Dual quantum spin Hall insulator by density-tuned correlations in TaIrTe4.

The convergence of topology and correlations represents a highly coveted realm in the pursuit of new quantum states of matter1. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order2-8, not possible in quantum Hall and Chern insulator systems. Here we report a new dual QSH insulator within the intrinsic monolayer crystal of TaIrTe4, arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe4 demonstrates the QSH insulator, manifesting enhanced nonlocal transport and quantized helical edge conductance. After introducing electrons from charge neutrality, TaIrTe4 shows metallic behaviour in only a small range of charge densities but quickly goes into a new insulating state, entirely unexpected on the basis of the single-particle band structure of TaIrTe4. This insulating state could arise from a strong electronic instability near the van Hove singularities, probably leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state. The observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands through CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism2-4,9,10.

A hybrid topological quantum state in an elemental solid.

Topology1-3 and interactions are foundational concepts in the modern understanding of quantum matter. Their nexus yields three important research directions: (1) the competition between distinct interactions, as in several intertwined phases, (2) the interplay between interactions and topology that drives the phenomena in twisted layered materials and topological magnets, and (3) the coalescence of several topological orders to generate distinct novel phases. The first two examples have grown into major areas of research, although the last example remains mostly unexplored, mainly because of the lack of a material platform for experimental studies. Here, using tunnelling microscopy, photoemission spectroscopy and a theoretical analysis, we unveil a 'hybrid' topological phase of matter in the simple elemental-solid arsenic. Through a unique bulk-surface-edge correspondence, we uncover that arsenic features a conjoined strong and higher-order topology that stabilizes a hybrid topological phase. Although momentum-space spectroscopy measurements show signs of topological surface states, real-space microscopy measurements unravel a unique geometry of topologically induced step-edge conduction channels revealed on various natural nanostructures on the surface. Using theoretical models, we show that the existence of gapless step-edge states in arsenic relies on the simultaneous presence of both a non-trivial strong Z2 invariant and a non-trivial higher-order topological invariant, which provide experimental evidence for hybrid topology. Our study highlights pathways for exploring the interplay of different band topologies and harnessing the associated topological conduction channels in engineered quantum or nano-devices.

Observation of a linked-loop quantum state in a topological magnet.

Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state1-13. Over the past decades, these invariants have come to play a central role in describing matter, providing the foundation for understanding superfluids5, magnets6,7, the quantum Hall effect3,8, topological insulators9,10, Weyl semimetals11-13 and other phenomena. Here we report an unusual linking-number (knot theory) invariant associated with loops of electronic band crossings in a mirror-symmetric ferromagnet14-20. Using state-of-the-art spectroscopic methods, we directly observe three intertwined degeneracy loops in the material's three-torus, T3, bulk Brillouin zone. We find that each loop links each other loop twice. Through systematic spectroscopic investigation of this linked-loop quantum state, we explicitly draw its link diagram and conclude, in analogy with knot theory, that it exhibits the linking number (2, 2, 2), providing a direct determination of the invariant structure from the experimental data. We further predict and observe, on the surface of our samples, Seifert boundary states protected by the bulk linked loops, suggestive of a remarkable Seifert bulk-boundary correspondence. Our observation of a quantum loop link motivates the application of knot theory to the exploration of magnetic and superconducting quantum matter.

Quantum-limit Chern topological magnetism in TbMn6Sn6.

The quantum-level interplay between geometry, topology and correlation is at the forefront of fundamental physics1-15. Kagome magnets are predicted to support intrinsic Chern quantum phases owing to their unusual lattice geometry and breaking of time-reversal symmetry14,15. However, quantum materials hosting ideal spin-orbit-coupled kagome lattices with strong out-of-plane magnetization are lacking16-21. Here, using scanning tunnelling microscopy, we identify a new topological kagome magnet, TbMn6Sn6, that is close to satisfying these criteria. We visualize its effectively defect-free, purely manganese-based ferromagnetic kagome lattice with atomic resolution. Remarkably, its electronic state shows distinct Landau quantization on application of a magnetic field, and the quantized Landau fan structure features spin-polarized Dirac dispersion with a large Chern gap. We further demonstrate the bulk-boundary correspondence between the Chern gap and the topological edge state, as well as the Berry curvature field correspondence of Chern gapped Dirac fermions. Our results point to the realization of a quantum-limit Chern phase in TbMn6Sn6, and may enable the observation of topological quantum phenomena in the RMn6Sn6 (where R is a rare earth element) family with a variety of magnetic structures. Our visualization of the magnetic bulk-boundary-Berry correspondence covering real space and momentum space demonstrates a proof-of-principle method for revealing topological magnets.

Van Hove annihilation and nematic instability on a kagome lattice.

A nematic phase breaks the point-group symmetry of the crystal lattice and is known to emerge in correlated materials. Here we report the observation of an intra-unit-cell nematic order and associated Fermi surface deformation in the kagome metal ScV6Sn6. Using scanning tunnelling microscopy and scanning tunnelling spectroscopy, we reveal a stripe-like nematic order breaking the crystal rotational symmetry within the kagome lattice itself. Moreover, we identify a set of Van Hove singularities adhering to the kagome-layer electrons, which appear along one direction of the Brillouin zone and are annihilated along other high-symmetry directions, revealing rotational symmetry breaking. Via detailed spectroscopic maps, we further observe an elliptical deformation of the Fermi surface, which provides direct evidence for an electronically mediated nematic order. Our work not only bridges the gap between electronic nematicity and kagome physics but also sheds light on the potential mechanism for realizing symmetry-broken phases in correlated electron systems.

Topological chiral crystals with helicoid-arc quantum states.

The quantum behaviour of electrons in materials is the foundation of modern electronics and information technology1-11, and quantum materials with topological electronic and optical properties are essential for realizing quantized electronic responses that can be used for next generation technology. Here we report the first observation of topological quantum properties of chiral crystals6,7 in the RhSi family. We find that this material class hosts a quantum phase of matter that exhibits nearly ideal topological surface properties originating from the crystals' structural chirality. Electrons on the surface of these crystals show a highly unusual helicoid fermionic structure that spirals around two high-symmetry momenta, indicating electronic topological chirality. The existence of bulk multiply degenerate band fermions is guaranteed by the crystal symmetries; however, to determine the topological invariant or charge in these chiral crystals, it is essential to identify and study the helicoid topology of the arc states. The helicoid arcs that we observe on the surface characterize the topological charges of ±2, which arise from bulk higher-spin chiral fermions. These topological conductors exhibit giant Fermi arcs of maximum length (π), which are orders of magnitude larger than those found in known chiral Weyl fermion semimetals5,8-11. Our results demonstrate an electronic topological state of matter on structurally chiral crystals featuring helicoid-arc quantum states. Such exotic multifold chiral fermion semimetal states could be used to detect a quantized photogalvanic optical response, the chiral magnetic effect and other optoelectronic phenomena predicted for this class of materials6.

Nonlinear Optics: feature issue introduction.

This joint issue of Optics Express and Optical Materials Express showcases 29 articles that report the latest advancements in nonlinear optics. These articles include contributions from authors who participated in the Optica Nonlinear Optics Topical Meeting, which took place in Honolulu, Hawaii, from July 10th to July 14th, 2023. The conference was organized by Optica (formerly known as OSA). As an introduction, the editors provide a summary of these articles, which cover a broad range of topics in nonlinear optics, spanning from fundamental nonlinear optical concepts to novel nonlinear effects, and from innovative nonlinear materials to topics such as ultrafast optics, machine learning empowered nonlinear optics, and unconventional applications. This diverse array of contributions reflects the dynamic and interdisciplinary nature of contemporary research in the field of nonlinear optics while showcasing some of the most recent developments.

Giant and anisotropic many-body spin-orbit tunability in a strongly correlated kagome magnet.

Owing to the unusual geometry of kagome lattices-lattices made of corner-sharing triangles-their electrons are useful for studying the physics of frustrated, correlated and topological quantum electronic states1-9. In the presence of strong spin-orbit coupling, the magnetic and electronic structures of kagome lattices are further entangled, which can lead to hitherto unknown spin-orbit phenomena. Here we use a combination of vector-magnetic-field capability and scanning tunnelling microscopy to elucidate the spin-orbit nature of the kagome ferromagnet Fe3Sn2 and explore the associated exotic correlated phenomena. We discover that a many-body electronic state from the kagome lattice couples strongly to the vector field with three-dimensional anisotropy, exhibiting a magnetization-driven giant nematic (two-fold-symmetric) energy shift. Probing the fermionic quasi-particle interference reveals consistent spontaneous nematicity-a clear indication of electron correlation-and vector magnetization is capable of altering this state, thus controlling the many-body electronic symmetry. These spin-driven giant electronic responses go well beyond Zeeman physics and point to the realization of an underlying correlated magnetic topological phase. The tunability of this kagome magnet reveals a strong interplay between an externally applied field, electronic excitations and nematicity, providing new ways of controlling spin-orbit properties and exploring emergent phenomena in topological or quantum materials10-12.

High power optical frequency comb with 10-19 frequency instability.

Optical frequency combs with more than 10 W have paved the way for extreme ultraviolet combs generation by interaction with inert gases, leading to extreme nonlinear spectroscopy and the ultraviolet nuclear clock. Recently, the demand for an ultra-long-distance time and frequency space transfer via optical dual-comb proposes a new challenge for high power frequency comb in respect of power scaling and optical frequency stability. Here we present a frequency comb based on fiber chirped pulse amplification (CPA), which can offer more than 20 W output power. We further characterize the amplifier branch noise contribution by comparing two methods of locking to an optical reference and measure the out-of-loop frequency instability by heterodyning two identical high-power combs. Thanks to the low noise CPA, reasonable locking method, and optical path-controlled amplifiers, the out-of-loop beat note between two combs demonstrates the unprecedented frequency stability of 4.35 × 10-17 at 1s and 6.54 × 10-19 at 1000 s.

High-power, high-repetition-rate tunable longwave mid-IR sources based on DFG in the OPA regime.

We demonstrate high-power longwave mid-IR ultrafast sources based on a high-power Er-fiber laser system at 1.55 µm with a 32-MHz repetition rate. Compared with previous 1.03-µm-driven difference frequency generation (DFG), our current configuration allows tighter focusing in the GaSe crystal thanks to an increased damage threshold at 1.55 µm. Consequently, the 1.55-µm-driven DFG can operate in the regime of optical parametric amplification (OPA), in which the mid-IR power grows exponentially with respect to the square root of the pumping power. We experimentally demonstrate this operation regime and achieve broadband mid-IR pulses that are tunable in the 7.7-17.3 µm range with a maximum average power of 58.3 mW, which is also confirmed by our numerical simulation.

Visualizing Higher-Fold Topology in Chiral Crystals.

Novel topological phases of matter are fruitful platforms for the discovery of unconventional electromagnetic phenomena. Higher-fold topology is one example, where the low-energy description goes beyond standard model analogs. Despite intensive experimental studies, conclusive evidence remains elusive for the multigap topological nature of higher-fold chiral fermions. In this Letter, we leverage a combination of fine-tuned chemical engineering and photoemission spectroscopy with photon energy contrast to discover the higher-fold topology of a chiral crystal. We identify all bulk branches of a higher-fold chiral fermion for the first time, critically important for allowing us to explore unique Fermi arc surface states in multiple interband gaps, which exhibit an emergent ladder structure. Through designer chemical gating of the samples in combination with our measurements, we uncover an unprecedented multigap bulk boundary correspondence. Our demonstration of multigap electronic topology will propel future research on unconventional topological responses.

Nonreciprocal Transport in a Bilayer of MnBi2Te4 and Pt.

MnBi2Te4 (MBT) is the first intrinsic magnetic topological insulator with the interaction of spin-momentum locked surface electrons and intrinsic magnetism, and it exhibits novel magnetic and topological phenomena. Recent studies suggested that the interaction of electrons and magnetism can be affected by the Mn-doped Bi2Te3 phase at the surface due to inevitable structural defects. Here, we report an observation of nonreciprocal transport, that is, current-direction-dependent resistance, in a bilayer composed of antiferromagnetic MBT and nonmagnetic Pt. The emergence of the nonreciprocal response below the Néel temperature confirms a correlation between nonreciprocity and intrinsic magnetism in the surface state of MBT. The angular dependence of the nonreciprocal transport indicates that nonreciprocal response originates from the asymmetry scattering of electrons at the surface of MBT mediated by magnon. Our work provides an insight into nonreciprocity arising from the correlation between magnetism and Dirac surface electrons in intrinsic magnetic topological insulators.

Unconventional chiral charge order in kagome superconductor KV3Sb5.

Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics1-4. A charge-density-wave-like order with orbital currents has been proposed for achieving the quantum anomalous Hall effect5,6 in topological materials and for the hidden phase in cuprate high-temperature superconductors7,8. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy to discover an unconventional chiral charge order in a kagome material, KV3Sb5, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2 × 2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2 × 2 charge modulation exhibits an intensity reversal in real space, signalling charge ordering. At the impurity-pinning-free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Theoretical analysis of our experiments suggests a tantalizing unconventional chiral charge density wave in the frustrated kagome lattice, which can not only lead to a large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity.

On the frequency spanning of SPM-enabled spectral broadening: analytical solutions.

We present an analytical treatment of ultra-short pulses propagating in an optical fiber in the strong nonlinearity regime, in which the interaction between self-phase modulation (SPM) and group-velocity dispersion (GVD) substantially broadens the input spectrum. Supported by excellent agreement with the simulation results, these analytical solutions provide a convenient and reasonable accurate estimation of the peak position of the outermost spectral lobes as well as the full width at half maximum of the broadened spectrum. We show that our unified solutions are valid for either Gaussian pulse or hyperbolic secant pulse propagating inside an optical fiber with positive or negative GVD. Our findings shed light on the optimization of SPM-enabled spectral broadening in various applications.

Discovery of Charge Order and Corresponding Edge State in Kagome Magnet FeGe.

Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge density wave, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to nonkagome surface layers. Here, we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifies a 2×2 charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin mapping across steps of unit cell height demonstrates the existence of spin-polarized electrons with an antiferromagnetic stacking order. We further uncover the correlation between antiferromagnetism and charge order anisotropy, highlighting the unusual magnetic coupling of the charge order. Finally, we detect a pronounced edge state within the charge order energy gap, which is robust against the irregular shape fluctuations of the kagome lattice edges. We discuss our results with the theoretically considered topological features of the kagome charge order including unconventional magnetism and bulk-boundary correspondence.

Embryonic ethanol exposure induces ectopic Hcrt and MCH neurons outside hypothalamus in rats and zebrafish: Role in ethanol-induced behavioural disturbances.

Embryonic exposure to ethanol increases the risk for alcohol use disorder in humans and stimulates alcohol-related behaviours in different animal models. Evidence in rats and zebrafish suggests that this phenomenon induced by ethanol at low-moderate concentrations involves a stimulatory effect on neurogenesis and density of hypothalamic neurons expressing the peptides, hypocretin/orexin (Hcrt) and melanin-concentrating hormone (MCH), known to promote alcohol consumption. Building on our report in zebrafish showing that ethanol induces ectopic expression of Hcrt neurons outside the hypothalamus, we investigated here whether embryonic ethanol exposure also induces ectopic peptide neurons in rats similar to zebrafish and affects their morphological characteristics and if these ectopic neurons are functional and have a role in the ethanol-induced disturbances in behaviour. We demonstrate in rats that ethanol at a low-moderate dose, in addition to increasing Hcrt and MCH neurons in the lateral hypothalamus where they are normally concentrated, induces ectopic expression of these peptide neurons further anterior in the nucleus accumbens core and ventromedial caudate putamen where they have not been previously observed and causes morphological changes relative to normally located hypothalamic neurons. Similar to rats, embryonic ethanol exposure at a low-moderate dose in zebrafish induces ectopic Hcrt neurons anterior to the hypothalamus and alters their morphology. Notably, laser ablation of these ectopic Hcrt neurons blocks the behavioural effects induced by ethanol exposure, including increased anxiety and locomotor activity. These findings suggest that the ectopic peptide neurons are functional and contribute to the ethanol-induced behavioural disturbances related to the overconsumption of alcohol.

Pre-chirp managed divided-pulse amplification using composite birefringent plates for pulse division and recombination: en route toward GW peak power.

Pre-chirp managed amplification (PCMA) allows the generation of optical pulses with a duration well below 100 fs. However, the pulse peak power is limited to <50 MW due to poor energy scalability. In this paper, we combine PCMA and divided pulse amplification to overcome this bottleneck. The resulting pre-chirp managed divided-pulse amplification (PCM-DPA) employs birefringent plates as the pulse divider/recombiner thanks to the picosecond pulse duration in the amplifier. Our numerical analysis shows that the group-delay dispersion (GDD) difference among pulse replicas results in reduced combining efficiency with increased replica numbers. We propose using composite birefringent plates to construct the divider/recombiner that features negligible GDD-difference. An Yb-fiber PCM-DPA system incorporating such composite-plate based divider/recombiner for 64 replicas can produce 121-µJ, 44-fs pulses with 2.3-GW peak power. To have a compact system, we further propose a hybrid design which can deliver 61-µJ, 48-fs pulses with 1.13-GW peak power. These results represent >30 times improvement in both pulse energy and peak power compared with current Yb-fiber PCMA systems.

Particle swarm optimization of SPM-enabled spectral selection to achieve an octave-spanning wavelength-shift.

SPM-enabled spectral selection (SESS) constitutes a powerful fiber-optic technique to generate wavelength broadly tunable femtosecond pulses. In the current demonstration, the maximum tuning range is 400 nm and the energy conversion efficiency from the pump source to the outmost spectral lobes is ∼25%. In this submission, we apply the particle swarm optimization method to the generalized nonlinear Schrödinger equation to identify the optimal parameters that maximize both the tuning range and the conversion efficiency. We show that SESS in an optical fiber with the optimized dispersion can deliver SESS pulses tunable in one octave wavelength range and the conversion efficiency can be as high as 80%. We further show the feasibility of experimental implementation based on specially designed fibers or on-chip waveguides.

Double-pass pre-chirp managed amplification with high gain and high average power.

We demonstrate, to the best of our knowledge, the first double-pass pre-chirp managed fiber amplifier. The double-pass fiber amplifier exhibits high gain allowing us to amplify chirped picosecond pulses from 20 mW to 113 W in a rod-type Yb-fiber corresponding to 38 dB gain. We study the dependence of static mode degradation (SMD) on the nonlinear phase shift (NPS) accumulated by the amplified pulse. Our results indicate that a larger nonlinear phase shift results in stronger nonlinear polarization evolution of the fundamental mode and leads to a lower threshold for SMD. After optimization, our pre-chirp managed amplifier seeded by 80 mW pulses delivers 102 W amplified power from the main output. The amplified pulses are compressed to 37 (55) fs with 90 (100) W average power by a grating pair (chirped mirrors). The double-pass configuration significantly simplifies the implementation of pre-chirp managed fiber amplifiers leading to an extremely compact system.

Signatures of Weyl Fermion Annihilation in a Correlated Kagome Magnet.

The manipulation of topological states in quantum matter is an essential pursuit of fundamental physics and next-generation quantum technology. Here we report the magnetic manipulation of Weyl fermions in the kagome spin-orbit semimetal Co_{3}Sn_{2}S_{2}, observed by high-resolution photoemission spectroscopy. We demonstrate the exchange collapse of spin-orbit-gapped ferromagnetic Weyl loops into paramagnetic Dirac loops under suppression of the magnetic order. We further observe that topological Fermi arcs disappear in the paramagnetic phase, suggesting the annihilation of exchange-split Weyl points. Our findings indicate that magnetic exchange collapse naturally drives Weyl fermion annihilation, opening new opportunities for engineering topology under correlated order parameters.