resonance modes and reduce the frequency of the Dirac cone by changing the connection form of the structure’s beams. The spatial inversion symmetry of the structure is broken to open a new band gap by introducing a mass difference in the resonator pair. The robustness of the designed structure’s topological valley waveguide under defects and bends is verified. Based on this characteristic, we introduce the gradient heights into the supercell structure where elastic waves at different frequencies split and stop significantly on the supercell structure to achieve sub-wavelength topological rainbow trapping. This design provides a theoretical reference for exploring the low-frequency elastic topological mode and the application of topological rainbow capture in sub-wavelength structures.

Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds

If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the amplitudes of Fourier modes of primordial scalar curvature perturbations. Topological boundary conditions replace the full set of Fourier modes with specific linear combinations of selected Fourier modes as the eigenmodes of the scalar Laplacian. We present formulas for eigenmodes in orientable Euclidean manifolds with the topologies E 1–E 6, E 11, E 12, E 16, and E 18 that encompass the full range of manifold parameters and observer positions, generalizing previous treatments. Under the assumption that the amplitudes of primordial scalar curvature eigenmodes are independent random variables, for each topology we obtain the correlation matrices of Fourier-mode amplitudes (of scalar fields linearly related to the scalar curvature) and the correlation matrices of spherical-harmonic coefficients of such fields sampled on a sphere, such as the temperature of the cosmic microwave background (CMB). We evaluate the detectability of these correlations given the cosmic variance of the observed CMB sky. We find that topologies where the distance to our nearest clone is less than about 1.2 times the diameter of the last scattering surface of the CMB give a correlation signal that is larger than cosmic variance noise in the CMB. This implies that if cosmic topology is the explanation of large-angle anomalies in the CMB, then the distance to our nearest clone is not much larger than the diameter of the last scattering surface. We argue that the topological information is likely to be better preserved in three-dimensional data, such as will eventually be available from large-scale structure surveys.

Disorder‐Enhanced Corner State and Topological Corner State Transfer in a 2D Rice–Mele Lattice

AbstractThe corner states in the 2D Su–Schrieffer–Heeger (SSH) lattice are usually sensitive to disorder. It is shown that the uniform disorder and exponentially decayed disorder both can enhance the localizations of the corner states when the alternative onsite energy is introduced into the 2D SSH lattice mapped by superconducting circuit. The enhanced corner states originate from the fluctuations of onsite energy induced by disorders, which gives an example of utilizing the harmful resources to induce the corner states. Furthermore, different from the traditional topological state transfer based on the usual topological boundary states, it is shown that the high order topological corner state transfer can also be implemented in present lattice via adding the special long‐range hopping. The topological corner state transfer demonstrates the feasibility of using topological corner state to transfer quantum information, which supplies the relevant investigations on the applications of high order topological state in quantum information processing.

Edge State, Band Topology, and Time Boundary Effect in the Fine-Grained Categorization of Chern Insulators.

We predict novel topological phases with broken time-reversal symmetry supporting the coexistence of opposite chiral edge states, which are fundamentally different from the photonic spin-Hall, valley-Hall, and higher-order topological phases. We find a fine-grained categorization of Chern insulators, their band topologies characterized by identical Chern numbers are completely different. Furthermore, we prove that different topologies cause zeros in their Bloch wave function overlaps, which imprint the band gap closing and appear at the degenerate points of topological phase transition. The Bloch wave function overlaps predict the reflection and refraction at a topological time boundary, and the overlap zeros ensure the existence of vanishing revival amplitude at critical times even though different topologies before and after the time boundary have identical Chern numbers. Our findings create new opportunities for topological metamaterials, uncover the topological feature hidden in the time boundary effect as a probe of topology, and open a venue for the exploration of the rich physics originating from the long-range couplings.

A spectral dichotomy for commuting m-isometries with negative core operator

Let T=(T1,T2) be a pair of commuting operators such that the Taylor spectrum σ(T) of T is contained in the closed unit bidisc D‾2 and the left spectrum of either of T1 or T2 is contained in the unit circle ∂D. If the core operator of T is negative, then we show that σ(T) is either contained in ∂D2 or equal to D‾2. This fact applies in particular to a commuting pair of m-isometries with negative core operator. Our method of proof relies on a strictly 2-variable fact about the topological boundary of the Taylor spectrum. We also present several applications of this dichotomy to the multivariate Fredholm theory.