Topological Edge Modes Research Articles

Understanding of topological mode and skin mode morphing in 1D and 2D non-Hermitian resonance-based meta-lattices

Recent advances have demonstrated that the non-Hermitian skin effect (NHSE), induced by system non-Hermiticity, can manipulate the localization of in-gap topological edge modes (TEMs) within mechanical topological insulators. This study introduces a straightforward analytical framework to elucidate the competition between NHSE and TEM localization in a classical mechanical meta-lattice, highlighting its impact on the dynamic behavior of TEMs within separate Bragg scattering band gaps (BSBGs). We propose a 1D non-Hermitian meta-lattice featuring a locally resonant system with active feedback control, characterized by a real-valued transfer function. This local resonance creates two separate BSBGs, each hosting a TEM defined by non-Hermitian bulk-edge correspondence. Our theoretical and numerical analyses reveal that the NHSE, with its asymmetric localization within the two BSBGs, can shift the localization of TEMs in distinct ways. This leads to an asymmetric phase transition, wherein one TEM can be delocalized and relocalized by tuning the transfer function, while the other maintains its initial localization. Moreover, we extend the mechanism of 1D asymmetric TEM delocalization to the non-Hermitian morphing of TEMs, showcasing notable examples such as temporal and spatial topological wave pumping with space- and time-dependent transfer functions in 1D time-varying and 2D stacked meta-lattices. This research bridges a gap between non-Hermitian mechanical constructs and their potential applications in classical mechanics, reinterpreting known topological wave control in 1D and uncovering new mechanisms in 2D.

Manipulation of edge states in non-Hermitian acoustic Su Schrieffer Heeger chains

A distinctive feature of topology is its unique ability to obtain and control robust interface states. Among other elements, it has been shown that non-Hermiticity alone can trigger topological phase transition in physical systems. In this work, we construct acoustic Su Schrieffer Heeger(SSH) chains using different unit cells where only the non Hermitian components differ due to different distributions of onsite losses. Our study focus on exploring the emergence of edge states at the interfaces between two chains composed of different unit cells. Our findings delineate three distinct types of edge modes. The topological, cavity and Parity-Time edge modes originate from the topological phase of the unit cells, the local parity symmetry at the interface and the existence of a Parity Time symmetric domain wall, respectively. We then compare the robustness of these different edge modes against disorder, confirming the robustness of the topological edge modes. Parity Time edge states demonstrate superior robustness compared to classical cavity modes for low level of disorder. However, beyond a certain threshold, their eigenfrequencies importantly diverge.

Chiral Bulk Solitons in Photonic Graphene with Decorated Boundaries

AbstractA chiral bulk soliton in a nonlinear photonic lattice with decorated boundaries, presenting a novel approach to manipulate photonic transport without extensive bulk modifications is proposed. Unlike traditional methods that rely on topological edge and corner modes, this strategy leverages the robust chiral propagation of bulk modes. By introducing nonlinearity into the system, a stable bulk soliton, akin to the topological valley Hall effects is found. The chiral bulk soliton exhibits remarkable stability; the energy does not decay even after a long‐distance propagation; and the corresponding Fourier spectrum confirms the absence of inter‐valley scattering indicating a valley‐locking property. The findings not only contribute to the fundamental understanding of nonlinear photonic systems but also hold significant practical implications for the design and optimization of photonic devices.

Quantization of topological edge mode in a one-dimensional photonic crystal heterostructure

The study of topological phases of matter has seen significant advancements in recent years, largely driven by the discovery and exploration of their distinctive topological edge states. Here, we delve into the edge properties of a one-dimensional periodic multilayer structure. The analysis reveals that this system exhibits characteristics akin to the Su–Schrieffer–Heeger model in optics. The theoretical analysis explores the impact of multiple interfaces on the emergence of a topological edge mode (TEM) within the structure. The proposed heterostructure functions as a general beam splitter. Moreover, when the interface is doubled, the heterostructure exhibits two TEM states, resulting from the quantization of an incoming beam into its two equally orthogonal constituents. As the number of interfaces increases, more quantized TEM states occur within the photonic bandgap. Also, it identifies that the quality factor of the original TEM mode at 382.08 THz frequency linearly increases with respect to the number of interfaces. The outcome suggests potential applications in photonic sensors, optoelectronics, and photonic devices, indicating the heterostructure’s pivotal role in advancing these fields.

Engineering ideal helical topological networks in stanene via Zn decoration

The xene family of topological insulators plays a key role in many proposals for topological electronic, spintronic, and valleytronic devices. These proposals rely on applying local perturbations, including electric fields and proximity magnetism, to induce topological phase transitions in xenes. However, these techniques lack control over the geometry of interfaces between topological regions, a critical aspect of engineering topological devices. We propose adatom decoration as a method for engineering atomically precise topological edge modes in xenes. Our first-principles calculations show that decorating stanene with Zn adatoms exclusively on one of two sublattices induces a topological phase transition from the quantum spin Hall (QSH) to quantum valley Hall (QVH) phase and confirm the existence of spin-valley polarized edge modes propagating at QSH/QVH interfaces. We conclude by discussing technological applications of these edge modes that are enabled by the atomic precision afforded by recent advances in adatom manipulation technology.

Topologically Protected Single Edge Mode Lasing in Photonic Crystal Su–Schrieffer–Heeger Lattice with Directional Loss Control

AbstractTopological photonics is considered to be a robust and flexible platform for the design of nanophotonic devices against structural imperfections and performance degradation. Combining with parity‐time (PT) symmetry systems based on spatially distributed gain and loss, photonic crystal (PhC) lasers with micron‐size carrier reservoirs offer an ideal test bed for lasing mode competition and topological protection in nanophotonic structures. In this study, single topological edge mode (TEM) lasing is demonstrated in PhC lasers with a Su–Schrieffer–Heeger lattice comprised of coupled nanoresonators. By inducing directional loss control, a mode selection strategy is implemented, that achieves single TEM lasing with a side‐mode‐suppression ratio exceeding 30 dB. One of the TEMs exhibits remarkable robustness against local potential variation introduced by additional loss channels. This strategy integrating both topological protection and PT symmetry in nanophotonics would open up new prospects for the development of on‐chip single‐mode topological lasers unperturbed by output channels in nanophotonic integrated circuits.

Controlling acoustic non-Hermitian skin effect via synthetic magnetic fields

Non-Hermitian skin effect (NHSE) is an intrinsic non-Hermitian phenomenon where an extensive number of eigenmodes, called skin modes, are localized at the boundary of a system. Recent theories have suggested that the NHSE can be well-tuned by external fields, opening a route to manipulating wave localization. Here, we experimentally demonstrate the diverse interactions between NHSE and synthetic magnetic fields (SMFs) in coupled acoustic ring resonator lattices. We observe that the NHSE and SMFs can, via different physical mechanisms, compete or synergize, resulting in either the suppression or the creation of NHSE. With the aid of the complex frequency excitation technique, we experimentally observe that SMFs can suppress the NHSE by introducing Landau quantization, causing localization to move toward the bulk. In contrast, we show that the presence of SMF generates topological edge modes in the lattice, which then become corner skin modes by the second-order NHSE. Our results evidence the rich physics and diverse consequences that arise from the interplay of magnetic fields and NHSE, paving the way for actively controlling wave localization.

Broadband and fabrication-tolerant 3-dB couplers with topological valley edge modes

3-dB couplers, which are commonly used in photonic integrated circuits for on-chip information processing, precision measurement, and quantum computing, face challenges in achieving robust performance due to their limited 3-dB bandwidths and sensitivity to fabrication errors. To address this, we introduce topological physics to nanophotonics, developing a framework for topological 3-dB couplers. These couplers exhibit broad working wavelength range and robustness against fabrication dimensional errors. By leveraging valley-Hall topology and mirror symmetry, the photonic-crystal-slab couplers achieve ideal 3-dB splitting characterized by a wavelength-insensitive scattering matrix. Tolerance analysis confirms the superiority on broad bandwidth of 48 nm and robust splitting against dimensional errors of 20 nm. We further propose a topological interferometer for on-chip distance measurement, which also exhibits robustness against dimensional errors. This extension of topological principles to the fields of interferometers, may open up new possibilities for constructing robust wavelength division multiplexing, temperature-drift-insensitive sensing, and optical coherence tomography applications.

Compact topological edge modes through hybrid coupling of orbital angular momentum modes

Compact topological edge modes through hybrid coupling of orbital angular momentum modes

Real-space detection and manipulation of topological edge modes with ultracold atoms

Real-space detection and manipulation of topological edge modes with ultracold atoms

Asymmetric frequency multiplexing topological devices based on a floating edge band

Topological photonics provides a platform for robust energy transport regardless of sharp corners and defects. Recently, the frequency multiplexing topological devices have attracted much attention due to the ability to separate optical signals by wavelength and hence the potential application in optical communication systems. Existing frequency multiplexing topological devices are generally based on the slow light effect. However, the resulting static local spatial mode or finely tuned flat band has zero-group velocity, making it difficult for both experimental excitation and channel out-coupling. Here, we propose and experimentally demonstrate an alternative prototype of asymmetric frequency multiplexing devices including a topological rainbow and frequency router based on floating topological edge mode (instead of localized ones); hence the multiple wavelength channels can be collectively excited with a point source and efficiently routed to separate output ports. The channel separation in our design is achieved by gradually tuning the band gap truncation on a topological edge band over a wide range of frequencies. A crucial feature lies in that the topological edge band is detached from bulk states and floating within the upper and lower photonic band gaps. More interestingly, due to the sandwiched morphology of the edge band, the top and bottom band gaps will each truncate into transport channels that support topological propagation towards opposite directions, and the asymmetrical transportation is realized for the frequency multiplexing topological devices.

Magnetically controllable multimode interference in topological photonic crystals

Topological photonic insulators show promise for applications in compact integrated photonic circuits due to their ability to transport light robustly through sharp bendings. The number of topological edge states relies on the difference between the bulk Chern numbers across the boundary, as dictated by the bulk edge correspondence. The interference among multiple topological edge modes in topological photonics systems may allow for controllable functionalities that are particularly desirable for constructing reconfigurable photonic devices. In this work, we demonstrate magnetically controllable multimode interference based on gyromagnetic topological photonic insulators that support two unidirectional edge modes with different dispersions. We successfully achieve controllable power splitting in experiments by engineering multimode interference with the magnetic field intensity or the frequency of wave. Our work demonstrates that manipulating the interference among multiple chiral edge modes can facilitate the advancement of highly efficient and adaptable microwave devices.

On-chip topological phononic crystal acoustic waveguide based on lithium niobate thin films

This Letter introduces an on-chip topological phononic crystal (PnC) acoustic waveguide employing lithium niobate thin films. Utilizing a C3v symmetry-breaking mechanism, the topological PnC acoustic waveguide is achieved, operating at frequencies exceeding 430 MHz. A SH0 mode acoustic transceiver is designed, enabling highly efficient on-chip acoustic wave transmission and reception. The fabricated topological PnC waveguide demonstrates a propagation loss of 11.3 dB/mm at the edge mode. An acoustic beam splitter utilizing topological edge mode has been demonstrated, showing the configurability of the topological PnC acoustic waveguide. These results offer significant promise for advancing the development of hybrid phononic circuits tailored for high-frequency acoustic information processing, sensing, and manipulation.

Nonlinearity-induced topological phase transition characterized by the nonlinear Chern number

As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize the robust properties of condensed-matter systems immune to the existence of disorder. The bulk–boundary correspondence guarantees the emergence of gapless boundary modes in a topological system whose bulk exhibits non-zero topological invariants. Although some recent studies have suggested a possible extension of the notion of topology to nonlinear systems, the nonlinear counterpart of a topological invariant has not yet been understood. Here we propose a nonlinear extension of the Chern number based on the nonlinear eigenvalue problems in two-dimensional systems and show the existence of bulk–boundary correspondence beyond the weakly nonlinear regime. Specifically, we find nonlinearity-induced topological phase transitions, in which the existence of topological edge modes depends on the amplitude of oscillatory modes. We propose and analyse a minimal model of a nonlinear Chern insulator whose exact bulk solutions are analytically obtained. The model exhibits the amplitude dependence of the nonlinear Chern number, for which we confirm the nonlinear extension of the bulk–boundary correspondence. Thus, our result reveals the existence of genuinely nonlinear topological phases that are adiabatically disconnected from the linear regime.

Charge transfer and spin-valley locking in 4Hb-TaS2

Abstract4Hb-TaS2 is a superconductor that exhibits unique characteristics such as time-reversal symmetry breaking, hidden magnetic memory, and topological edge modes. It is a naturally occurring heterostructure comprising of alternating layers of 1H-TaS2 and 1T-TaS2. The former is a well-known superconductor, while the latter is a correlated insulator with a possible non- trivial magnetic ground state. In this study, we use angle resolved photoemission spectroscopy to investigate the normal state electronic structure of this unconventional superconductor. Our findings reveal that the band structure of 4Hb-TaS2 fundamentally differs from that of its constituent materials. Specifically, we observe a significant charge transfer from the 1T layers to the 1H layers that drives the 1T layers away from half-filling. In addition, we find a substantial reduction in inter-layer coupling in 4Hb-TaS2 compared to the coupling in 2H-TaS2 that results in a pronounced spin-valley locking within 4Hb-TaS2.

A rigorous mathematical theory for topological phases and edge modes in spring-mass mechanical systems

In this work, we examine the topological phases of the spring-mass lattices when the spatial inversion symmetry of the system is broken and prove the existence of edge modes when two lattices with different topological phases are glued together. In particular, for the one-dimensional lattice consisting of an infinite array of masses connected by springs, we show that the Zak phase of the lattice is quantized, only taking the value 0 or π . We also prove the existence of an edge mode when two semi-infinite lattices with distinct Zak phases are connected. For the two-dimensional honeycomb lattice, we characterize the valley Chern numbers of the lattice when the masses on the lattice vertices are uneven. The existence of edge modes is proved for a joint honeycomb lattice formed by gluing two semi-infinite lattices with opposite valley Chern numbers together.

Realizing Synthetic Dimensions and Artificial Magnetic Flux in a Trapped-Ion Quantum Simulator.

Synthetic dimension is a potent tool in quantum simulation of topological phases of matter. Here we propose and demonstrate a scheme to simulate an anisotropic Harper-Hofstadter model with controllable magnetic flux on a two-leg ladder using the spin and motional states of a single trapped ion. We verify the successful simulation of this model by comparing the measured dynamics with theoretical predictions under various coupling strength and magnetic flux, and we observe the chiral motion of wave packets on the ladder as evidence of the topological chiral edge modes. We develop a quench path to adiabatically prepare the ground states for varying magnetic flux and coupling strength, and we measure the chiral current on the ladder for the prepared ground states, which allows us to probe the quantum phase transition between the Meissner phase and the vortex phase. Our work demonstrates the trapped ion as a powerful quantum simulation platform for topological quantum matter.

Majorana-fermion origin of the planar thermal Hall effect in the Kitaev magnet α-RuCl3.

The field-induced quantum-disordered state of layered honeycomb magnet α-RuCl3 is a prime candidate for Kitaev spin liquids hosting Majorana fermions and non-Abelian anyons. Recent observations of anomalous planar thermal Hall effect demonstrate a topological edge mode, but whether it originates from Majorana fermions or bosonic magnons remains controversial. Here, we distinguish these origins from combined low-temperature measurements of high-resolution specific heat and thermal Hall conductivity with rotating magnetic fields within the honeycomb plane. A distinct closure of the low-energy bulk gap is observed for the fields in the Ru-Ru bond direction, and the gap opens rapidly when the field is tilted. Notably, this change occurs concomitantly with the sign reversal of the Hall effect. General discussions of topological bands show that this is the hallmark of an angle rotation-induced topological transition of fermions, providing conclusive evidence for the Majorana-fermion origin of the thermal Hall effect in α-RuCl3.

Anomalous and Chern topological waves in hyperbolic networks

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental work has been limited to time-reversal invariant systems made of coupled discrete resonances, leaving the more interesting case of robust, unidirectional edge wave transport completely unobserved. Here, we report a non-reciprocal hyperbolic network that exhibits both Chern and anomalous chiral edge modes, and implement it on a planar microwave platform. We experimentally evidence the unidirectional character of the topological edge modes by direct field mapping. We demonstrate the topological origin of these hyperbolic chiral edge modes by an explicit topological invariant measurement, performed from external probes. Our work extends the reach of topological wave physics by allowing for backscattering-immune transport in materials with synthetic non-Euclidean behavior.

150 Gbps THz Chipscale Topological Photonic Diplexer.

Photonic diplexers are being widely investigated for high data transfer rates in on-chip communication. However, dividing the available spectrum into nonoverlapping multicarrier frequency sub-bands has remained a challenge in designing frequency-selective time-invariant channels. Here, an on-chip topological diplexer is reported exhibiting terahertz frequency band filtering through Klein tunneling of topological edge modes. The silicon topological diplexer chip facilitates two high-speed channels with quadrature amplitude modulation (QAM) over a broad bandwidth of 12.5 GHz each. These channels operate at carrier frequencies of 305 and 321.6 GHz, achieving a combined diplexer capacity of 150 Gbits-1. To ensure minimal interference between adjacent channels, a guard band is implemented. Topologically protected edge modes suppress the frequency selective fading of the broadband signals and hold promise for diverse integrated photonic applications spanning terahertz and telecommunication realms, including the design of lossless topological multiplexers, interconnects, antennas, and modulators for the sixth to X generation (6G to XG) wireless.