Valley Hall Insulator Research Articles

Topologically Protected Parametric Wavelength Conversion in a Valley Hall Insulator (Laser Photonics Rev. 18(9)/2024)

Topologically Protected Parametric Wavelength Conversion in a Valley Hall Insulator (Laser Photonics Rev. 18(9)/2024)

Topologically Protected Parametric Wavelength Conversion in a Valley Hall Insulator

AbstractNonlinear phenomena are investigated in a topological photonic valley Hall insulator (VHI) using a Kagome system designed to have localized topological boundary state (TBS) at telecommunications wavelengths. Valley Hall topologically protected nonlinear phenomena are demonstrated. Similar transmission properties and parametric wavelength conversion of up to −12 dB are experimentally achieved using sub‐milliwatt average powers in a zigzag interface without back‐scattering, compared with a straight interface. Furthermore, a 7 dB slow light enhancement is observed in the conversion efficiency near the red edge in the transmission band of the boundary state, demonstrating how slow light‐induced backscattering may be circumvented by leveraging the topologically protected boundary state. A Kerr‐induced delocalization of the valley Hall topological state (VHTS) is further experimentally observed, which can be harnessed to control the properties of topological edge states.

A second wave of topological phenomena in photonics and acoustics.

Light and sound are the most ubiquitous forms of waves, associated with a variety of phenomena and physical effects such as rainbows and echoes. Light and sound, both categorized as classical waves, have lately been brought into unexpected connections with exotic topological phases of matter. We are currently witnessing the onset of a second wave of active research into this topic. The past decade has been marked by fundamental advances comprising two-dimensional quantum Hall insulators and quantum spin and valley Hall insulators, whose topological properties are characterized using linear band topology. Here, going beyond these conventional topological systems, we focus on the latest frontiers, including non-Hermitian, nonlinear and non-Abelian topology as well as topological defects, for which the characterization of the topological features goes beyond the standard band-topology language. In addition to an overview of the current state of the art, we also survey future research directions for valuable applications.

Tunable topological phase transition in the telecommunication wavelength

Recent progress in the Valley Hall insulator has demonstrated a nontrivial topology property due to the distinct valley index in 2D semiconductor systems. In this work, we propose a highly tunable topological phase transition based on valley photonic crystals. The topological phase transition is realized by the inversion symmetry broken due to the refractive index change of structures consisting of optical phase change material (OPCM) with thermal excitation of different sites in a honeycomb lattice structure. Besides, simulations of light propagation at sharp corners and pseudo-spin photon coupling are conducted to quantitatively examine the topological protection. Compared with other electro-optical materials based on reconfigurable topological photonics, a wider bandwidth and greater tunability of both central bandgap frequency and topological phase transition can happen in the proposed scheme. Our platform has great potential in practical applications in lasing, light sensing, and high-contrast tunable optical filters.

A three-dimensional magnetoelastic valley Hall insulator with tunable elastic wave route and frequency

Topological insulators (TIs) are a new type of quantum state materials. Due to their novel physical properties, such as topological protection defect immunity to edge states, TIs have become the focus of attention in condensed matter and material physics. At present, the research on TIs has been gradually extended to classical wave fields such as electromagnetic waves, acoustic waves, and elastic waves, and has aroused extensive research interest. However, for elastic wave systems, most TIs cannot actively control topological interface states due to the limitation of fixed structure, which hinders their application in practical situations. Here, we propose a kind of tunable three-dimensional (3D) valley Hall insulator composed of magnetoelastic materials. First, the topological phase transition can be induced by the asymmetric geometry. Then, the working frequency of topological interface states can be changed by using static magnetic fields. Second, topological phase transformation can also be induced by independently tuning the distribution of static magnetic fields or pre-stress in each unit. Based on this, reconfigurable propagation routes of interface states with arbitrary shapes can be realized by tuning the distribution of static magnetic fields or pre-stress in each unit. Finally, considering the sandwich structure composed of different magnetic fields or pre-stress distribution modes, the waveguide with tunable width and route is designed by coupling edge and bulk states, which is convenient for application and better energy transfer. This study provides a reference for the design of a tunable intelligent elastic waveguide.

Two-dimensional quadratic double Weyl semimetal

Unconventional Weyl semimetals have attracted intensive research interest in condensed-matter physics and materials science, but they are very rare in two dimensions. In this work, based on symmetry analysis and first-principles electronic structure calculations, we predict that the Si/Bi van der Waals heterostructure is a two-dimensional unconventional quadratic double Weyl semimetal with strong spin-orbit coupling (SOC). Although unprotected by the ${C}_{3v}$ double group symmetry of the heterostructure, the two-dimensional quadratic double Weyl semimetal is stable for compressive strains up to 6.64%. The system transforms into a trivial semimetal with further increasing strain, where the phase boundary is a two-dimensional triply degenerate semimetal state. Furthermore, the Kane-Mele tight-binding model calculations show that the quadratic double Weyl phase is derived from the competition between the Rashba SOC and the proximity-effect-enhanced intrinsic SOC. On the other hand, by breaking mirror symmetry, the quadratic double Weyl semimetal transforms into a quantum spin Hall insulator as well as a quantum valley Hall insulator phase. Thus, the Si/Bi heterostructure is an excellent platform for studying the exotic physics of the two-dimensional double Weyl semimetal and other novel topological phases.

Optimal design of topological waveguides by machine learning

Topological insulators supply robust edge states and can be used to compose novel waveguides to protect energy propagation against various defects. For practical applications, topological waveguides with a large working bandwidth and highly localized interface mode are desired. In the present work, mechanical valley Hall insulators are described by explicit geometry parameters using the moving morphable component method first. From the geometry parameters, artificial neural networks (ANN) are then well-trained to predict the topological property and the bounds of nontrivial bandgaps. Incorporating those ANN models, mathematical formulation for designing optimal mechanical topological waveguides can be solved efficiently, with an acceleration of more than 10,000 times than the traditional topology optimization approach.

MX family: an efficient platform for topological spintronics based on Rashba and Zeeman-like spin splittings

Taking various combinations of M = (Mo, W) and X = (C, S, Se) as examples, we propose that MX (M = transition metals, X = IV,V or VI elements) family can establish an excellent platform for both conventional and topological spintronics applications based on anisotropic Rashba-like and non-magnetic Zeeman-type spin splittings with electrically tunable nature. In particular, we observe sizeable Zeeman-like and Rashba-like spin splittings with an anisotropic nature. Meanwhile, they exhibit Rashba-like and topologically robust helical edge states when grown in ferroelectric and paraelectric phases, respectively. These MX monolayers are realized to be quantum valley Hall insulators due to valley contrasting Berry curvatures. The carriers in these MX monolayers can be selectively excited from opposite valleys depending on the polarity of circularly polarized light. The amplitude of the spin splitting can be further tuned by applying external means such as strain, electric field or alloy engineering. Furthermore, considering graphene sheet over the WC monolayer as a prototype example, we show that these MX monolayers can boost the relativistic effect by coupling with the systems exhibiting extremely weak spin–orbit coupling (SOC). Depending on the surface of WC monolayer in contact with the graphene sheet, graphene over WC monolayer passes through the transformation from the semiconducting junction to the Shotcky barrier-free contact. Finally, we reveal that these MX monolayers could also be grown on the substrates such as WS and GaTe (001) with type-II band alignment, where electron and hole become layer splitted across the interface. Our analysis should be fairly applied to other systems with strong SOC and an equivalent geometrical structure to the MX monolayers.

Gapped edge states and quantum valley Hall effect in a planar honeycomb monolayer of group III–V binary compounds of the form BX (X = N, P, and As)

Although a gapless edge state is a characteristic of topologically nontrivial insulators, we show that in quantum valley Hall insulators with staggered AB-sublattice potentials, a gapless edge state can be shifted by large on-site potentials of an abrupt domain wall, leading to a gapped edge state. At a smooth domain wall, a gapless edge state occurs regardless of the strength of the staggered potentials. Our density functional theory calculations show that a wide-gap semiconductor BX (X = N, P, and As) monolayer can be a quantum valley Hall insulator with gapped edge states. We found that a BX monolayer has gapped edge states at an abrupt domain wall. However, robust gapless edge states for ripple-induced smooth scattering potentials were identified at the bare edge of BP and BAs nanoribbons. In the BN monolayer, only gapped edge states were found, which appears to be due to too large on-site potentials.

Two-dimensional anisotropic Dirac materials PtN4C2 and Pt2N8C6 with quantum spin and valley Hall effects

We propose two different two-dimensional topological Dirac materials, planar ${\mathrm{PtN}}_{4}{\mathrm{C}}_{2}$ and ${\mathrm{Pt}}_{2}{\mathrm{N}}_{8}{\mathrm{C}}_{6}$, which exhibit graphenelike electronic structures with linearly dispersive Dirac-cone states exactly at the Fermi level. Moreover, the Dirac cone is anisotropic, resulting in anisotropic Fermi velocities and making it possible to realize orientation-dependent quantum devices. Using first-principles electronic structure calculations, we have systemically studied the structural, electronic, and topological properties. We find that spin-orbit coupling opens a sizable topological band gap so that the materials can be classified as quantum spin Hall insulators as well as quantum valley Hall insulators. Helical edge states that reside in the insulating band gap connecting the bulk conduction and valence bands are observed. Our work not only expands the Dirac-cone material family, but also provides another avenue to search for more two-dimensional topological quantum spin and valley Hall insulators.

Rashba Splitting and Electronic Valley Characteristics of Janus Sb and Bi Topological Monolayers.

Janus Sb and Bi monolayers as a new class of 2D topological insulator materials, which could be fulfilled by asymmetrical functionalizations with methyl or hydroxyl, are demonstrated by first-principles spin–orbit coupling (SOC) electronic structure calculations to conflate nontrivial topology, Rashba splitting and valley-contrast circular dichroism. Cohesive energies and phonon frequency dispersion spectra indicate that all Janus Sb and Bi monolayers possess a structural stability in energetic statics but represent virtual acoustic phonon vibrations of the hydrogen atoms passivating on monolayer surfaces. Band structures of Janus Sb and Bi monolayers and their nanoribbons demonstrate they are nontrivial topological insulators. Rashba spin splitting at G point in Brillouin zone of Janus Bi monolayers arises from the strong SOC px and py orbitals of Bi bonding atoms together with the internal out-of-plane electric field caused by asymmetrical functionalization. Janus Sb and Bi monolayers render direct and indirect giant bandgaps, respectively, which are derived from the strong SOC px and py orbitals at band-valley Brillouin points K and K′ where valley-selective circular dichroism of spin valley Hall insulators is also exhibited.

Probing Two Distinct Types of Topological Rainbow Concentrators Related to the Acoustic Valley Hall Insulator in Synthesized Three-Dimensional Space

Synthesized three-dimensional space provides us with a platform to explore the intriguing acoustic valley Hall insulator. In this paper, a rotational degree of freedom is introduced to construct a synthetic three-dimensional space. Based on simulations, our results show that Weyl points and Fermi arcs and topologically nontrivial edge modes appear in a synthetic space. Not only rotational operation but also boundary truncation can modulate the frequencies of nontrivial edge states, which result in two completely different edge states at the upper and lower boundaries. Using frequencies of edge states protected by Weyl points, we devise two different acoustic topological rainbow devices. The two devices are able to trap states with different frequency components at different spatial positions: one device is capable of capturing low-frequency components at close range, while the other has the ability to confine low-frequency components at long distances. This work may boost further the development of topological rainbow devices in a synthetic space related to the acoustic valley Hall insulator.

Ultra-broadband edge-state pair for zigzag-interfaced valley Hall insulators

Ultra-broadband edge-state pair for zigzag-interfaced valley Hall insulators

Valley-Polarized Quantum Anomalous Hall State in Moiré MoTe_{2}/WSe_{2} Heterobilayers.

Moiré heterobilayer transition metal dichalcogenides (TMDs) emerge as an ideal system for simulating the single-band Hubbard model and interesting correlated phases have been observed in these systems. Nevertheless, the moiré bands in heterobilayer TMDs were believed to be topologically trivial. Recently, it was reported that both a quantum valley Hall insulating state at filling ν=2 (two holes per moiré unit cell) and a valley-polarized quantum anomalous Hall state at filling ν=1 were observed in AB stacked moiré MoTe_{2}/WSe_{2} heterobilayers. However, how the topologically nontrivial states emerge is not known. In this Letter, we propose that the pseudomagnetic fields induced by lattice relaxation in moiré MoTe_{2}/WSe_{2} heterobilayers could naturally give rise to moiré bands with finite Chern numbers. We show that a time-reversal invariant quantum valley Hall insulator is formed at full filling ν=2, when two moiré bands with opposite Chern numbers are filled. At half filling ν=1, the Coulomb interaction lifts the valley degeneracy and results in a valley-polarized quantum anomalous Hall state, as observed in the experiment. Our theory identifies a new way to achieve topologically nontrivial states in heterobilayer TMD materials.

Research progress of elastic topological materials

Topological insulators, originated in quantum systems, are recently generalized to electromagnetic, acoustic, and elastic wave fields due to interesting wave controlling provides, such as unidirectional and dissipationless energy transportation. This new kind of materials provide unprecedented possibilities for engineering wave flows. This paper will introduce the basic theory of topological insulators and summarize the research progress of topological insulators in elastic fields. Based on one-dimensional and two-dimensional discrete models, preliminary concepts of topological insulators, such as Dirac cone, band inversion, Berry curvatures, topological invariants, are introduced. The design and progress of valley Hall insulators, Chern insulators as well as spin Hall insulators are introduced afterward, followed by discussions on high-order topological insulators. The last part of this paper covers topological phenomena in static mechanics, including topological solitons and toplogical zero energy modes.

Robust Fano resonance in the photonic valley Hall states

Rapidly developing photonics brings many interesting resonant optical phenomena, in which the Fano resonance (FR) always intrigues researchers because of its applications in optical switching and sensing. However, its sensitive dependence on environmental conditions makes it hard to implement in experiments. We in this work suggest a topologically-protected FR based on the photonic valley Hall insulators, immune to the system impurities. The topologically-protected FR is achieved by coupling the valley-dependent topological edge states (TESs) with one double-degenerate cavity. The $\delta$-type photonic transport theory we build reveals that this topological FR dates from the interference of the two transmissions that are attributed to the parity-odd cavity mode and the parity-even one. We confirm that the induced Fano line shape of the transmission spectra is robust against the bending domain walls and disorders. Our work may provoke exciting frontiers for manipulating the valley transport and pave a way for the topologically protected photonic devices such as optical switches, low-threshold lasers, and ultra-sensitive sensors.

Multichannel Topological Transport in an Acoustic Valley Hall Insulator

Valley interface states, resulting in acoustic valley Hall topological insulators, have recently become a hot topic in the study of acoustic systems. On the basis of structural diversity and potential applications, we construct a two-dimensional triangular-lattice phononic crystal with ${C}_{3v}$-symmetric scatterers, and obtain two distinct valley Hall phases with nonvanishing valley Chern indices by rotating the scatterers. We numerically calculate the dispersion relations of these valley Hall phases including two kinds of interfaces, and find that valley interface states exist at not only the zigzag interface but also the armchair interface. We demonstrate the acoustic splitting and merging of valley interface states in the cross-waveguides, and numerically achieve the xor and or logic functions. We also design three complicated waveguides by assembling phononic crystals with distinct valley Hall phases. By experimental measurements in these waveguides, we successfully implement one-, two-, and three-channel topological transport. This research possibly provides a design route exploiting valley interface states to fabricate multichannel acoustic communication devices.

Strain-induced topological phase transition with inversion of the in-plane electric polarization in tiny-gap semiconductor SiGe monolayer

Our density functional theory calculations show that tiny-gap semiconductor SiGe monolayer is a quantum valley Hall insulator with a spontaneous electric polarization and, under a small biaxial strain, undergoes a topological phase transition between the states with opposite valley Chern numbers. The topological phase transition entails abrupt inversion of the in-plane electric polarization corresponding to inversion of the sublattice pseudospin polarization, while the out-of-plane electric polarization shows a linear response to the biaxial strain as well as to the perpendicular electric field regardless of the phase transition. Thus, the quantum valley Hall state entails in-plane ferroelectricity corresponding to a sublattice pseudospin ferromagnetism.

Nature of topological protection in photonic spin and valley Hall insulators

Recent interest in optical analogues to the quantum spin Hall and quantum valley Hall effects is driven by the promise to establish topologically protected photonic edge modes at telecommunication and optical wavelengths on a simple platform suitable for industrial applications. While first theoretical and experimental efforts have been made, these approaches so far both lack a rigorous understanding of the nature of topological protection and the limits of backscattering immunity. We here use a generic group theoretical methodology to fill this gap and obtain general design principles for purely dielectric two-dimensional topological photonic systems. The method comprehensively characterizes possible 2D hexagonal designs and reveals their topological nature, potential and limits.

Acoustic topological devices based on emulating and multiplexing of pseudospin and valley indices

We present a design paradigm for acoustic devices in which robust and controllable transport of wave signals can be realized. These devices are based on a simple acoustic platform, where different topological phases such as acoustic quantum spin Hall and quantum valley Hall insulators are emulated by engineering the spatial symmetries of the structure. Edge states along interfaces between different topological phases are shown to be promising information channels, where the multiplexing of pseudospin and/or valley degrees of freedom is unambiguously demonstrated in various devices including a multiport valve for acoustic power dividing and feeding. The information capacity in the input channel is substantially enhanced due to the creating of an extra dimension for the data carriers. The topological devices proposed here, when integrated with other state-of-the-art communication techniques, may suggest a significant step towards acoustic communication circuits with complex functionalities.