Helical Edge Research Articles

Double Quantum Spin Hall Phase in Moiré WSe2.

Quantum spin Hall (QSH) insulators are topologically protected phases of matter in two dimensions that can support a pair of helical edge states surrounding an insulating bulk. A higher (even) number of helical edge state pairs is usually not possible in real materials because spin mixing would gap out the edge states. Here, we report experimental evidence for a QSH phase with one and two pairs of helical edge states in twisted bilayer WSe2 at Moiré hole filling factor ν = 2 and 4, respectively. We observe nearly quantized (within 10%) resistance plateaus of and large nonlocal transport at ν = 2 and 4 while the bulk is insulating. The resistance is independent of the out-of-plane magnetic field and increases under an in-plane magnetic field. The results agree with quantum transport of helical edge states in a material with high spin Chern bands protected by Ising spin conservation symmetry.

Time-resolved counterpropagating edge transport in the topological insulating phase

We have investigated the time-resolved low-energy charge dynamics in counterpropagating edge channels formed in the quantum Hall regime of an electron-hole bilayer system in band-inverted InAs/InGaSb composite quantum wells. In the studied magnetic field range, the system remains in the topological phase where an equal number of counterpropagating electronlike and holelike edge channels exist in the bulk energy gap, analogous to the helical edge channels in a quantum spin Hall insulator. When the Fermi level was set in the conduction band, the injected charge pulses propagated unidirectionally as chiral edge magnetoplasmon (EMP) wave packets. In contrast, in the nonchiral regime with the Fermi level set in the band gap, the injected charge pulses propagated identically in both directions with significantly reduced velocity. In addition, as the channel length increased, we observed a sharp crossover from EMP transport to diffusive transport, manifested as pronounced waveform broadening and dissipation. Simulations using a distributed capacitance model including interchannel tunneling well reproduced the observed behavior in both chiral and nonchiral regimes, revealing that interchannel charge transfer between counterpropagating channels plays a crucial role. The slow EMP transport in the nonchiral regime and its crossover to diffusive transport are consequences of the strong interchannel interaction and interchannel tunneling, respectively. Our results will thus provide insights into charge dynamics and scattering mechanism in analogous one-dimensional systems, including a quantum spin Hall insulator with helical edge modes and its expected Tomonaga-Luttinger liquid behavior. Published by the American Physical Society 2024

Multiferroic properties and the layer-stacking quantum anomalous Hall effect in two-dimensional RuOHX (X = F, Cl, Br)

Exploring the physics coupled with layer degrees of freedom in materials has become a hot topic in quantum layertronics. We propose a robust second-order topological insulator monolayer RuOHX (X = F, Cl, and Br), a two-dimensional ferromagnetic semiconductor with large valley polarization, capable of undergoing topological phase transition induced by strain effect. In the bilayer RuOHX, we achieve layer-polarized anomalous Hall effect through interlayer sliding, originating from layer-stacking Berry curvature. Moreover, it can be controlled and reversed by the direction of ferroelectric polarization. Under appropriate biaxial strain, the bilayer RuOHX exhibits quantum layer spin Hall effect in which the helical edge states are manifested as spin-chirality-locking, due to the degeneracy of layer-polarized quantum anomalous Hall effect. Our work explores the potential application via layer-stacking topological properties for future quantum device applications.

Composite helical edges from Abelian fractional topological insulators

Composite helical edges from Abelian fractional topological insulators

Realization of Time-Reversal Invariant Photonic Topological Anderson Insulators.

Disorder, which is ubiquitous in nature, has been extensively explored in photonics for understanding the fundamental principles of light diffusion and localization, as well as for applications in functional resonators and random lasers. Recently, the investigation of disorder in topological photonics has led to the realization of topological Anderson insulators characterized by an unexpected disorder-induced phase transition. However, the observed photonic topological Anderson insulators so far are limited to the time-reversal symmetry breaking systems. Here, we propose and realize a photonic quantum spin Hall topological Anderson insulator without breaking time-reversal symmetry. The disorder-induced topological phase transition is comprehensively confirmed through the theoretical effective Dirac Hamiltonian, numerical analysis of bulk transmission, and experimental examination of bulk and edge transmissions. We present convincing evidence for the unidirectional propagation and robust transport of helical edge modes, which are the key features of nontrivial time-reversal invariant topological Anderson insulators. Furthermore, we demonstrate disorder-induced beam steering, highlighting the potential of disorder as a new degree of freedom to manipulate light propagation in magnetic-free systems. Our work not only paves the way for observing unique topological photonic phases but also suggests potential device applications through the utilization of disorder.

Spin-Dependent Localization of Helical Edge States in a Non-Hermitian Phononic Crystal.

As a distinctive feature unique to non-Hermitian systems, non-Hermitian skin effect displays fruitful exotic phenomena in one or higher dimensions, especially when conventional topological phases are involved. Among them, hybrid skin-topological effect is theoretically proposed recently, which exhibits anomalous localization of topological boundary states at lower-dimensional boundaries accompanied by extended bulk states. Here, we experimentally realize the hybrid skin-topological effect in a non-Hermitian phononic crystal. The phononic crystal, before tuning to be non-Hermitian, is an ideal acoustic realization of the Kane-Mele model, which hosts gapless helical edge states at the boundaries. By introducing a staggered distribution of loss, the spin-dependent edge modes pile up to opposite corners, leading to a direct observation of the spin-dependent hybrid skin-topological effect. Our Letter highlights the interplay between topology and non-Hermiticity and opens new routes to non-Hermitian wave manipulations.

Phonon Landau Quantization and Enhanced Lifetime in Deformed Graphene.

The pseudomagnetic field effect may offer unique opportunities for the emergence of intriguing phenomena. To date, investigations into pseudomagnetic field effects on phonons have been limited to sound waves in metamaterials. The revelation of this exotic effect on the atomic vibration of natural materials remains elusive. Our simulations of twisted graphene nanoribbons reveal well-defined Landau spectra and sublattice polarization of phonon states, mimicking the behavior of Dirac Fermions in magnetic fields. Both valley-specified helical edge currents and snake orbits are obtained. Analysis of dynamics indicates that phonon Landau states have extended lifetimes, which are crucial for the realization of Landau-level lasing. Our findings demonstrate the occurrence of the phonon pseudomagnetic field effect in natural materials, which has important implications for the mechanical tuning of phonon quantum states at the atomic scale.

Molecular beam epitaxy growth of topological insulator Bi4Br4 on silicon for the infrared applications

Bi4Br4 is a material rich in intriguing topological properties. Monolayer Bi4Br4 film exhibits helical edge states characteristic of a quantum spin Hall insulator, while bulk Bi4Br4 represents a higher-order topological insulator with hinge states. However, direct exfoliation from single crystal can only obtain thin nanowires due to the weak van der Waals forces between Bi4Br4 chains, which limits its optical analysis and application, while the growth of Bi4Br4 thin films is also full of challenges due to the extremely narrow growth temperature range and the accurate control of the BiBr3 flux. Here, we reported the controlled growth of α-Bi4Br4 thin films on intrinsic silicon substrates using molecular beam epitaxy. The growth temperature, BiBr3 flux, and the flux ratio of Bi and BiBr3 were accurately controlled. Then, the morphology, composition, and bonding of the prepared films were investigated using atomic force microscopy, X-ray photoelectron spectroscopy and Raman spectroscopy. The growth of large, uniform thin films provides an ideal material platform for studying the physical properties of Bi4Br4. Additionally, we utilized Fourier-transform infrared spectroscopy to explore the film’s infrared characteristics, revealing strong absorption in the low frequency range due to the high proportion of one-dimensional topological edge states and laying the groundwork for further exploration of its potential applications in the optoelectronic field.

Ti3O MOenes: Quantum Spin Hall Effect and Promising Semiconductors for Light-Harvesting.

The continuous pursuit of novel two-dimensional (2D) materials with intriguing properties has been a driving force in advancing various scientific and technological frontiers. Here, based on a wide range of first-principles calculations, we predicted the existence of a novel family of 2D transition-metal oxides, the Ti3O MOenes (MXene-like 2D transition oxides), and determined its distinctive electronic and topological properties. A pair of 2D antiferromagnetic (AFM) Dirac points precisely located at the Fermi level in the absence of spin-orbit coupling (SOC) is observed in the 1T-Ti3O monolayer. Moreover, upon halogenation on a bare monolayer, 1T-Ti3OCl3 and 1T-Ti3OBr3 monolayers display the quantum spin Hall (QSH) effect with nontrivial helical edge states within the gapless bulk states. Specifically, single layer 1T-Ti3OF3 behaves as an indirect semiconductor with a gap of 0.81 eV, exhibiting a strong light-harvesting capability. The indirect-gap feature can be switched to a direct one by only exerting a small tensile strain of 1.5%. These findings broaden emerging phenomena in a rich family of MOenes, suggesting a novel platform for the development of next-generation nanodevices.

Half-quantum mirror Hall effect

We predict a half-quantized mirror Hall effect induced by mirror symmetry in strong topological insulator films. These films are known to host a pair of gapless Dirac cones in the first Brillouin zone associated with surface electrons. Our findings reveal that mirror symmetry assigns a unique mirror parity to each Dirac cone, resulting in a half-quantized Hall conductance of ±e22h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm \\! \\frac{{e}^{2}}{2h}$$\\end{document} for each cone. Despite the total electrical Hall conductance being null due to time-reversal invariance, the difference in the Hall conductance between the two cones yields a quantized Hall conductance of e2h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{{e}^{2}}{h}$$\\end{document} for the difference in mirror currents. The effect of helical edge mirror current - a crucial feature of this quantum effect - may, in principle, be determined by means of electrical measurements. The half-quantum mirror Hall effect reveals a type of mirror-symmetry induced quantum anomaly in a time-reversal invariant lattice system, giving rise to a topological metallic state of matter with time-reversal invariance.

(Invited) Synthesis and Functionalization of Nanographenes with Red to Near-Infrared Emission for Photonic Applications

Nanostructures of graphene demonstrate a wide range of optical, electronic, and magnetic properties depending on their size and chemical structures, which renders them promising as next-generation carbon-based nanomaterials, e.g., for nanoelectronics, spintronics, and photonics. However, it is challenging to accurately control the chemical structures while “cutting” graphene. To this end, large polycyclic aromatic hydrocarbons (PAHs) with nanoscale graphene structures are attracting a renewed attention as atomically precise nanographenes [1]. We have developed the synthesis of dibenzo[hi,st]ovalene (DBOV) as an unprecedented nanographene with high stability, strong red fluorescence, and stimulated emission, demonstrating the potential for organic lasers [2]. The functionalization of DBOV was achieved through regioselective bromination and Suzuki coupling, enabling the introduction of various substituents, for example fluoranthene imide (FAI) groups, inducing the red-shift of the emission to the near-infrared (NIR) region [3]. Different effects on the photophysical properties of the DBOV core have been observed by changing the peripheral functional groups. More recently, we have synthesized hexabenzoperihexacene (HBPH) with zigzag and fjord edges, which displayed high stability and NIR emission with maximum at ~800 nm [4]. Notably, HBPH could be made chiral by introducing bulky tert-butyl groups on the helical fjord edges, allowing the separation of the enantiomers and showing the circular dichroism responses up to 830 nm. These results provide a new insight into the structure-property relationship of such nanographenes and pave the way toward their photonic applications.[1] Paternò, G. M.; Goudappagouda,; Chen, Q.; Lanzani, G.; Scotognella, F; Narita A., Adv. Optical Mater. 2021, 9, 2100508.[2] Paternò, G. M.; Chen, Q.; Wang, X.-Y.; Liu, J.; Motti, S. G.; Petrozza, A.; Feng, X.; Lanzani, G.; Müllen, K.; Narita, A.; Scotognella, F., Angew. Chem. Int. Ed. 2017, 56, 6753–6757.[3] Paternò, G. M.; Chen, Q.; Muñoz-Mármol, R.; Guizzardi, M.; Bonal, V.; Kabe, R.; Barker, A. J.; Boj, P. G.; Chatterjee, S.; Ie, Y.; Villalvilla, J. M.; Quintana, J. A.; Scotognella, F.; Müllen, K.; Díaz-García, M. A.; Narita, A.; Lanzani, G., Mater. Horiz. 2022, 9, 393–402.[4] Xu, X.; Muñoz-Mármol, R.; Vasylevskyi, S.; Villa, A.; Folpini, G.; Scotognella, F.; Paternò, G. M.; Narita, A., Angew. Chem. Int. Ed. 2023, 62, e202218350.

Robust Edge States of Quasi-1D Material Ta2NiSe7 and Applications in Saturable Absorbers.

The helical edge states (ESs) protected by underlying Z2 topology in two-dimensional topological insulators (TIs) arouse upsurges in saturable absorptions thanks to the strong photon-electron coupling in ESs. However, limited TIs demonstrate clear signatures of topological ESs at liquid nitrogen temperatures, hindering the applications of such exotic quantum states. Here, we demonstrate the existence of one-dimensional (1D) ESs at the step edge of the quasi-1D material Ta2NiSe7 at 78 K by scanning tunneling microscopy. Such ESs are rather robust against the irregularity of the edges, suggesting a possible topological origin. The exfoliated Ta2NiSe7 flakes were used as saturable absorbers (SAs) in an Er-doped fiber laser, hosting a mode-locked pulse with a modulation depth of up to 52.6% and a short pulse duration of 225 fs, far outstripping existing TI-based SAs. This work demonstrates the existence of robust 1D ESs and the superior SA performance of Ta2NiSe7.

Two-Dimensional M-Chalcogene Family with Tunable Superconducting, Topological, and Magnetic Properties.

An interesting question is whether chalcogen atoms can emulate the role of carbon or boron elements stabilized between two transition metal layers, as observed in MXenes or MBenes. Here, we predict a new family of two-dimensional ternary compounds M4XY2 (where M = Pd, Y, Zr, etc.; X = S, Se, Te; and Y = Cl, Br, I), named M-chalcogene. Through first-principles calculations, we reveal diverse physical properties in these compounds, including superconducting, topological, and magnetic characteristics, where the bilayer transition metals play crucial roles. Moreover, the expected helical edge states and superconducting transition temperatures in Pd4SCl2 can be finely tuned by strains. Additionally, the Ti4SCl2 is predicted to be a topological insulator and shows promise as a gas sensor candidate for certain exotic gases. Our findings expand two-dimensional material families and provide promising platforms for diverse physical phenomena with efficient tunability by external stimuli for various applications.

Topology-optimized photonic topological crystalline insulators with multiband helical edge states

Abstract Photonic topological crystalline insulators (PTCIs) with helical edge states provide an alternative way to achieve robust electromagnetic wave transport and processing. However, most existing PTCIs only involve a single topological bandgap, and generally support a pair of gapped helical edge states, restricting the scope of applications in various fields such as multiband waveguides, filters, and communication systems. Here, we design dual-band PTCIs, in which multiple helical edge modes appear within two distinct bulk gaps, for transverse electric (TE) and transverse magnetic (TM) modes, respectively, by introducing the topology optimization method into the photonic crystals with glide symmetry. For PTCIs with TE modes, the mismatched frequency ranges of edge modes hosted by two orthometric boundaries offer an opportunity to realize a photonic demultiplexer. For PTCIs with TM modes, we show the enhanced second harmonic (SH) generation through the coupling of multiband edge modes by matching the frequency ranges of edge modes within the first and second bandgaps to fundamental and SH waves, respectively. This work provides a new way for designing multiband PTCIs with helical edge states, having promising potentials in developing multiband topological photonic devices for both linear and nonlinear applications.

Possible gapless helical edge states in hydrogenated graphene

Electronic band structures in hydrogenated graphene are theoretically investigated by means of first-principle calculations and an effective tight-binding model. It is shown that regularly designed hydrogenation to graphene gives rise to a large band gap about 1 eV. Remarkably, by changing the spatial pattern of the hydrogenation, topologically distinct states can be realized, where the topological nontriviality is detected by C2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_2$$\\end{document} parity indices in bulk and confirmed by the existence of gapless edge/interface states as protected by the mirror and sublattice symmetries. The analysis of the wave functions reveals that the helical edge states in hydrogenated graphene with the appropriate design carry pseudospin currents that are reminiscent of the quantum spin Hall effect. Our work shows the potential of hydrogenated graphene in pseudospin-based device applications.

Spin-filtering properties of topological structures based on stanene and bismuthene nanoribbons with one edge magnetism

The transport properties of spin filters based on two-dimensional magnetic topological insulators (TI) with magnetism at one edge are theoretically studied. The non-equilibrium-Green’s-function (NEGF) formalism based on density functional theory (DFT) derived Hamiltonian is used to study the one-way helical edge states in these structures. We investigated the electronic and magnetic properties of stanene and bismuthene nanoribbons with various metal edge modifications. Our DFT simulations predict the formation of one-way helical edge states in stanene nanoribbons with asymmetric edge passivation. Our results suggest that the spin filtering properties of such structures outperform a comparable spin filter based on spin-polarized quantum-anomalous-Hall effect, as it bypasses a need for a strict interplay of magnetism, topology, and a large electric field (around 2 V gate voltage difference).

Interplay of valley, layer and band topology towards interacting quantum phases in moiré bilayer graphene

In Bernal-stacked bilayer graphene (BBG), the Landau levels give rise to an intimate connection between valley and layer degrees of freedom. Adding a moiré superlattice potential enriches the BBG physics with the formation of topological minibands — potentially leading to tunable exotic quantum transport. Here, we present magnetotransport measurements of a high-quality bilayer graphene–hexagonal boron nitride (hBN) heterostructure. The zero-degree alignment generates a strong moiré superlattice potential for the electrons in BBG and the resulting Landau fan diagram of longitudinal and Hall resistance displays a Hofstadter butterfly pattern with a high level of detail. We demonstrate that the intricate relationship between valley and layer degrees of freedom controls the topology of moiré-induced bands, significantly influencing the energetics of interacting quantum phases in the BBG superlattice. We further observe signatures of field-induced correlated insulators, helical edge states and clear quantizations of interaction-driven topological quantum phases, such as symmetry broken Chern insulators.

Achievement splitting for topological states with pseudospin in phase modulation by using gyromagnetic photonic crystals

As we know, valley-Hall kink states or pseudospin helical edge states are excited by polarized-momentum-locking [left-handed circular polarization (LCP) and right-handed circular polarization (RCP)] because the valley-Hall kink modes or pseudospin polarized modes have intrinsic and local chirality, which is difficult for these states to achieve phase modulation. Here we theoretically design and study a compatible topological photonic system with coexistence of photonic quantum Hall phase and pseudospin Hall phase, which is composed of gyromagnetic photonic crystals with a deformed honeycomb lattice containing six cylinders. A typical kind of hybrid topological waveguide states with pseudospin-characteristic, magnetic field-dependent, and strong robustness against backscattering and perfect electric conductor (PEC) is realized in the present system. Furthermore, we re-design a structure with intersection-liked, achieve splitting for one-way pseudospin quantum Hall edge states by using phase modulation. Robustness of the one-way pseudospin-quantum Hall edge states in splitting has been demonstrated as well. Additionally, PEC inserted in transport channel brings optical path difference in waveguide transmission, which would influence splitting for hybrid topological waveguide states in phase difference modulation. This work not only provides a new way for manipulation (i.e., phase modulation) of hybrid topological waveguide states in compatible topological photonic system from distinct topological classes but also has potential in various applications, such as sensing, signal processing, and on-chip communications.

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.

Large-Gap Quantum Spin Hall Insulators in Two-Dimensional Hafnium Halides: Unraveling the Impact of Strain and Substrate.

Two-dimensional (2D) topological insulators (TIs) or quantum spin Hall (QSH) insulators, characterized by insulating 2D electronic band structures and metallic helical edge states protected by time-reversal symmetry, offer a platform for realizing the quantum spin Hall effect, making them promising candidates for future spintronic devices and quantum computing. However, observing a high-temperature quantum spin Hall effect requires large-gap 2D TIs, and only a few 2D systems have been experimentally confirmed to possess this property. In this study, we employ first-principles calculations, combined with a structural search based on an evolutionary algorithm, to predict a class of 2D QSH insulators in hafnium halides, namely, HfF, HfCl, and HfBr with sizable band gaps of 0.12, 0.19, and 0.38 eV. Their topological nontrivial nature is confirmed by a Z2 invariant which equals to 1 and the presence of gapless edge states. Furthermore, the QSH effect in these materials remains robust under biaxial tensile strain of up to 10%, and the use of h-BN as a substrate effectively preserves the QSH states in these materials. Our findings pave the way for future theoretical and experimental investigations of 2D hafnium halides and their potential for realizing the QSH effect.