Weyl Points Research Articles

Observation of chiral Landau levels in a synthetic acoustic Weyl semimetal

Band degeneracies, such as Dirac/Weyl points, play crucial roles in topological materials and condensed matter physics. Magnetic fields in Weyl systems induce the zeroth chiral Landau level, of which the concept has been extended to classical wave systems. While current research predominantly focuses on three-dimensional (3D) systems, exploring chiral Landau levels in two-dimensional (2D) systems, particularly through the introduction of an out-of-plane magnetic field, remains a vibrant area of study. Here, we report the observation of chiral Landau levels in 2D sonic crystals using the synthetic dimension methodology. By applying an out-of-plane pseudo-magnetic field generated through gradient deformation, we measure the dispersions of zeroth chiral Landau levels originating from synthetic Weyl points. Experiments also reveal sub-lattice polarizations of the chiral Landau levels. Our work demonstrates pseudo-magnetic-field-induced Weyl physics in a 2D system without breaking time-reversal symmetry, enabling exploration of topological phenomena and related acoustic wave control strategies.

Long-Range Interactions in Weyl-Dense Atomic Arrays Protected from Dissipation and Disorder.

Long-range interactions are a key resource in many quantum phenomena and technologies. Free-space photons mediate power-law interactions but lack tunability and suffer from decoherence processes due to their omnidirectional emission. Engineered dielectrics can yield tunable and coherent interactions, but typically at the expense of making them both shorter ranged and sensitive to material disorder and photon loss. Here, we propose a platform that can circumvent all these limitations based on three-dimensional subwavelength atomic arrays subjected to magnetic fields. Our key result is to show how to design the polaritonic bands of these atomic metamaterials to feature a pair of frequency-isolated Weyl points, i.e., points in reciprocal space around which the bands disperse linearly and defining monopoles of the Berry curvature. As predicted by recent works, such Weyl excitations can mediate interactions that are simultaneously long range, due to their gapless nature; robust, due to the topological protection of Weyl points; and decoherence-free, due to their subradiant character. We demonstrate the robustness of these isolated Weyl points for a large regime of interatomic distances and magnetic field values and characterize the emergence of their corresponding Fermi arcs surface states. The latter can lead to two-dimensional, nonreciprocal atomic interactions with no analogue in other chiral quantum optical setups.

Single Pair of Weyl Points Evolve From Spin Group‐Protected Nodal Line in Half‐Metallic Ferromagnet V3S4

AbstractSymmetry plays an essential role in classifying the phases and understanding the properties of materials. Recent discoveries have shown that certain properties of magnetic materials require further consideration of spin groups. Nevertheless, research on topological states and properties associated with spin groups is still in its infancy. In this work, a recipe is proposed to achieve the minimum number of Weyl points, i.e., a single pair of Weyl points (SP‐WPs) based on spin group and predict V3S4 as an ideal half‐metallic Weyl semimetal with SP‐WPs evolved from a spin group‐protected nodal line (NL). Specifically, this NL is protected by the combination of spin group symmetry and inversion symmetry. Furthermore, spin group symmetry broken induced by spin‐orbit coupling also results in a series of Berry curvature‐related anomalous transport phenomena. The SP‐WPs near the Fermi level contribute to exceptional anomalous transport properties, where the anomalous conductivity exhibits sharp peaks at the energy level of SP‐WPs, while remaining nearly zero at other energy levels. Therefore, the work not only provides a guide to search for minimum number of Weyl points in magnetic materials but also identifies a half‐metallic material as an excellent platform for spintronic devices.

Enhancing the circular photogalvanic effect in double Weyl semimetals via symmetry breaking

Weyl semimetals have emerged as a hot topic in condensed matter physics in last decade. Beyond their intriguing electrical transport phenomena, such as the negative magnetoresistance driven by the chiral anomaly and the anomalous Hall effect, they also exhibit intriguing second-order optoelectronic responses, such as the circular photogalvanic effect (CPGE). In this Letter, we investigate the CPGE in a class of double Weyl semimetal protected by the C3zT symmetry by using the effective model. Unlike double Weyl semimetal protected by Cnz (n = 4, 6) symmetry, when time-reversal symmetry T is broken, one C3zT-protected double Weyl point (WP) evolves into four single WPs, three of which are related by C3z symmetry, and these WPs share the same topological charge and reside at the same energy level. This unique configuration enhances the CPGE trace due to the combined topological charge of the three WPs, resulting in a higher quantized plateau. Our findings provide promising prospects for the development of optoelectronic devices in the future.

Magneto-optical Evidence of the Tilting Effect in Coupled Weyl Bands.

Theories have revealed the universality of the band tilting effect in topological Weyl semimetals (WSMs) and its implications for the material physical properties. However, the experimental identification of tilted Weyl bands remains less explored. Here, we report the magneto-optical evidence of the tilting effect in WSM niobium phosphide. Specifically, we observe Landau level transitions with rich features that are well reproduced within a model of coupled tilted Weyl points. Our analysis indicates that the tilting effect relaxes the selection rules and leads to transitions that would otherwise be forbidden in the non-tilt case. Additionally, we observe unconventional interband transitions with flat and negative magnetic field dispersions, highlighting the importance of coupling between Weyl points. Our results not only emphasize the significance of the tilting effect in the optical responses of WSMs but also demonstrate magneto-optics as an effective tool for probing the tilting effect in electronic band structures.

Robustness of large intrinsic anomalous Hall conductivity in Se-doped magnetic Weyl semimetal Co3Sn2S2

Robustness of large intrinsic anomalous Hall conductivity in Se-doped magnetic Weyl semimetal Co3Sn2S2

Observation of Copropagating Chiral Zero Modes in Magnetic Photonic Crystals.

Topological singularities, such as Weyl points (WPs) and Dirac points, can give rise to unidirectional propagation channels known as chiral zero modes (CZMs) when subject to a magnetic field. CZMs, as distinct zeroth Landau levels (bulk modes) with high degeneracy, are responsible for intriguing phenomena like the chiral anomaly in quantum systems. The propagation direction of each CZM is determined by both the applied magnetic field and the topological charge of the singularity point. While counterpropagating CZMs have been observed in 2D and 3D systems, the realization of copropagating CZMs has remained elusive. Here, we present the first experimental observation of copropagating CZMs in magnetic photonic crystals hosting a single pair of ideal Weyl points. By manipulating the crystal's structural configuration and applying a uniform bias magnetic field, we spatially alter the locations of the WPs, creating pseudo-magnetic fields of opposite directions for different WPs. This arrangement results in a pair of CZMs that possess the same group velocity and copropagate. Our work opens up new possibilities for the topological manipulation of wave propagation and may lead to advancements in optical waveguides, switches, and various other applications.

Synthesis of a semimetallic Weyl ferromagnet with point Fermi surface.

Quantum materials governed by emergent topological fermions have become a cornerstone of physics. Dirac fermions in graphene form the basis for moiré quantum matter and Dirac fermions in magnetic topological insulators enabled the discovery of the quantum anomalous Hall (QAH) effect1-3. By contrast, there are few materials whose electromagnetic response is dominated by emergent Weyl fermions4-6. Nearly all known Weyl materials are overwhelmingly metallic and are largely governed by irrelevant, conventional electrons. Here we theoretically predict and experimentally observe a semimetallic Weyl ferromagnet in van der Waals (Cr,Bi)2Te3. In transport, we find a record bulk anomalous Hall angle of greater than 0.5 along with non-metallic conductivity, a regime that is strongly distinct from conventional ferromagnets. Together with symmetry analysis, our data suggest a semimetallic Fermi surface composed of two Weyl points, with a giant separation of more than 75% of the linear dimension of the bulk Brillouin zone, and no other electronic states. Using state-of-the-art crystal-synthesis techniques, we widely tune the electronic structure, allowing us to annihilate the Weyl state and visualize a unique topological phase diagram exhibiting broad Chern insulating, Weyl semimetallic and magnetic semiconducting regions. Our observation of a semimetallic Weyl ferromagnet offers an avenue towards new correlated states and nonlinear phenomena, as well as zero-magnetic-field Weyl spintronic and optical devices.

Phase transitions, Dirac and Weyl semimetal states in Mn1−xGexBi2Te4

Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), an experimental and theoretical study of changes in the electronic structure (dispersion dependencies) and corresponding modification of the energy band gap at the Dirac point (DP) for topological insulator (TI) have been carried out with gradual replacement of magnetic Mn atoms by non-magnetic Ge atoms when concentration of the latter was varied from 10% to 75%. It was shown that when Ge concentration increases, the bulk band gap decreases and reaches zero plateau in the concentration range of 45–60% while trivial surface states (TrSS) are present and exhibit an energy splitting of 100 and 70 meV in different types of measurements. It was also shown that TSS disappear from the measured band dispersions at a Ge concentration of about 40%. DFT calculations of band structure were carried out to identify the nature of observed band dispersion features and to analyze the possibility of magnetic Weyl semimetal state formation in this system. These calculations were performed for both antiferromagnetic (AFM) and ferromagnetic (FM) ordering types while the spin-orbit coupling (SOC) strength was varied or a strain (compression or tension) along the c-axis was applied. Calculations show that two different series of topological phase transitions (TPTs) may be implemented in this system, depending on the magnetic ordering. In the case of AFM ordering, the transition between TI and the trivial insulator phase passes through the Dirac semimetal state, whereas for FM phase such route admits three intermediate states instead of one (TI—Dirac semimetal—Weyl semimetal—Dirac semimetal—trivial insulator). Weyl points that form in the FM system along the direction annihilate when either the SOC strength decreases or a sufficient tensile strain is applied, which is accompanied by the corresponding TPTs. Model calculations of the influence of local magnetic ordering in AFM were carried out by alternating Mn layers with Ge-doped layers and showed that the magnetic Weyl semimetal state in this system is reachable at a Ge concentration of approximately 40% without application of any external magnetic fields.

Correspondence between Euler charges and nodal-line topology in Euler semimetals.

Real multi-bandgap systems have non-abelian topological charges, with Euler semimetals being a prominent example characterized by real triple degeneracies (RTDs) in momentum space. These RTDs serve as "Weyl points" for real topological phases. Despite theoretical interest, experimental observations of RTDs have been lacking, and studies mainly focus on individual RTDs. Here, we experimentally demonstrate physical systems with multiple RTDs in crystals, analyzing the distribution of Euler charges and their global connectivity. Through Euler curvature fields, we reveal that type I RTDs have quantized point Euler charges, while type II RTDs show continuously distributed Euler charges along nodal lines. We discover a correspondence between the Euler number of RTDs and the abelian/non-abelian topological charges of nodal lines, extending the Poincaré-Hopf index theorem to Bloch fiber bundles and ensuring nodal line connectivity. In addition, we propose a "no-go" theorem for RTD systems, mandating the balance of positive and negative Euler charges within the Brillouin zone.

Magnetic topological Weyl fermions in half-metallic In2CoSe4

Magnetic Weyl semimetals (WSMs) have recently attracted much attention due to their potential in realizing strong anomalous Hall effects. Yet, how to design such systems remains unclear. Based on first-principles calculations, we show here that the ferromagnetic half-metallic compound In2CoSe4has several pairs of Weyl points and is hence a good candidate for magnetic WSM. These Weyl points would approach the Fermi level gradually as the HubbardUincreases, and finally disappear after a critical valueUc. The range of the HubbardUthat can realize the magnetic WSM state can be expanded by pressure, manifesting the practical utility of the present prediction. Moreover, by generating two surface terminations at Co or In atom after cleaving the compound at the Co-Se bonds, the nontrivial Fermi arcs connecting one pair of Weyl points with opposite chirality are discovered in surface states. Furthermore, it is possible to observe the nontrivial surface state experimentally, e.g. angle-resolved photoemission spectroscopy measurements. As such, the present findings imply strongly a new magnetic WSM which may host a large anomalous Hall conductivity.

Machine-learning approach to understanding ultrafast carrier dynamics in the three-dimensional Brillouin zone of PtBi2

Using time- and angle-resolved photoemission spectroscopy, we examine the unoccupied electronic structure and electron dynamics of the type-I Weyl semimetal PtBi2. Using the ability to change the probe photon energy over a wide range, we identify the predicted Weyl points in the unoccupied three-dimensional band structure and we discuss the effect of k⊥ broadening in the normally unoccupied states. We characterize the electron dynamics close to the Weyl points and in other parts of three-dimensional Brillouin zone using k-means, an unsupervised machine-learning technique. This reveals distinct differences—in particular, that the electron dynamics close to the Weyl points are slower than in Brillouin zone regions close to the bulk Fermi surface. Published by the American Physical Society 2025

Topological sonic whispering gallery protected by the synthetic Weyl points

Topological sonic whispering gallery protected by the synthetic Weyl points

Topological rainbow trapping of sound waves in synthesized three-dimensional space for square lattice

Abstract The three-dimensional (3D) synthetic space offers a platform for exploring the valley Hall insulator, which is usually constructed in graphene lattice. Here, based on the valley transports in the square lattice, we construct a synthetic space by treating the rotation angle as the third dimension and observe the emergent Weyl points in this synthetic space. Since the construction of synthetic Weyl points results in the formation of edge states between the phononic crystal (PC) and the hard boundary, and the factors of rotation angle and the distance from the PC to the hard boundary affect the frequency of these edge states, we can construct topological rainbow concentrator based on the above principles. We conduct a comprehensive numerical and experimental study to explore the characteristics of topological rainbow concentrators. This work may play a driving role in the development of topological rainbow devices.

Controllable topological phase transition via ferroelectric-paraelectric switching in a ferromagnetic single-layer MIMIIGe2X6 family.

Recently, the emergence of two-dimensional (2D) multiferroic materials has opened a new perspective for exploring topological states. However, instances of tuning topological phase transitions through ferroelectric (FE) polarization in 2D ferromagnetic (FM) materials are relatively rare. Here, we found that 11 single layer (SL) materials, named the MIMIIGe2X6 family, possess both FE and FM properties. Among them, 5 SL materials exhibit controllable topological phase transition via ferroelectric-paraelectric switching. Taking the SL ReIrGe2S6 as an example, we find that the paraelectric (PE) and FE phases exhibit half-metal and magnetic semiconductor behavior, respectively. In the spin-down channel of the PE phase, a critical-type Weyl point (WP) is observed with a robust Fermi arc edge state. In contrast, the FE phase of the SL ReIrGe2S6 clearly identifies 0D corner states in both spin channels. Therefore, under the control of external fields, the SL ReIrGe2S6 undergoes a transformation from PE to FE by overcoming the energy barrier of 0.62 eV, subsequently realizing the phase transition from the Weyl semimetal to the high order topological insulator. These findings not only combine topological states with multiferroics but also pave the way for the experimental discovery of 2D tunable topological phase transition.

Time-Reversal Symmetry Breaking Superconductivity in HfRhGe: A Noncentrosymmetric Weyl Semimetal.

Weyl semimetals are a novel class of topological materials with unique electronic structures and distinct properties. HfRhGe stands out as a noncentrosymmetric Weyl semimetal with unconventional superconducting characteristics. Using muon-spin rotation and relaxation (µSR) spectroscopy and thermodynamic measurements, a fully gapped superconducting state is identified in HfRhGe that breaks time-reversal symmetry at the superconducting transition. This breaking can trigger a topological phase transition, as time-reversal symmetry protects the normal-state Weyl topology characterized by comprehensive first-principles calculations. Ginzburg-Landau analysis suggests an unconventional loop supercurrent superconducting state realized in HfRhGe. The presence of multiple Weyl points near the Fermi level and surface Fermi arcs dispersing across the Fermi level further support HfRhGe as a promising platform for topological superconductivity. Additionally, its noncentrosymmetric nature with time-reversal symmetry breaking superconducting state suggests that it can exhibit an intrinsic superconducting diode effect, offering novel optical and transport properties, with potential applications in dissipationless quantumelectronics.

Enhanced Weyl semimetal signature in Co3Sn2S2 Kagome ferromagnet by chlorine doping

Weyl fermions are chiral massless fermions with exotic properties. In the first established magnetic Weyl semimetal, Co3Sn2S2, a giant anomalous Hall effect has been observed, while its Fermi energy remaining 60 meV from the Weyl points. Shifting the Fermi energy closer to the Weyl points may assist in the identification of Weyl Fermion related transport signatures. Here we show that effective chlorine doping has resulted in a shift of the Fermi energy by 15 meV towards the Weyl points, which is confirmed by a combination of the systematic angular-resolved photoemission spectroscopy measurements and density function theory calculations. A five-fold reduction in resistivity is observed in the ferromagnetic phase, accompanied by a pronounced magnetoresistance of over 150%. The anomalous Hall conductivity shows a peak of 1680 Scm−1 at 40 K, which is 30% higher than the undoped sample due to a stronger Weyl point contribution. This work demonstrates the essential role of doping in Co3Sn2S2 for an enhanced Weyl semimetal signature.

Upper bound on the number of Weyl points born from a nongeneric degeneracy point

Upper bound on the number of Weyl points born from a nongeneric degeneracy point

Floquet analysis on an irradiated nodal surface semimetal with non-symmorphic symmetry

A nodal surface semimetal (NSSM) features symmetry enforced band crossings along a surface within the three-dimensional (3D) Brillouin zone (BZ) and a presence of a nonsymmorphic symmetry there pushes such surfaces to stick to the BZ center or boundaries. The topological robustness of the same does not always come with nonzero Berry fluxes. We consider two such NS, one with zero and another with nonzero topological charges and investigate the effect of light irradiation on them. We find that depending on the state of polarization, one can obtain additional Weyl points/NS in the corresponding Floquet Hamiltonians. Particularly, using a simple two band spinless/spin polarized models with no spin orbit coupling, we emphasize the low energy behavior of the continuum Hamiltonians close to the band crossings and its evolution in a Floquet system in the high frequency limit. In the Floquet system, we also find the NS to perish or new multi Weyl points to get popped up for different polarization scenario or different NSSM Hamiltonians. Our findings open up important avenues on what out of equilibrium NSSM systems can offer in many active fields including quantum computations.

In-Plane Anomalous Hall Effect Associated with Orbital Magnetization: Measurements of Low-Carrier Density Films of a Magnetic Weyl Semimetal.

For over a century, the Hall effect, a transverse effect under an out-of-plane magnetic field or magnetization, has been a cornerstone for magnetotransport studies and applications. Modern theoretical formulation based on the Berry curvature has revealed the potential that even an in-plane magnetic field can induce an anomalous Hall effect, but its experimental demonstration has remained difficult due to its potentially small magnitude and strict symmetry requirements. Here, we report observation of the in-plane anomalous Hall effect by measuring low-carrier density films of magnetic Weyl semimetal EuCd_{2}Sb_{2}. Anomalous Hall resistance exhibits distinct threefold rotational symmetry for changes in the in-plane field component, and this can be understood in terms of out-of-plane Weyl points splitting or orbital magnetization induced by the in-plane field, as also confirmed by model calculation. Our findings demonstrate the importance of the in-plane field to control the Hall effect, accelerating materials development and further exploration of various in-plane field-induced phenomena.