Chiral Edge States Research Articles

Large quantum anomalous Hall effect in spin-orbit proximitized rhombohedral graphene

The quantum anomalous Hall effect (QAHE) is a robust topological phenomenon that features quantized Hall resistance at zero magnetic field. We report the QAHE in a rhombohedral pentalayer graphene-monolayer tungsten disulfide (WS 2 ) heterostructure. Distinct from other experimentally confirmed QAHE systems, this system has neither magnetic element nor moiré superlattice effect. The QAH states emerge at charge neutrality and feature Chern numbers C = ±5 at temperatures of up to about 1.5 kelvin. This large QAHE arises from the synergy of the electron correlation in intrinsic flat bands of pentalayer graphene, the gate-tuning effect, and the proximity-induced Ising spin-orbit coupling. Our experiment demonstrates the potential of crystalline two-dimensional materials for intertwined electron correlation and band topology physics and may enable a route for engineering chiral Majorana edge states.

Anti-scattering propagation in multiple-bend valley phononic crystals

Valley topological phononic crystals (PCs) have attracted wide attention due to the topological properties of their edge states. In general, valley interface states can exist in the interfaces that are constructed by opposite valley topological phases. Here we study the anti-scattering propagation properties of edge states in a single valley PC. We present that the edge states can exist in different boundary terminations with different band dispersions. The boundary transport behaviors of acoustic waves along the two designed PCs are demonstrated numerically. The results show that the chiral edge states are immune against additional scatterers that preserve the valley pseudospins, but the backscattering can happen when intervalley scattering is included. Nevertheless, the anti-scattering propagation in complex multiple-bend structures can be realized by the smooth transition between the edge states and the valley interface states. Similar to the designed frequency-selective device, more prospective applications can be anticipated in the manipulation of acoustic wave propagation.

Observation of Landau levels and chiral edge states in photonic crystals through pseudomagnetic fields induced by synthetic strain

Observation of Landau levels and chiral edge states in photonic crystals through pseudomagnetic fields induced by synthetic strain

Valley-Polarized Quantum Hall Phase in a Strain-Controlled Dirac System.

In multivalley systems, the valley pseudospin offers rich physics going from encoding of information by its polarization (valleytronics), to exploring novel phases of matter when its degeneracy is changed. Here, by strain engineering, we reveal fully valley-polarized quantum Hall phases in the Pb_{1-x}Sn_{x}Se Dirac system. Remarkably, when the valley energy splitting exceeds the fundamental band gap, we observe a "bipolar quantum Hall phase," heralded by the coexistence of hole and electron chiral edge states at distinct valleys in the same quantum well. This suggests that spatially overlaid counterpropagating chiral edge states emerging at different valleys do not interfere with each other.

Hybrid plasmonic valley-Hall topological insulators

Abstract The emerging field of photonic topological insulators offers promising platforms for high-performance optical communication, computing, and sensing. However, conventional photonic topological insulator designs typically operate within the diffraction limit due to their dielectric nature. This limitation imposes constraints on device miniaturization, reduces light–matter interaction, and decreases overall device sensitivity. Introducing a new valley-Hall hybrid plasmonic topological insulator, we overcome this limitation by exploiting the coupling of surface plasmon oscillations with the optical modes of a dielectric photonic crystal, allowing for sub-diffraction vertical confinement of light. Deep-subwavelength chiral edge states can, therefore, be generated and robustly guided along disordered Z-shaped topological boundaries with much lower propagation loss compared to purely plasmonic platforms. Such extreme manipulation of light on an integrated chip platform maximizes light–matter interaction and opens the door for truly compact and efficient optical modulators, molecular sensors, and next-generation nanophotonic and quantum devices.

A first-principles study of bilayer 1T'-WTe2/CrI3: a candidate topological spin filter

The ability to manipulate electronic spin channels in 2D materials is crucial for realizing next-generation spintronics. Spin filters are spintronic components that polarize spins using external electromagnetic fields or intrinsic material properties like magnetism. Recently, topological protection from backscattering has emerged as an enticing feature that can be leveraged to enhance the robustness of 2D spin filters. In this work, we propose and then characterize one of the first 2D topological spin filters: bilayer CrI3/1T’-WTe2. To do so, we use a combination of density functional theory, maximally localized Wannier functions, and quantum transport calculations to demonstrate that a terraced bilayer satisfies the principal criteria for being a topological spin filter: namely, that it is gapless, exhibits spin-polarized charge transfer from WTe2 to CrI3 that renders the bilayer metallic, and has a topological boundary which retains the edge conductance of monolayer 1T’-WTe2. In particular, we observe that small negative ferromagnetic moments are induced on the W atoms in the bilayer, and the atomic magnetic moments on the Cr are approximately 3.2 μB/Cr compared to 2.9 μB/Cr in freestanding monolayer CrI3. Subtracting the charge and spin densities of the constituent monolayers from those of the bilayer further reveals spin-orbit coupling-enhanced spin-polarized charge transfer from WTe2 to CrI3. We demonstrate that the bilayer is topologically trivial by showing that its Chern number is zero. Lastly, we show that interfacial scattering at the boundary between the terraced materials does not remove WTe2’s edge conductance. Altogether, this evidence indicates that BL 1T’-WTe2/CrI3 is gapless, magnetic, and topologically trivial, meaning that a terraced WTe2/CrI3 bilayer heterostructure in which only a portion of a WTe2 monolayer is topped with CrI3 is a promising candidate for a 2D topological spin filter. Our results further suggest that 1D chiral edge states may be realized by stacking strongly ferromagnetic monolayers, like CrI3, atop 2D nonmagnetic Weyl semimetals like 1T’-WTe2.

Multiple Brillouin Zone Winding of Topological Chiral Edge States for Slow Light Applications.

Photonic Chern insulators are known for their topological chiral edge states (CESs), whose absolute existence is determined by the bulk band topology, but concrete dispersion can be engineered to exhibit various properties. For example, the previous theory suggested that the edge dispersion can wind many times around the Brillouin zone to slow down light, which can potentially overcome fundamental limitations in conventional slow-light devices: narrow bandwidth and keen sensitivity to fabrication imperfection. Here, we report the first experimental demonstration of this idea, achieved by coupling CESs with resonance-induced nearly flat bands. We show that the backscattering-immune hybridized CESs are significantly slowed down over a relatively broad bandwidth. Our work thus paves an avenue to broadband topological slow-light devices.

Strain-induced high-Chern-number spin-unlocked edge states in monolayer MnAsO3 with intrinsic quantum anomalous Hall effect

Two-dimensional intrinsic magnetic topological materials that can realize device miniaturization have attracted significant attention recently based on their chiral dissipationless edge states. However, since the experimental observation of quantum anomalous Hall effect (QAHE) is still limited by low temperature, high operating temperature and large nontrivial gap are urgently needed. Here, monolayer MnAsO3 is predicted to be a room-temperature intrinsic magnetic topological material with high Chern number C = 3 based on first-principles calculations, which offers the possibility of achieving high-speed and low-energy-consumption electron transport in the future. Furthermore, the large and experimental feasible nontrivial gap up to 79.09 meV is obtained under compressive strain modulation. Moreover, the high-Chern-number topological phase transition and strain-induced spin-unlocked edge states are observed, indicating the possibility of tuning the electron transport of QAHE. All these findings suggest that monolayer MnAsO3 is a suitable and promising material for fabricating low-energy-consumption spintronics devices.

Realization of a quadrupole topological insulator phase in a gyromagnetic photonic crystal

ABSTRACT The field of topological photonics was initiated with the realization of a Chern insulator phase in a gyromagnetic photonic crystal (PhC) with broken time-reversal symmetry (T), hosting chiral edge states that are topologically protected propagating modes. Along a separate line of research, a quadrupole topological insulator was the first higher-order topological phase supporting localized corner states, but has been so far limited to T-invariant systems, as T is a key ingredient in early models. Here we report the realization of a quadrupole topological insulator phase in a gyromagnetic PhC, as a consequence of topological phase transition from the previously demonstrated Chern insulator phase. The phase transition has been demonstrated with microwave measurements, which characterize the evolution from propagating chiral edge states to localized corner states. We also demonstrate the migration of topological boundary states into the continuum, when the gyromagnetic PhC is magnetically tuned. These results extend the quadrupole topological insulator phase into T-broken systems, and integrate topologically protected propagating and localized modes in a magnetically tunable photonic crystal platform.

Optically-modulated edge states and resonant tunneling based on valley-Zeeman spin–orbit coupling

The valley-Zeeman spin–orbit coupling (VZSOC) in graphene provides a platform to discover novel edge states and enrich the quantum transport phenomena. In this work, based on the VZSOC induced helical edge states regarded as two copies of chiral edge states, we investigate the modulation of the edge state and corresponding resonant tunneling with the well-defined transmission peaks under off-resonant circularly polarized (ORCP) light. It shows that the spin-up or spin-down chiral edge state can be transformed into two types of antichiral edge state where the edge states propagate in the same direction at two parallel boundaries and the bulk states propagate in opposite direction, and reversed chiral edge states by the intensity and polarized direction of the ORCP light, finally leading to fascinated edge states. These edge-state transitions are attributed to regulating the Dirac gaps by the ORCP light. Particularly, some novel resonant tunneling in junctions consisting of different edge states are discovered, most of which can be intuitively understood as different types of the loop currents that the current flows in a loop. Interestingly, the combined effect of the backscattering and loop current also plays an important role in generating resonant tunneling. These results provide a new view to manipulate helical edge state induced by the VZSOC and understand rich physics of the resonant tunneling by the loop current.

Optically and electrically controlled switchers and electron beam splitters based on topological edge states

Recently, topological edge states have attracted rapid attention for designing low-power consumption electronics due to their topological protection and suppression of backscattering. We study the transport properties of inner and outer edge states in a three-terminal device composed of hybrid zigzag graphene nanoribbons based on our derived formulas of local bond current and transmission coefficient with the wave-function matching technique. Particularly, by electrically modulating inner edge state in the conductor region, the valley current can be flipped as the charge current that is switched into one lead or split into two transmitted leads, leading to the charge switchers and electron beam splitters when the incident lead and transmitted leads are set as antichiral inner edge state and chiral edge states, respectively. Furthermore, when three leads are both modulated as antichiral inner edge state by the spatially varying off-resonant circularly polarized (ORCP) light, the charge switchers and electron beam splitters are accordingly converted into the valley switchers and electron beam splitters. The behavior of the switchers and splitters originates from the cooperative effects of the lager wave-vector mismatch between different valleys, and the distributions of lateral and vertical inner edge states. Moreover, the proposed devices could be cut off by the staggered electric field due to the gap effect, and are robust against the edge magnetism and the spin-orbit coupling. These findings are expected to apply for optically and electrically controlled topological devices.

Half quantized Hall effect

Here we report a half-quantized Hall effect in a metal or semimetal. The Hall conductance is half quantized and the longitudinal conductance is nonzero. Consequently, the Hall resistivity is not quantized. The half quantization occurs when the parity symmetry or time reversal symmetry emerges near the Fermi surface or Fermi level while the symmetry is broken in the whole system. A recent experiment reports the observation of the half-quantized Hall conductance in a magnetically-doped topological insulator. We discover that a single gapless Dirac cone exists in the band structure and has half-quantized conductance when the Fermi level intercepts the gapless surface states in which the parity symmetry is invariant. As there are no localized chiral edge states in the gapless and metallic system, we find that the chiral edge current is carried by the gapless surface states. The current density peaks at the edge and decays in a power law rather than the exponential decay as in the conventional quantum anomalous Hall effect. The half quantized Hall conductance is a signature of parity anomaly in a single gapless Dirac cone on a lattice. We term the nontrivial quantum phase as “parity anomalous semimetal”. The work opens the door to exploring novel topological states of matter with fractional topological invariants.

Imaging the Breakdown and Restoration of Topological Protection in Magnetic Topological Insulator MnBi2Te4.

Quantum anomalous Hall (QAH) insulators transport charge without resistance along topologically protected chiral 1D edge states. Yet, in magnetic topological insulators to date, topological protection is far from robust, with zero-magnetic field QAH effect only realized at temperatures an order of magnitude below the Néel temperature TN, though small magnetic fields can stabilize QAH effect. Understanding why topological protection breaks down is therefore essential to realizing QAH effect at higher temperatures. Here a scanning tunneling microscope is used to directly map the size of exchange gap (Eg,ex) and its spatial fluctuation in the QAH insulator 5-layer MnBi2Te4. Long-range fluctuations of Eg,ex are observed, with values ranging between 0 (gapless) and 70 meV, appearing to be uncorrelated to individual surface point defects. The breakdown of topological protection is directly imaged, showing that the gapless edge state, the hallmark signature of a QAH insulator, hybridizes with extended gapless regions in the bulk. Finally, it is unambiguously demonstrated that the gapless regions originate from magnetic disorder, by demonstrating that a small magnetic field restores Eg,ex in these regions, explaining the recovery of topological protection in magnetic fields. The results indicate that overcoming magnetic disorder is the key to exploiting the unique properties of QAH insulators.

Localization of Chiral Edge States by the Non-Hermitian Skin Effect

Localization of Chiral Edge States by the Non-Hermitian Skin Effect

Cn -symmetric quasi-periodic Chern insulators

Chern insulators have been recently extended to quasicrystal systems, namely the quasi-periodic Chern insulators (QCIs). Here we study the topological properties and topological response of QCIs on two-dimensional singular surfaces. Such singular QCIs with arbitrary n− fold rotational symmetry (i.e. C n -symmetric QCIs) can be constructed by ‘cutting and gluing’ unit sectors on the Dürer’s pentagonal tiling. Chiral edge states and real-space Chern number can well characterize the topological properties of C n -symmetric QCIs. Intriguingly, we numerically identify the emergence of charge fractionalization in unit of e/10 around the singular center in Cn -symmetric QCIs though their bulk densities are inhomogeneous. In addition, we explore the phase transitions of these C n -symmetric QCIs.

Edge State, Band Topology, and Time Boundary Effect in the Fine-Grained Categorization of Chern Insulators.

We predict novel topological phases with broken time-reversal symmetry supporting the coexistence of opposite chiral edge states, which are fundamentally different from the photonic spin-Hall, valley-Hall, and higher-order topological phases. We find a fine-grained categorization of Chern insulators, their band topologies characterized by identical Chern numbers are completely different. Furthermore, we prove that different topologies cause zeros in their Bloch wave function overlaps, which imprint the band gap closing and appear at the degenerate points of topological phase transition. The Bloch wave function overlaps predict the reflection and refraction at a topological time boundary, and the overlap zeros ensure the existence of vanishing revival amplitude at critical times even though different topologies before and after the time boundary have identical Chern numbers. Our findings create new opportunities for topological metamaterials, uncover the topological feature hidden in the time boundary effect as a probe of topology, and open a venue for the exploration of the rich physics originating from the long-range couplings.

Haldane model with chiral edge states using a synthetic dimension

We explicitly show that the differences, with respect to the appearance of topological phases, between the traditional Haldane model, which utilizes a honeycomb lattice structure, and the Haldane model imbued onto a brick-wall lattice geometry are inconsequential. A proposal is then put forward to realize the Haldane model by exploiting the internal degrees of freedom of atoms as a synthetic dimension. This leads to a convenient platform for the investigation of chiral edge states due to the hard boundaries provided by the hyperfine manifold. We make some cursory comments on the effects of interactions in the system. Published by the American Physical Society 2024

Valley kink states and valley-polarized chiral edge states in substrate-integrated topological photonic crystals

Valley kink states and valley-polarized chiral edge states in substrate-integrated topological photonic crystals

Edge magnetoplasmon dispersion and time-resolved plasmon transport in a quantum anomalous Hall insulator

A quantum anomalous Hall (QAH) insulator breaks reciprocity by combining magnetic polarization and spin-orbit coupling to generate a unidirectional transmission of signals in the absence of an external magnetic field. Such behavior makes QAH materials a good platform for the innovation of circulator technologies. However, it remains elusive as to how the wavelength of the chiral edge plasmon relates to its frequency and how the plasmon wave packet is excited in the time domain in a QAH insulator. Here, we investigate the edge magnetoplasmon (EMP) resonances in Cr-(Bi,Sb)2Te3 by frequency and time domain measurements. From disk shaped samples with various dimensions, we obtain the dispersion relation of EMPs and extract the drift velocity of the chiral edge state. From the time-resolved transport measurements, we identify the velocity of the plasmon wave packet and observe a transition from the edge to bulk transport at an elevated temperature. We show that the frequency and time domain measurements are well modeled by loss from the microwave induced dissipative channels in the bulk area. Our results demonstrate that the EMP decay rate can be significantly reduced by applying a low microwave power and fabricating devices of larger diameter ≥100µm. In a R=125µm sample, a nonreciprocity of 20 dB has been realized at 1.3 GHz, shining light on using QAH insulators to develop on-chip nonreciprocal devices. Published by the American Physical Society 2024

Photonic antichiral edge states induced by magnetic surface plasmon resonance

Chiral edge states are a hallmark feature of photonic Chern insulators, where waves propagate in opposite directions along two parallel edges of a strip sample. Different from the chiral edge states, at recently discovered counterintuitive antichiral edge states, where waves propagate in the same direction on the two edges, the antichiral edge states are modeled by the modified Haldane model. Here, we theoretically propose, experimentally observe the antichiral edge states induced by magnetic surface plasmon resonance, and realize the antichiral edge states in a gyromagnetic photonic crystal with rectangular lattice. Through microwave experiments and photonic band calculations, the unique properties of this antichiral edge states have been confirmed, including edge dispersion without Dirac points frequencies shift, unidirectional transmission without ancillary cladding, and the operating frequency of the edge states that can be flexibly controlled by the external magnetic field. These results extend the scope of antichiral edge states and supplement the current understanding of antichiral edge states.