Topological Valley Research Articles

Direct observation of terahertz topological valley transport.

Topological photonics offers the possibility of robust transport and efficiency enhancement of information processing. Terahertz (THz) devices, such as waveguides and beam splitters, are prone to reflection loss owing to their sensitivity to defects and lack of robustness against sharp corners. Thus, it is a challenge to reduce backscattering loss at THz frequencies. In this work, we constructed THz photonic topological insulators and experimentally demonstrated robust, topologically protected valley transport in THz photonic crystals. The THz valley photonic crystal (VPC) was composed of metallic cylinders situated in a triangular lattice. By tuning the relevant location of metallic cylinders in the unit cell, mirror symmetry was broken, and the degenerated states were lifted at the K and K' valleys in the band structure. Consequently, a bandgap of THz VPC was opened, and a nontrivial band structure was created. Based on the calculated band structure, THz field distributions, and valley Berry curvature, we verified the topological phase transition in such type of THz photonic crystals. Further, we showed the emergence of valley-polarized topological edge states between the topologically distinct VPCs. The angle-resolved transmittance measurements identified the bulk bandgap in the band structure of the VPC. The measured time-domain spectra demonstrated the topological transport of valley edge states between distinct VPCs and their robustness against bending and defects. Furthermore, experiments conducted on a topological multi-channel intersectional device revealed the valley-polarized characteristic of the topological edge states. This work provides a unique approach to reduce backscattering loss at the THz regime. It also demonstrates potential high-efficiency THz functional devices such as topologically protected beam splitters, low-loss waveguides, and robust delay lines.

Coexisting valley and pseudo-spin topological edge states in photonic topological insulators made of distorted Kekulé lattices

Photonic topological insulators protected by the lattice spatial symmetry (e.g., inversion and rotation symmetry) mainly support single type edge state, interpreted by either valley or pseudo-spin. Here, we demonstrate theoretically, numerically, and experimentally that a type of judiciously designed two-dimensional Kekulé photonic crystal with time reversal symmetry can possess topological valley and pseudo-spin edge states in different frequency bands. Topologically robust transportation of both the valley and pseudo-spin edge states was confirmed by measuring the transmission of straight and z-shaped interface supported edge mode and comparing with bulk modes in the microwave frequency regime. In addition, we show that due to the distinct topological origins, valley and pseudo-spin edge states can be distinguished by examining their end-scattering into the free space. Our system provides an alternative way in manipulating electromagnetic waves with additional degree-of-freedom, which has potential applications for robust and high-capacity waveguiding and multi-mode dividing.

Valley topological line-defects for Terahertz waveguides and power divider

Topological edge states exhibit low backscattering, unidirectional energy propagation, and robust immunity to sharp bends and defects in photonic topological waveguides. These properties of topological waveguides are expected to be applied in terahertz (THz) technology and expand to functional devices. Here, we introduce a line-defect into valley Hall photonic crystals (VPCs) and discuss the influence of line-defect to edge states of valley Hall photonic topological waveguide. The introduction of line-defect can greatly improve the design freedom of topological waveguides, and is expected to be extended to functional devices. We constructed a straight VPC waveguide and a Z-shaped VPC waveguide to verify the topological valley line-defect edge state and the single-mode transmission of topological line-defect states is excited by a rectangular waveguide with a tapered coupling structure. The VPC waveguide has low bending loss and a working bandwidth (return loss < −10 dB) from 0.4 to 0.422 THz. We propose a topological power divider (TPD) operating at THz frequencies and achieved −3.3 per port equal power divide. Furthermore, this TPD is robust against defects and is promising for on-chip THz integration.

Gigahertz topological valley Hall effect in nanoelectromechanical phononic crystals

Topological phononics offers numerous opportunities in manipulating elastic waves that can propagate in solids without being backscattered. Due to the lack of nanoscale imaging tools that aid the system design, however, acoustic topological metamaterials have been mostly demonstrated in macroscale systems operating at low (kilohertz to megahertz) frequencies. Here, we report the realization of gigahertz topological valley Hall effect in nanoelectromechanical AlN membranes. Propagation of elastic wave through phononic crystals is directly visualized by microwave microscopy with unprecedented sensitivity and spatial resolution. The valley Hall edge states, protected by band topology, are vividly seen in both real- and momentum-space. The robust valley-polarized transport is evident from the wave transmission across local disorder and around sharp corners, as well as the power distribution into multiple edge channels. Our work paves the way to exploit topological physics in integrated acousto-electronic systems for classical and quantum information processing in the microwave regime.

Electronic phase transition, spin filtering effect, and spin Seebeck effect in 2D high-spin-polarized VSi2X4 (X = N, P, As)

Spin gapless semiconductors (SGSs) and bipolar magnetic semiconductors (BMSs) are highly desirable for advanced spintronic applications due to their unique electronic and magnetic properties. Being inspired by the recent synthesis of the 2D MA2X4 family with various electronic properties, including nontrivial topological properties, 2D ferromagnetism, Ising superconductivity, and robust valley polarization, we systematically studied the electron structure, magnetism, and spin transport properties for VSi2X4 (X = N, P, As) monolayers by the density functional theory combined with the nonequilibrium Green's function method. The results show that VSi2X4 monolayers are ferromagnetic type-II SGS and BMS with high Curie temperatures 230–250 K. The interesting electronic phase transitions of type-II-SGS-to-metal-to-type-I-SGS for VSi2P4 and BMS-to-type-I-SGS-to-type-II-SGS for VSi2As4 can be achieved by applying the biaxial strain. Furthermore, the VSi2P4 monolayer exhibits the bias-dependent spin filtering effect and the temperature-driven spin Seebeck effect. The high Curie temperature, the versatile strain-tuned electronic phase transitions, and the excellent spin transport characteristics make 2D VSi2X4 the promising candidate for spintronic applications and will stimulate intensive studies on this class of high-spin-polarized 2D systems.

Topological cavity laser with valley edge states.

Topological edge states (ES) arise at the boundary between spatial domains with diverse topological properties in photonic crystals, which can transmit unidirectionally to suppress the backscattering and robustly to be immune to defects and disorders. In addition, optical devices with arbitrary geometries of cavities, such as lasers, are expected to be designed on the basis of ES. Herein, we first propose a topological cavity laser based on a honeycomb lattice of ring holes with the bearded interface in two-dimensional (2D) all-dielectric valley photonic crystals (VPhCs) at telecommunication wavelengths. Specifically, we construct a topological cavity using topological valley edge states (VES) and further study the lasing action of the optically pumped cavity with high-quality factors. Our findings could provide opportunities for practical applications of VES-based lasers as ultra-small light sources with the topological protection.

Observation of topological valley waveguide transport of elastic waves in snowflake plates

In elastic systems, the researchers have observed the topological valley edge states. However, the topological valley edge states can only enable elastic waves to propagate along the narrow interfaces. Here, we obtain the topological valley waveguide states (TVWSs) by constructing the sandwich-like plates. By virtue of the TVWSs, the transport of elastic waves in the wide straight and bent waveguides is achieved. In addition, we realize the splitting effect and converging of elastic waves according to the valley-locking property. Our research may promote the design of innovative devices about energy harvesting, sensing, and information processing.

Plasmon-induced transparency in a reconfigurable composite valley photonic crystal.

We propose a new kind of reconfigurable topological valley photonic crystal (TVPC), and a novel topological waveguide can be formed by constructing a domain wall between two TVPCs with opposite valley-Chern indices. The topological waveguide mode in the composite TVPC has large group refractive index. A topologically protected coupled waveguide cavity system is then designed by introducing a hexagonal ring cavity at the center of the straight domain wall of a combined TVPC, in which a narrow plasmon induced transparency window rises at 3.8848 GHz with a Q-factor of 1387 and a maximum group refractive index as high as 186. We propose a notch filter with a resonant frequency of 3.8852 GHz and a very high Q-factor of 10224. By changing the refractive index of liquid crystals via an external voltage applied between two parallel metal plates, the filter can be switched between band-pass and band-stop based on the reconfigurable topological interface state.

Tunable and programmable topological valley transport in photonic crystals with liquid crystals

Topological valley transport in photonic crystals (PCs) has attracted great attention owing to its edge modes immune to backscattering. However, flexibly dynamically controlling and reconfiguring the pathway of the topological one-way propagation is still challenging. Here, we propose a tunable and programmable valley PC structure based on nematic liquid crystals (LCs). Inversion symmetry breaking and topological transition are implemented through controlling the relative permittivity of the LC cells. Topological protection of valley edge states and valley-locked beam splitting are demonstrated. Moreover, the LC-based PC can be discretized to a number of supercells, each of which can be coded with ‘0’ or ‘1’. The wave propagation pathway can be dynamically reconfigured by programming different coding patterns.

Acoustic source localization in three-dimensional space based on acoustic valley-Hall topological insulators

Acoustic valley-Hall topological insulators (VHTIs), as a kind of acoustic metamaterials, possess the attractive characteristics of both directional sound reception and regulating the propagation path of sound wave. Based on these two characteristics of acoustic VHTIs, a VHTIs-based acoustic source localization method is developed here. Firstly, the topological valley transport in the acoustic VHTIs is investigated by emitting sound to the topological interface from the routes of the entrance of the topological interface and the domain wall. We find that sound waves emitting from the entrance of the topological interface and the domain wall into the topological interface possess different angular sensitivity. Furthermore, utilizing the different angular sensitivities of the sound propagation from the two routes to the topological interface, the thin films placed at the front of the entrance of the topological interface are designed to improve the directional sound reception to a targeted sound source. The simulated and experimental results demonstrate that the half-power beamwidth can be decreased by means of placement of the film. Finally, a method of acoustic source localization by using three acoustic VHTIs is proposed and verified via experiments.

Terahertz Band Communications With Topological Valley Photonic Crystal Waveguide

The sixth generation (6 G) communication standard is expected to include support for very-high data rates (over 100 Gbit/s) and device electronics will require processors with on-chip communications able to support such high bandwidths. Although the terahertz band possesses ample bandwidth, conventional THz waveguides suffer from high bending losses and are sensitive to process defects. The recent revelation of the topological valley photonic crystal (VPC), which exhibits near zero-loss bends, zero back-scattering and zero junction-area, holds much promise for future high speed inter-device communications. Low dispersion in the photonic bandgap region as the number of bends increase is demonstrated through simulation and experiment of the transmission and group delay characteristics. Through comprehensive communications experiments we demonstrate online results below the forward error correction level including an 108-Gbit/s bit rate using multi-level modulation for a 10 mm straight VPC waveguide and a 62.5-Gbit/s bit-rate for a ten sharp bended structure.

Tunable topological valley Hall edge state based on large optical Kerr effect

Most of the photonic valley-Hall edge states were constructed by changing structures to break the spatial inversion symmetry, restricting the practical application potential. In this paper, we construct a tunable topological valley-Hall edge state based on the large optical Kerr effect. It is demonstrated that topological phase transition happens by engineering the intensity of the injected pump and that a valley-Hall edge state can be generated at the interface between two regions with different topological properties. In addition, eigenfrequency and transmission characteristics of the edge state as a function of applied pump intensity are investigated. The topological protected valley-dependent transmission is studied under non-uniform distributed pump intensity. This work may open a new path toward designing reconfigurable all-optical metadevices.

Valley Hall edge solitons in a photonic graphene.

We predict the existence and study properties of the valley Hall edge solitons in a composite photonic graphene with a domain wall between two honeycomb lattices with broken inversion symmetry. Inversion symmetry in our system is broken due to detuning introduced into constituent sublattices of the honeycomb structure. We show that nonlinear valley Hall edge states with sufficiently high amplitude bifurcating from the linear valley Hall edge state supported by the domain wall, can split into sets of bright spots due to development of the modulational instability, and that such an instability is a precursor for the formation of topological bright valley Hall edge solitons localized due to nonlinear self-action and travelling along the domain wall over large distances. Topological protection of the valley Hall edge solitons is demonstrated by modeling their passage through sharp corners of the Ω-shaped domain wall.

Topological protection of continuous frequency entangled biphoton states

Abstract Topological quantum optics that manipulates the topological protection of quantum states has attracted special interests in recent years. Here we demonstrate valley photonic crystals implementing topologically protected transport of the continuous frequency entangled biphoton states. We numerically simulate the nonlinear four-wave mixing interaction of topological valley kink states propagating along the interface between two valley photonic crystals. We theoretically clarify that the signal and idler photons generated from the four-wave mixing interaction are continuous frequency entangled. The numerical simulation results imply that the entangled biphoton states are robust against the sharp bends and scattering, giving clear evidence of topological protection of entangled photon pairs. Our proposal paves a concrete way to perform topological protection of entangled quantum states operating at telecommunication wavelengths.

Topological valley and charge pumping in multi-Weyl semimetals

We investigate the topological pumping effect in multi-Weyl semimetals, modulated by two orthogonal ac electric fields. In order to investigate the influence of the anisotropic energy–momentum relation on the pumping, we consider two different electric field configurations, i.e., (I) the electric fields along x and y directions, and (II) along y and z directions. It is found that both in the two configurations, there appear a pumping current in the direction perpendicular to electric field plane, whose direction is determined by the chirality, and the amount of the Weyl fermions pumped per cycle is given by the monopole charges. This indicates that the pumping effect is isotropic though the energy dispersion is anisotropic. Because the Weyl points of opposite chiralities always come in pairs in Weyl semimetals, the total particle current is vanishing, the pump giving rise to a net valley current. However, by using a valley-polarized electrode, one Weyl valley will be suppressed, and a charge current could be measured.

Resonant-scattering hybrid device for multiband acoustic topology valley transmission

This paper proposes a hybrid resonant-scattering device combining local resonance and Bragg scattering to achieve simultaneous topological valley-state transport in multiple frequency bands. This acoustic structure was obtained by integrating two types of Helmholtz resonators arranged in a triangular lattice pattern in an air environment. The Dirac point frequency was dominated by the combined strength of resonance and Bragg scattering, presenting a dynamic change process, according to which four designable Dirac points were obtained at frequencies below 14 kHz. Four independently designed and regulated acoustic topological valley transports appeared along the interface separating the topologically diverse sonic crystals after introducing a rotating-scatterer mechanism, as demonstrated by the numerical calculations and experimental results. In addition, since the valley edge states located in the separated edge bands caused by combining resonance and Bragg scattering were interface dependent, a right-hand rule was proposed to evaluate the interface type. This study paves the way for the engineering application of multiband acoustic antennas, acoustic logic control, and other multifunctional acoustic devices.

Control of Giant Topological Magnetic Moment and Valley Splitting in Trilayer Graphene.

Bloch states of electrons in honeycomb two-dimensional crystals with multivalley band structure and broken inversion symmetry have orbital magnetic moments of a topological nature. In crystals with two degenerate valleys, a perpendicular magnetic field lifts the valley degeneracy via a Zeeman effect due to these magnetic moments, leading to magnetoelectric effects which can be leveraged for creating valleytronic devices. In this work, we demonstrate that trilayer graphene with Bernal stacking (ABA TLG), hosts topological magnetic moments with a large and widely tunable valley g factor (g_{ν}), reaching a value g_{ν}∼1050 at the extreme of the studied parametric range. The reported experiment consists in sublattice-resolved scanning tunneling spectroscopy under perpendicular electric and magnetic fields that control the TLG bands. The tunneling spectra agree very well with the results of theoretical modeling that includes the full details of the TLG tight-binding model and accounts for a quantum-dot-like potential profile formed electrostatically under the scanning tunneling microscope tip.

Acoustic topological valley transport with multimode edge states

Acoustic transport through topological edge states in phononic crystals improves the suppression of backscattering, which gives these systems significant potential for controlling sound waves. Recent research shows that only one acoustic edge state caused by topological valley phases can transmit in phononic crystals. This paper proposes a genre of valley phases with one, two, and three topological edge states created by transforming the structure of unit cells. The bulk-edge correspondence indicates that these edge states are topological based on the topological invariant number (i.e., the valley Chern number of one, two, and three) of this system coinciding with the number of topological edge states. Different types of defects are introduced into the phononic crystals, whose transmission spectra show that they can withstand bending defects. These results indicate that these systems have significant potential for application in noise control, acoustic communication, and acoustic-electrical integration.

Topologically protected vector edge states and polarization beam splitter by all-dielectric valley photonic crystal slabs

The polarization beam splitter (PBS) is the essential optical component, which is widely used in various optical instruments. Its robustness against perturbation is very necessary to all-optical classical and quantum networks. Here, we report the design of topologically protected vector edge states (dual-polarization with transverse electric and transverse magnetic modes) and PBS based on all-dielectric topological valley photonic crystal slabs. The topologically protected vector edge states have been realized for the first time using germanium photonic crystal slab with silica substrate. Based on such edge states, the topologically protected PBS has been designed and its robust property has been demonstrated by exact numerical simulations. Our proposed PBS is expected to be widespread applications for photonic integrated circuits and quantum information processing.

Dark topological valley Hall edge solitons

Abstract Topological edge solitons propagating along the edge of a photonic topological insulator are localized self-sustained hybrid states that are immune to defects/disorders due to the protection of the edge states stemming from the nontrivial topology of the system. Here, we predict that exceptionally robust dark valley Hall edge solitons may form at the domain walls between two honeycomb lattices with broken inversion symmetry. The underlying structure can be created with femtosecond laser inscription, it possesses a large bandgap where well-localized dark edge solitons form, and in contrast to systems with broken time-reversal symmetry, it does not require external magnetic fields or complex longitudinal waveguide modulations for the realization of the topological phase. We present the envelope equation allowing constructing dark valley Hall edge solitons analytically. Such solitons propagate without radiation into the bulk of the lattice and can circumvent sharp corners, which allows observing their persistent circulation along the closed triangular domain wall boundary. They survive over huge distances even in the presence of disorder in the underlying lattice. We also investigate interactions of closely located dark topological valley Hall edge solitons and show that they are repulsive and lead to the formation of two gray edge solitons, moving with different group velocities departing from group velocity of the linear edge state on which initial dark solitons were constructed. Our results illustrate that nonlinear valley Hall systems can support a rich variety of new self-sustained topological states and may inspire their investigation in other nonlinear systems, such as atomic vapors and polariton condensates.