Topological Phase Research Articles

Phase diagrams and topological mixed edge states in silicene with intrinsic and extrinsic Rashba effects

We investigate the topological phases and corresponding edge states in silicene with fixed intrinsic and extrinsic Rashba spin-orbit couplings. The results show that silicene can exhibit four distinct topological phases, such as two types of valley-polarized quantum anomalous Hall effect (QAHE) and two types of QAHE that can be effectively controlled by the exchange field and electric field. In addition, these topological phases only correspond to the valley edge states distributed at the boundary of silicene. In particular, when the off-resonant circularly polarized (ORCP) light is further considered, silicene can host richer topological phases that are characterized by the Chern numbers from C=−3 to C=3, where the corresponding mixed edge states—where the valley and nonvalley edge states could coexist—can remarkably appear. More interestingly, the special higher Chern numbers C=±3 determine two valley edge states and one nonvalley edge state, with the right-moving or left-moving direction. These peculiar edge states are attributed to the ORCP light destroying the collapse of the Dirac cones that the valley edge states bridge. Additionally, silicene can experience multiple edge-state transitions for identical Chern numbers C=±2 between the valley edge state, nonvalley edge state, and two types of mixed edge state, under the ORCP light. This work may provide a platform and point of view for investigating other forms of topological edge state and is beneficial for designing multifunctional topological devices. Published by the American Physical Society 2024

Chirality reversal quantum phase transition in flat-band topological insulators.

Quantum anomalous Hall effect generates dissipationless chiral conductive edge states in materials with large spin-orbit coupling and strong, intrinsic, or proximity magnetization. The topological indexes of the energy bands are robust to smooth variations in the relevant parameters. Topological quantum phase transitions between states with different Chern numbers require the closing of the bulk bandgap: C=1→C=1/2 corresponds to the transition from a topological insulator to gapless in k=0 state- quantum anomalous semimetal. Within the Bernevig-Hughes-Zhang model of 2D topological quantum well, this study identifies another type of topological phase transition induced by a magnetic field. The transition C=±1→C=∓1occurs when the monotonic Zeeman field reaches the threshold value and thus triggers the reversal of edge modes chirality. The calculated threshold depends on the width of the conduction and valence bands and is more experimentally achievable the flatter the bands. The effect of the topological phase transition ∆C=2 can be observed experimentally as a jump in magnetoresistance.&#xD.

Layered hybrid superlattices as designable quantum solids.

Crystalline solids typically show robust long-range structural ordering, vital for their remarkable electronic properties and use in functional electronics, albeit with limited customization space. By contrast, synthetic molecular systems provide highly tunable structural topologies and versatile functionalities but are often too delicate for scalable electronic integration. Combining these two systems could harness the strengths of both, yet realizing this integration is challenging owing to distinct chemical bonding structures and processing conditions. Two-dimensional atomic crystals comprise crystalline atomic layers separated by non-bonding van der Waals gaps, allowing diverse atomic or molecular intercalants to be inserted without disrupting existing covalent bonds. This enables the creation of a diverse set of layered hybrid superlattices (LHSLs) composed of alternating crystalline atomic layers of variable electronic properties and self-assembled atomic or molecular interlayers featuring customizable chemical compositions and structural motifs. Here we outline strategies to prepare LHSLs and discuss emergent properties. With the versatile molecular design strategies and modular assembly processes, LHSLs offer vast flexibility for weaving distinct chemical constituents and quantum properties into monolithic artificial solids with a designable three-dimensional potential landscape. This opens unprecedented opportunities to tailor charge correlations, quantum properties and topological phases, thereby defining a rich material platform for advancing quantum information science.

Anisotropic quantum transport in a programmable photonic topological insulator

Quantum transport in materials describes the behavior of particles at the quantum level. Topological materials exhibit nontrivial transport properties with topological invariants, leading to the emergence of protected states that are immune against disorders at the material boundaries. In many real-world materials, especially those with anisotropic crystal structures, the transport properties can vary significantly along different directions within the material bulk. Here, we experimentally observe counterintuitive quantum transport phenomena in anisotropic topological insulators with controllable anisotropy and disorder, implemented on a programmable topological photonic chip. We examine phase transition from the topological phase to the Anderson phase, between which a new quasi-diffusive phase emerges. Anisotropic topological transport demonstrates unconventional superior robustness in the bulk mode compared to the edge mode, in the presence of disorder and loss in realistic systems. Peculiar topological transport with sophisticated gradient anisotropy, emulating stretched topological materials, occurs at the gradient domain wall that can be reconfigured. Our findings provide fresh insights into the intricate interplay between anisotropy within the bulk and robustness at the boundary of topological materials, which could lead to advancements in the field of topological material science and the development of topological devices with tailored functionalities.

Mapping the topology-localization phase diagram with quasiperiodic disorder using a programmable superconducting simulator

We explore a topology-localization phase diagram by simulating a one-dimensional Su-Schrieffer-Heeger model with quasiperiodic disorder using a programmable superconducting simulator. We experimentally map out and identify various trivial and topological phases with extended, critical, and localized bulk states. We find that with increasing disorder strength, some extended states can be first replaced by localized states and then by critical states before the system finally becomes fully localized. The critical states exhibit typical features such as multifractality and self-similarity, which lead to surprisingly rich phases with different types of mobility edges and scaling behaviors on the phase boundaries. Our results shed light on the investigation of the topological and localization phenomena in condensed-matter physics. Published by the American Physical Society 2024

Emerging Anomalous Hall Effect in (111)‐Oriented Artificial Iridate Honeycomb Lattices

AbstractComplex Ir oxides provide a promising platform for investigating cooperativity and competition between Mott physics and spin‐orbit coupling in condensed matter physics. These materials have the potential to reveal intriguing phases, such as topological phases and the Kitaev spin liquid state, an exactly solvable S = 1/2 spin model describing Ir4+ ions on a 2D honeycomb lattice. However, experimental confirmation of such phases in iridate films has been hindered by the difficulty of preparing (111)‐oriented samples of the perovskite phase. Herein, by constructing SrIrO3/SrTiO3 superlattices on SrTiO3 (111) substrates, (111)‐oriented perovskite phase SrIrO3 films are achieved with the unprecedentedly large thickness of 6 unit cells. Electrical and magnetic characterizations reveal that these films exhibit anomalous Hall insulating behavior, significant charge fluctuations, and long‐range antiferromagnetic order. Moreover, these properties can be tuned by varying the thickness of the SrIrO₃ layer. These emergent phenomena underscore the complex interactions among spin‐orbit coupling, electron–electron correlations, and crystal structure in (111)‐oriented artificial iridate honeycomb lattices. Further, spin fractionalization and topological quantum spin liquid may be achieved by tuning the spin–orbit coupling and crystal field intensity from interface engineering.

Building 1D lattice models with $G$-graded fusion category

We construct a family of one-dimensional (1D) quantum lattice models based on GG-graded unitary fusion category \mathcal{C}_G𝒞G. This family realize an interpolation between the anyon-chain models and edge models of 2D symmetry-protected topological states, and can be thought of as edge models of 2D symmetry-enriched topological states. The models display a set of unconventional global symmetries that are characterized by the input category \mathcal{C}_G𝒞G. While spontaneous symmetry breaking is also possible, our numerical evidence shows that the category symmetry constrains the models to the extent that the low-energy physics has a large likelihood to be gapless.

All-optical switching in nonlinear topological waveguide arrays

Photonic topological states are prospective in integrated optical devices due to their robustness to perturbations and defects. When taking into account the nonlinear effects of the system, the functionality of topological photonics can be further enhanced. Here, we investigated the interplay between topological edge states and nonlinear effects based on the Su–Schrieffer–Heeger (SSH) model. Relying on the theory prediction that topological edge states would shift upward under the action of nonlinearity, two types of optical switching are designed and experimentally realized in femtosecond laser direct-write waveguide arrays. This work provides a new, to the best of our knowledge, approach to preparing all-optical switches and offers a new perspective on the application of nonlinearity in topological optical devices.

Spin-valley locked topological phase transitions in reversible strain-tailoring honeycomb motifs

Using an effective low-energy k·p model on the frontier px,y orbitals, we establish a general phase diagram of spin-valley locked band inversion by introducing a mechanical strain field into nonmagnetic honeycomb motifs with robust spin–orbit coupling and intrinsically broken inversion symmetry. Using first-principles calculations, we realize such multiple topological phase transitions in a strained InTe monolayer within experimental reach with the Weyl semimetal as the nontrivial boundary state at two critical strains. The massless Weyl fermions endow the spin and valley Hall effects with ultrafast and dissipationless transport over a broad low-energy window. The valley selective circular dichroism can be regulated by strain-induced band inversion. A crossover between the topologically trivial and nontrivial regimes with sizable bandgaps makes InTe suitable for room-temperature (RT) topological strain-effect transistors. Our work not only demonstrates a fundamental mechanism for exploring tunable topological states and valley physics but also provides a potential platform for realizing many exotic phenomena and RT quantum devices.

Manipulating winding numbers and multiple topological bound states via long-range coupling in chiral photonic lattices

The topological bound states are limited to one pair in traditional one-dimensional (1D) topological chiral models as the winding number can only take the value of 0 or 1. It was increased to 2 or 3 via long-range couplings (LRCs) that were restricted to second- or third-order in recent experimental or theoretical researches. How to generate larger winding number to manipulate more topological bound states remains a challenge. Here, we propose an effective method by introducing arbitrary Nth order LRC stronger than the sum of other order couplings. The resulting winding number has been computed by getting the winding loop's envelope in parameter space. The coupling-inverted 1D photonic topological insulators supporting up to three pairs of highly localized multiple topological bound states are realized by fabricating photonic lattices with multi-layer waveguide arrays. Furthermore, these topological bound states are closely spaced, offering a promising implementation approach of multimode topological lasers in gain media. Our work highlights the advantages of LRCs in manipulating the topological phases of matter. Published by the American Physical Society 2024

Three-dimensional fracton topological orders with boundary Toeplitz braiding

Three-dimensional fracton topological orders with boundary Toeplitz braiding

3D 3,44T19 Type Carbon Allotrope (3,44T19‐CA): An Ideal Candidate with Phononic Stiefel–Whitney Topology and Multi–Dimensional Boundary Vibrational Modes

The Stiefel–Whitney (SW) insulator, which lacks spin‐orbit coupling and has space–time inversion () symmetry, has attracted significant interest due to its fragile topological state and unconventional bulk‐boundary correspondence. Previously, the identification of SW insulators has been widely proposed for 2D phononic systems, but it has received little attention for 3D phononic systems. Herein, it is recognized that the 3D 3,44T19 type carbon allotrope (3,44T19‐CA) possesses the possibility to attain the nontrivial phononic SW topology characterized by a nontrivial second SW number, specifically w2 = 1. In addition, the 3D 3,44T19‐CA has 2D surface vibrational modes and 1D hinge vibrational modes, providing an excellent platform for multi–dimensional topological phononic boundaries research.

An architecture for two-qubit encoding in neutral ytterbium-171 atoms

We present an architecture for encoding two qubits within the optical “clock” transition and nuclear spin-1/2 degree of freedom of neutral ytterbium-171 atoms. Inspired by recent high-fidelity control of all pairs of states within this four-dimensional quotes space, we present a toolbox for intra-ququart (single-atom) one- and two-qubit gates, inter-ququart (two-atom) Rydberg-based two- and four-qubit gates, and quantum nondemolition (QND) readout. We then use this toolbox to demonstrate the advantages of the ququart encoding for entanglement distillation and quantum error correction which exhibit superior hardware efficiency and better performance in some cases since fewer two-atom operations are required. Finally, leveraging single-state QND readout in our ququart encoding, we present a unique approach to studying interactive circuits and to realizing a symmetry protected topological phase of a spin-1 chain with a shallow, constant-depth circuit.

Valley switch effect in an α-T3 lattice-based superconducting interferometer

Abstract Dirac electrons possess a valley degree of freedom, which is currently under investigation as a potential information carrier. We propose an approach to generate and manipulate the valley-switching current (VSC) through Andreev reflection using an interferometer-based superconductor hybrid junction. The interferometer comprises a ring-shaped structure formed by topological kink states in the α-T3 lattice via carefully designed electrostatic potentials. Our results demonstrate the feasibility of achieving a fully polarized VSC in this device without contamination from cotunneling electrons sharing the same valley as the incident electron. Furthermore, we show that control over the fully polarized VSC can be achieved by applying a nonlocal gate voltage or modifying the global parameter α. The former alters the dynamic phase of electrons while the latter provides an α-dependent Berry phase, both directly influencing quantum interference and thereby affecting performance in terms of generating and manipulating VSC, crucial for advancements in valleytronics.

TTMGNet: Tree Topology Mamba-Guided Network Collaborative Hierarchical Incremental Aggregation for Change Detection

Change detection (CD) identifies surface changes by analyzing bi-temporal remote sensing (RS) images of the same region and is essential for effective urban planning, ensuring the optimal allocation of resources, and supporting disaster management efforts. However, deep-learning-based CD methods struggle with background noise and pseudo-changes due to local receptive field limitations or computing resource constraints, which limits long-range dependency capture and feature integration, normally resulting in fragmented detections and high false positive rates. To address these challenges, we propose a tree topology Mamba-guided network (TTMGNet) based on Mamba architecture, which combines the Mamba architecture for effectively capturing global features, a unique tree topology structure for retaining fine local details, and a hierarchical feature fusion mechanism that enhances multi-scale feature integration and robustness against noise. Specifically, the a Tree Topology Mamba Feature Extractor (TTMFE) leverages the similarity of pixels to generate minimum spanning tree (MST) topology sequences, guiding information aggregation and transmission. This approach utilizes a Tree Topology State Space Model (TTSSM) to embed spatial and positional information while preserving the global feature extraction capability, thereby retaining local features. Subsequently, the Hierarchical Incremental Aggregation Module is utilized to gradually align and merge features from deep to shallow layers to facilitate hierarchical feature integration. Through residual connections and cross-channel attention (CCA), HIAM enhances the interaction between neighboring feature maps, ensuring that critical features are retained and effectively utilized during the fusion process, thereby enabling more accurate detection results in CD. The proposed TTMGNet achieved F1 scores of 92.31% on LEVIR-CD, 90.94% on WHU-CD, and 77.25% on CL-CD, outperforming current mainstream methods in suppressing the impact of background noise and pseudo-change and more accurately identifying change regions.

Tight-binding model of Pt-based jacutingaites as combination of the honeycomb and kagome lattices

We introduce a refined tight-binding (TB) model for Pt-based jacutingaite materialsPt2NX3, (N= Zn, Cd, Hg; X = S, Se, Te), offering a detailed representation of the low-energy physics of its monolayers. This model incorporates all elements with significant spin-orbit coupling contributions, which are essential for understanding the topological energy gaps in these materials. Through comparison with first-principles calculations, we meticulously fitted the TB parameters, ensuring an accurate depiction of the energy bands near the Fermi level. Our model reveals the intricate interplay between the Pt 3eandNmetal orbitals, forming distinct kagome and honeycomb lattice structures. Applying this model, we explore the edge states of Pt-based jacutingaite monolayer nanoribbons, highlighting the sensitivity of the topological edge states dispersion bands to the nanostructures geometric configurations. These insights not only deepen our understanding of jacutingaite materials but also assist in tailoring their electronic properties for future applications.

Bonding Interactions Can Drive Topological Phase Transitions in a Zintl Antiferromagnetic Insulator

AbstractWhile ∼30% of materials are reported to be topological, topological insulators are rare. Magnetic topological insulators (MTI) are even harder to find. Identifying crystallographic features that can host the coexistence of a topological insulating phase with magnetic order is vital for finding intrinsic MTI materials. Thus far, most materials that are investigated for the determination of an MTI are some combination of known topological insulators with a magnetic ion such as MnBi2Te4. Motivated by the recent success of EuIn2As2, the role of chemical pressure on topologically trivial insulator is investigated, Eu5In2Sb6 via Ga substitution. Eu5Ga2Sb6 is predicted to be topological but is synthetically difficult to stabilize. The intermediate compositions between Eu5In2Sb6 and Eu5Ga2Sb6 are observed through theoretical works to explore a topological phase transition and band inversion mechanism. The band inversion mechanism is attributed to changes in Eu–Sb hybridization as Ga is substituted for In due to chemical pressure. Eu5In4/3Ga2/3Sb6 is also synthesized, the highest Ga concentration in Eu5In2‐xGaxSb6, and report the thermodynamic, magnetic, transport, and Hall properties. Overall, the work paints a picture of a possible MTI via band engineering and explains why Eu‐based Zintl compounds are suitable for the co‐existence of magnetism and topology.

Hierarchical zero- and one-dimensional topological states in symmetry-controllable grain boundary

Structural imperfections can be a promising testbed to engineer the symmetries and topological states of solid-state platforms. Here, we present direct evidence of hierarchical transitions of zero- (0D) and one-dimensional (1D) topological states in symmetry-enforced grain boundaries (GB) in 1T′–MoTe2. Using a scanning tunneling microscope tip press-and-pulse procedure, we construct two distinct types of GBs, which are differentiated by the underlying symmorphic and nonsymmorphic symmetries. The GBs with the nonsymmorphic rotation symmetry harbor first-order topological edge states protected by a nonsymmorphic band degeneracy. On the other hand, the edge state of the symmorphic GBs attains a band gap. More interestingly, the gapped edge state realizes a hierarchical topological phase, evidenced by the additional 0D boundary states at the GB ends. We anticipate our experiments will pioneer the material platform for the hierarchical realization of first-order and higher-order topology.

Uniform Diffusion of Cooper Pairing Mediated by Hole Carriers in Topological Sb2Te3/Nb.

Spin-helical Dirac Fermions at a doped topological insulator's boundaries can support Majorana quasiparticles when coupled with s-wave superconductors, but in n-doped systems, the requisite induced Cooper pairing in topological states is often buried at heterointerfaces or complicated by degenerate coupling with bulk conduction carriers. Rarely probed are p-doped topological structures with nondegenerate Dirac and bulk valence bands at the Fermi level, which may foster long-range superconductivity without sacrificing Majorana physics. Using ultrahigh-resolution photoemission, we report proximity pairing with a large decay length in p-doped topological Sb2Te3 on superconducting Nb. Despite no momentum-space degeneracy, the topological and bulk states of Sb2Te3/Nb exhibit the same isotropic superconducting gaps at low temperatures. Our results unify principles for realizing accessible pairing in Dirac Fermions relevant to topological superconductivity.

Topological phase transitions via attosecond x-ray absorption spectroscopy

We present a numerical experiment that demonstrates the possibility to capture topological phase transitions via an x-ray absorption spectroscopy scheme. We consider a Chern insulator whose topological phase is tuned via a second-order hopping. We perform time-dynamics simulations of the out-of-equilibrium laser-driven electron motion that enables us to model a realistic attosecond spectroscopy scheme. In particular, we use an ultrafast scheme with a circularly polarized IR pump pulse and an attosecond x-ray probe pulse. A laser-induced dichroism-type spectrum shows a clear signature of the topological phase transition. We are able to connect these signatures with the Berry structure of the system. This work extend the applications of attosecond absorption spectroscopy to systems presenting a non-trivial topological phase.