Quantum Valley Hall Research Articles

Broadband large-scale acoustic topological waveguides

The acoustic topological waveguide (ATW) hosting topologically protected waveguide modes provides a unique opportunity for achieving large-scale sound transport with robustness. However, prevailing ATWs are typically designed by forward-designed sonic crystals (SCs) based on physical intuitions, unavoidably leading to restricted bandwidths. Here, using the inverse-designed SCs with maximized topological bandgaps, we construct broadband ATWs based on both the quantum spin Hall effect and the quantum valley Hall effect. Broadband large-scale transportation, spin-locked one-way transportation, and the squeezing effect of acoustic waves are demonstrated. This study ushers a new path for designing topological devices with broadband performance for large-scale acoustic wave transportation.

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.

High-temperature quantum valley Hall effect with quantized resistance and a topological switch.

Edge states of a topological insulator can be used to explore fundamental science emerging at the interface of low dimensionality and topology. Achieving a robust conductance quantization, however, has proven challenging for helical edge states. In this work, we show wide resistance plateaus in kink states-a manifestation of the quantum valley Hall effect in Bernal bilayer graphene-quantized to the predicted value at zero magnetic field. The plateau resistance has a very weak temperature dependence up to 50 kelvin and is flat within a dc bias window of tens of millivolts. We demonstrate the electrical operation of a topology-controlled switch with an on/off ratio of 200. These results demonstrate the robustness and tunability of the kink states and its promise in constructing electron quantum optics devices.

Topological phonons and thermal conductivity of two-dimensional Dirac semimetal PtN4C2

PtN4C2 is a recently predicted two-dimensional (2D) Dirac semimetal exhibiting significant topological quantum spin and valley Hall effects. Herein, we explore its topological phonon states and thermal transport properties from first-principles calculations. In terms of symmetry arguments, we predict the existence of multiple topologically protected phononic Dirac points in the frequency range of 0–20 THz, which are evidenced by the relevant irreducible representations and calculated nontrivial edge states on the (100) surface. In addition, anharmonic phonon renormalization is found to play a significant role in determining the phonon spectrum, especially for the out-of-plane flexural acoustic (ZA) branch. Moreover, we explicitly consider three-phonon scattering, four-phonon scattering, and phonon renormalization to predict the lattice thermal conductivity κl of PtN4C2, by solving the Boltzmann transport equation. With the incorporation of four-phonon scattering, we predict that the intrinsic κl is 68 W/mK at room temperature, which is reduced by about 45% as compared to the value obtained by only including three-phonon scattering. This reduction is found to arise mainly from the ZA phonons, whose contribution to κl is significantly suppressed by four-phonon scattering, due to the restriction of the mirror symmetry-induced selection rules on three-phonon processes. We also unveil that the presence of Dirac points steepens the surrounding phonon dispersion and thus greatly increases the phonon group velocities, thereby making a considerable contribution to κl. This work establishes a thorough understanding of intrinsic topological phonons and thermal transport in PtN4C2 and highlights the importance of phonon renormalization and higher-order anharmonicity in determining the phonon transport properties of 2D materials.

Selective topological valley transport of elastic waves in a Bragg-type phononic crystal plate

Based on the quantum valley Hall effect analogy, this work proposes a phononic crystal plate with ligament-type beams to obtain the topological valley transmission of elastic waves. A pure Bragg degenerate state appears in the high-frequency region with a resonator introduced. By rotating the central scatterer and the beams, the mirror symmetry is broken to form a topological bandgap. Subsequently, this work finds that two selective edge states also appear beside the commonly non-trivial crossing edge states in the topological bandgap by calculating the projected band and eigenvalue spectrum of the supercell with different valley Hall phases phononic crystals. Their appearance is due to band separation of the topological edge states caused by an increase in the rotation angle. Both selective edge states can transmit topologically in specific paths. They will help further to broaden the width of the frequency band of topological transmission. Besides, an elastic wave splitter is designed and demonstrated numerically, which can form two channels and three channels in different frequency bands. With the topological selective edge state disappearing, a topological corner state exists in the edge bandgap. This work provides a theoretical reference for practical applications of broadband elastic wave topological transmission and elastic energy trapping.

Experimental demonstration of an electroacoustic transistor

We experimentally demonstrate a topologically protected electroacoustic transistor. We construct a reconfigurable phononic analog of the quantum valley-Hall insulator composed of electrically shunted piezoelectric disks bonded to a patterned plate forming a monolithic structure. The device can be dynamically reconfigured to host one or more topological interface states via breaking inversion symmetry through selective powering of shunt circuits. Above a threshold, the amplitude of wave energy at a chosen location in one topological interface creates a second interface by dynamically switching power between two groups of shunts using relays. This enables the flow of wave energy between two locations in the reconfigured interface analogous to the voltage-controlled electron flow in a field effect transistor. The amplitude of wave energy in the second interface is used for bit abstraction to implement acoustic logic. We illustrate the various states of the transistor and experimentally demonstrate wave-based switching. The proposed electroacoustic transistor is envisioned to find applications in wave-based devices and edge computing in extreme environments and inspire novel technologies leveraging acoustic logic.

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.

Programmable topological insulators based on a reconfigurable electroacoustic material platform

Topological insulators (TIs), exhibiting topologically protected edge and interface waves, have recently emerged in phononic systems. Reconfigurabilty is essential for enabling TI-based applications. One potential means for achieving reconfigurability employs shunted piezoelectric (PZT) disks in which a unit cell’s mechanical impedance is altered using negative capacitance circuits. Dynamic reconfigurability and programmability of such material platforms can then be obtained through simple on/off switching. In this vein, we propose and experimentally verify an electroacoustic TI which exhibits programmable topologically protected edge states useful for acoustic multiplexers, demultiplexers, and transistors. This reconfigurable structure is composed of an elastic hexagonal lattice whose unit cell contains two shunted PZT disks, each connected to a negative capacitance circuit by an on/off switch. Closing one or the other circuit results in the breaking of mirror symmetry and yields mechanical behavior analogous to the quantum valley Hall effect. By interfacing two topologically distinct materials, a domain wall is introduced exhibiting a localized interface state topologically protected from backscattering at defects and sharp edges. Through the use of programmable time-division, in which domain walls appear and disappear in time, we demonstrate multiplexing and demultiplexing. We also demonstrate an acoustic transistor using the same programmable platform, before closing with a discussion on future research directions.

Spin resolved topological bulk state in acoustics

Extremely rare topologically protected acoustic energy sink is presented in this article. Acoustic topological phenomena are generally described using quantum anomalous hall effects (QAHE), quantum valley hall effects (QVHE), and quantum spin hall effects (QSHE) where spin orbit coupling is predominant. Topological edge states are demonstrated by bulk-boundary distinction when the bulk is insulated. In this article topological acoustic conductor and its phenomena are theoretically demonstrated where the boundaries are insulated. This is exactly opposite to the behavior of a topological acoustic insulator. Phenomena presented in this article could not be explained by any of the trio Quantum Hall effects. To explain the phenomenon phononic crystals or PnCs were designed to obtain accidental triple degeneracies, resulting a Dirac-like cone at the Γ point (k→=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overrightarrow{k}=0$$\\end{document}). The phenomenon is microarchitecture and microrotation field independent. Here time reversal symmetry or the space inversion symmetry is not broken, and the degenerated ‘Deaf band’ dominates the local dispersion with a syncline top band. This scenario results in continuously changing ‘up spin’ and ‘down spin’ of the wave energy in the media and remain trapped without specific preferential direction of wave transport. The spin was found to generate the spin angular momentum, causing the switching in geometric phase from 0-2π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0-2\\pi$$\\end{document} in cyclic pattern, keeping the energy trapped inside the bulk media.

Multifrequency and Multimode Topological Waveguides in a Stampfli‐Triangle Photonic Crystal with Large Valley Chern Numbers

AbstractThe multifrequency quantum valley Hall effect (QVHE) has been realized to significantly improve the transmission capacity of topological waveguides, and the multimode QVHE with a large valley Chern number has been realized to increase the mode density of topological waveguides. However, multifrequency and multimode QVHEs have not been realized simultaneously. In this work, using tight‐binding model calculations and numerical simulations, a valley photonic crystal (VPC) consisting of a Stampfli‐triangle photonic crystal is constructed, and its multiple degeneracies in the low‐frequency and high‐frequency bands split simultaneously to realize the QVHE with multiple topological edge states (TESs). The multifrequency and multimode topological transmission with two low‐frequency modes and four high‐frequency modes is realized by means of simulations and experiments through a Z‐shaped waveguide constructed using two VPCs with opposite valley Chern numbers to prove the realization of a large valley Chern number in the two frequency bands. The two low‐frequency modes are successfully distinguished with position‐dependent selective excitations, which experimentally demonstrate the occurrence of a large valley Chern number. A frequency‐dependent multimode beam splitter is theoretically proposed for high‐performance integrated photonic device applications. These results provide new ideas for high‐efficiency and high‐capacity optical transmission and communication devices and their integration; furthermore, they broaden the application range of TESs.

High-Q two-dimensional perovskite topological laser.

Quasi-two-dimensional perovskites have attracted widespread interest in developing low-cost high-quality small lasers. The nano cavity based on topologically protected valley edge states can be robust against special defects. Here, we report a high-quality two-dimensional perovskite topological photonic crystal laser based on the quantum valley Hall effect. By adjusting the position of the air holes relative to the pillar, radiation leakage in topological edge states is reduced to a large extent, electric field distribution becomes more uniform and the quality factor can be as high as 3.6 × 104. Our findings could provide opportunities for the development of high-power, stable perovskite lasers with topological protection.

Transport properties of Hall-type quantum states in disordered bismuthene

Bismuthene, an inherently hexagonal structure characterized by a huge bulk gap, offers a versatile platform for investigating the electronic transport of various topological quantum states. Using nonequilibrium Green’s function method and Landauer–Büttiker formula, we thoroughly investigate the transport properties of various Hall-type quantum states, including quantum spin Hall (QSH) edge states, quantum valley Hall kink (QVHK) states, and quantum spin–valley Hall kink (QSVHK) states, in the presence of various disorders. Based on the exotic transport features, a spin–valley filter, capable of generating a highly spin- and valley-polarized current, is proposed. The valley index and the spin index of the filtered QSVHK state are determined by the staggered potential and the intrinsic spin–orbit coupling, respectively. The efficiency of the spin–valley filter is supported by the spacial current distribution, the valley-resolved conductance, and the spin-resolved conductance. Compared with a sandwich structure for QSVHK, our proposed spin–valley filter can work with a much smaller size and is more accessible in the experiment.

Armchair edge states in shear-strained graphene: Magnetic properties and quantum valley Hall edge states

Armchair edge states in shear-strained graphene: Magnetic properties and quantum valley Hall edge states

Phononic band calculations and experimental imaging of topological boundary modes in a hexagonal flexural wave machine

We construct a two-dimensional mechanical wave machine based on a hexagonal lattice to investigate low-frequency flexural plate waves whose propagation mimicks a topological quantum valley Hall system. We thereby demonstrate “mechanical graphene” by extension of the one-dimensional Shive wave machine to two dimensions. Imaging experiments, backed up by simulations, reveal the presence of boundary modes along a topological interface. This work provides an alternative route for the investigation of topological phononic crystals, and should lead to new insights into the design and observation of artificial phononic structures.

Topological light transport in low-symmetry valley photonic crystals

Valley photonic crystals represent a cornerstone in the field of topological photonics, which promotes the development of cutting-edge photonic waveguides. These waveguides support robust transmission by using valley-dependent edge states. This innovation marks a great leap forward in enhancing transmission efficiency, (especially in sharp bends), thus opening up a new way for efficient optical information transmission. However, although the role of symmetry in topology and photonic crystals cannot be exaggerated, it is worth noting that valley photonic crystals provide a unique platform for exploring the interplay between symmetry and topological phenomena. An intriguing analogy between valley photonic crystals and the quantum valley Hall effect is an example, which will be shown when the symmetry of spatial inversion is broken. At present, the characteristic of most valley photonic crystals is <i>C</i><sub>3</sub>-rotational symmetry, which leads to an interesting study, that is, whether crystals with lower symmetry can also support topological light transmission. In order to solve this problem head-on, our work focuses on constructing and characterizing valley photonic crystals with low symmetry by carefully adjusting the unit cell morphology. Through theoretical analysis and numerical simulation, we unveil the remarkable ability of these low-symmetry valley photonic crystals to facilitate topological light transport. Initially, we analyze the bulk bands of these low-symmetry crystals, observing a narrowed photonic band gap and a shift in the irreducible Brillouin zone compared with <i>C</i><sub>3</sub>-rotation symmetric crystals. To examine edge state transmission, we calculate dispersion relations and electric field distributions, revealing two edge states with opposite phase chirality at the same frequency. Using this point, we achieve unidirectional excitation of edge states. Additionally, we manipulate the refractive index of the surrounding medium and explore various scenarios of external light beam coupling. Moreover, we investigate the robust transmission of edge states, demonstrating smooth passage of light through sharp corners in <i>Z</i>-shaped bend waveguides without backscattering. In conclusion, our findings underscore the pivotal role played by edge states in facilitating unidirectional excitation and robust transmission in low-symmetry valley photonic crystals. By enriching the diversity of topological photonic structures and providing valuable insights into the behavior of topological light transport in structures with lower symmetry, our work contributes to the ongoing quest for novel photonic platforms with enhanced functions and performance.

Simultaneous pseudospin and valley topological edge states of elastic waves in phononic crystals made of distorted Kekulé lattices

Topological metamaterials protected by the spatial inversion symmetry mainly support single type edge state, interpreted by either the quantum valley Hall effect or the quantum spin Hall effect. However, owing to the existence of the complicated couplings and waveform conversions during elastic wave propagation, realizing topologically protected edge states that support both pseudospin and valley degrees of freedom in elastic system remains a great challenge. Here, we propose a two-dimensional Kekulé phononic crystal (PC) that can simultaneously possess pseudospin- and valley-Hall edge states in different frequency bands. By inhomogeneously changing the elliptical direction in a Kekulé lattice of elliptical cylinders, three complete phononic bandgaps exhibiting distinct topological phase transitions can be obtained, one of which supports a pair of pseudospin-Hall edge states and the other hosts valley-Hall edge states in the low and high frequency regime. Furthermore, a sandwiched PC heterostructure and a four-channel cross-waveguide splitter are constructed to achieve selective excitation and topological robust propagation of pseudospin- and valley-momentum locking edge states in a single configuration. These results provide new possibilities for manipulating in-plane bulk elastic waves with both pseudospin and valley degrees of freedom in a single configuration, which has potential applications for multiband and multifunctional waveguiding.

Experimental Realization of Anti‐Unitary Wave‐Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics

AbstractWorking in analogy with topological insulators in condensed matter, photonic topological insulators (PTI) have been experimentally realized, and protected electromagnetic edge‐modes have been demonstrated in such systems. Moreover, PTI technology also emulates a synthetic spin‐1/2 degree of freedom (DOF) in the reflectionless topological modes. The spin‐1/2 DOF is carried by quantum valley Hall (QVH)/quantum spin Hall (QSH) interface modes created from the bianisotropic meta waveguide platform and realized both in simulation and experiment. The PTI setting is employed to build an ensemble of wave chaotic 1D metric graphs that display statistical properties consistent with Gaussian symplectic ensemble (GSE) statistics. The two critical ingredients required to create a physical system in the GSE universality class, the half‐integer‐spin DOF and preserved time‐reversal invariance, are clearly realized in the QVH/QSH interface modes. The anti‐unitary T‐operator is identified for the PTI Hamiltonian underlying the experimental realization. An ensemble of PTI‐edgemode metric graphs are proposed and experimentally demonstrated. Then, the Kramers degeneracy of eigenmodes of the PTI‐graph systems is demonstrated with both numerical and experimental studies. Further, spectral statistical studies of the edgemode graphs are studied, and good agreement with the GSE theoretical predictions is found. The PTI chaotic graph structures present an innovative and easily extendable platform for continued future investigation of GSE systems.

Gapless edge states localized to odd/even layers of AA′-stacked honeycomb multilayers with staggered AB-sublattice potentials

In honeycomb multilayers with staggered AB-sublattice potentials, we predict gapless edge states localized to either of the odd and the even layers for the AA^{prime } stacking order in which the sublattice-pseudospin polarizations of adjacent layers are antiparallel. Gaps in the projected layer-pseudospin spectrum suppress interlayer hopping between odd and even layers. The layer-valley Chern number corresponding to the edge states was obtained by decomposing the occupied state into two layer-pseudospin sectors by using a projected layer-pseudospin operator. For the AB^{prime } stacking, the sublattice-pseudospin polarizations of adjacent layers are antiparallel, but the layer-pseudospin spectrum gap closes at the interface of the topologically different states, leading to gapped edge states. For the AA and AB stackings where the sublattice-pseudospin polarizations of the adjacent layers are parallel, the gapless edge states corresponding to quantum valley Hall states are evenly distributed across the layers.

Valley-dependent topological phase transition in monolayer ferrovalley materials RuXY (X, Y = F, Cl, Br)

Due to the breaking of the time reversal symmetry and spatial inversion symmetry, hexagonal ferrovalley materials have intrinsic large valley polarization. Model analysis shows that tuning the two different band gaps of valleys can realize phase transitions between ferrovalley semiconductors, half valley metals, and valley-polarized quantum anomalous Hall semiconductors. Through first-principle calculations, monolayer ferrovalley materials RuXY (X, Y = F, Cl, Br), which exhibit valley splitting at the top valence band and the bottom conduction band, are predicted to achieve this valley-dependent topological phase transition. Due to the different orbital proportions of d orbitals, the valley splitting at the top valence band is much greater than that at the bottom conduction band. Strain can regulate the interaction between orbitals, thus producing valley-dependent band inversion, leading to the quantum spin or valley Hall effect. The chiral edge states are demonstrated under appropriate biaxial strain. The topological phase transition is related to the inversion of the band structure and Berry curvatures at K and K′ valleys. These results have certain significance for the design of two-dimensional valley-dependent quantum materials and the application of valleytronic devices.

Quantum valley and subvalley Hall effect in large-angle twisted bilayer graphene

Quantum valley and subvalley Hall effect in large-angle twisted bilayer graphene