Weyl Points Research Articles

Designed two dimensional triangle lattice Ti3X5 (X=S, Se): Stable quantum anomalous Hall states with high Chern number

Although much efforts have been made into exploration of quantum anomalous Hall (QAH) effects in theory and experiment, the QAH materials with high Chern number are still rare to people. Here, by first-principles calculations, we theoretically predicted stable 2D robust QAH monolayers, Ti3X5 (X = S, Se) with high Chern number |C| = 2. In the absence of spin–orbital coupling (SOC), the ferromagnetism polarizes the system into a half semimetal with eight Weyl points in the whole Brillouin zone. When SOC is turned on, the bandgap is opened with two chiral edge modes. Additionally, a topological phase transition from C = −2 to C = 2 is realized by rotating the magnetization direction from z axis to −z axis. In addition, a phase transition from C = −2 to C = 0 can be manipulated by applying external strains or varying electronic correlation Ueff. Our work provides potential high Chern number QAH candidates for the practical electronic application.

Type-II Weyl points and one-way interface transmission in a three-dimensional gyromagnetic photonic crystal

Type-II Weyl points and one-way interface transmission in a three-dimensional gyromagnetic photonic crystal

Berry Curvature Dipole Induced Giant Mid-Infrared Second-Harmonic Generation in 2D Weyl Semiconductor.

Due to its inversion-broken triple helix structure and the nature of Weyl semiconductor, 2D Tellurene (2D Te) is promising to possess a strong nonlinear optical response in the infrared region, which is rarely reported in 2D materials. Here, a giant nonlinear infrared response induced by large Berry curvature dipole (BCD) is demonstrated in the Weyl semiconductor 2D Te. Ultrahigh second-harmonic generation response is acquired from 2D Te with a large second-order nonlinear optical susceptibility (χ(2) ), which is up to 23.3 times higher than that of monolayer MoS2 in the range of 700-1500nm. Notably, distinct from other 2D nonlinear semiconductors, χ(2) of 2D Te increases extraordinarily with increasing wavelength and reaches up to 5.58nmV-1 at ≈2300nm, which is the best infrared performance among the reported 2D nonlinear materials. Large χ(2) of 2D Te also enables the high-intensity sum-frequency generation with an ultralow continuous-wave (CW) pump power. Theoretical calculations reveal that the exceptional performance is attributed to the presence of large BCD located at the Weyl points of 2D Te. These results unravel a new linkage between Weyl semiconductor and strong optical nonlinear responses, rendering 2D Te a competitive candidate for highly efficient nonlinear 2D semiconductors in the infrared region.

Colossal negative magnetoresistance in field-induced Weyl semimetal of magnetic half-Heusler compound

The discovery of topological insulators and semimetals triggered enormous interest in exploring emergent electromagnetic responses in solids. Particular attention has been focused on ternary half-Heusler compounds, whose electronic structure bears analogy to the topological zinc-blende compounds while also including magnetic rare-earth ions coupled to conduction electrons. However, most of the research in this system has been in band-inverted zero-gap semiconductors such as GdPtBi, which still does not fully exhaust the large potential of this material class. Here, we report a less-studied member of half-Heusler compounds, HoAuSn, which we show is a trivial semimetal or narrow-gap semiconductor at zero magnetic field but undergoes a field-induced transition to a Weyl semimetal, with a negative magnetoresistance exceeding four orders of magnitude at low temperatures. The combined study of Shubnikov-de Haas oscillations and first-principles calculation suggests that the exchange field from Ho 4f moments reconstructs the band structure to induce Weyl points which play a key role in the strong suppression of large-angle carrier scattering. Our findings demonstrate the unique mechanism of colossal negative magnetoresistance and provide pathways towards realizing topological electronic states in a large class of magnetic half-Heusler compounds.

Two-dimensional antiferromagnetic type-II Weyl fermions in monolayer ZnSb and type-I Weyl fermions and topological insulator in bilayer ZnSb

Two-dimensional (2D) topological materials have attracted extensive attention due to the discovery of graphene. In addition, their counterparts in magnetic materials are also a fascinating subject of research. However, it remains challenging to find 2D materials that have the desired topological phases. Here, based on first-principles calculations, we investigate the properties of a newly synthesized 2D material, monolayer/bilayer (ML/BL) ZnSb. We find that the ML ZnSb is antiferromagnetic (AFM) and that its magnetism can be changed by an external strain, from AFM to ferromagnetic. Without any external strain, the ML ZnSb can be considered as an almost ideal 2D type-II Weyl material with a pair of type-II Weyl fermions exactly located at the Fermi level. When taking into account spin–orbit coupling (SOC), a gap can be introduced at the Weyl point. We further show that by applying a biaxial strain to the BL ZnSb material, it is possible to open different gaps at the Weyl points, leading to a topological phase transition without breaking symmetry. When SOC is included, these Weyl points become topological insulators with a large bandgap, where the helical edge states can be identified. Overall, this study provides an example of a material that can be used to explore the physical consequences of 2D topological phases and provide a promising candidate for future research in this field.

Vector-chirality driven topological phase transitions in noncollinear antiferromagnets and its impact on anomalous Hall effect

Magnetic materials showing topologically nontrivial quantum states with high tunability is an undoubtedly important topic in condensed matter physics and material science. Based on the first-principles electronic structure calculations and subsequent symmetry adapted effective low-energy k.p theory, we show in a noncollinear antiferromagnet (AFM), Mn3Sn, that the switching of the vector-chirality, κ, is an unconventional route to topological phase transition from a nodal-ring to a Weyl point semimetal. Specifically, we find that the switching of κ via staggered rotation leads to gapping out an elliptic nodal-ring everywhere at the Fermi-level except for a pair of points on the ring. As a consequence, the topological phase transition switches the anomalous Hall conductivity (AHC) from zero to a giant value. Furthermore, we theoretically demonstrate how the controlled manipulation of the chiral AFM order keeping κ unaltered favors unusual rotation of Weyl-points on the ring. In fact, without staggered rotation, this enables us to tune and switch the sign of in-plane components of the AHC by a collective uniform rotations of spins in the AFM unit cell.

Catalog of maximally charged Weyl points hosting nearly emanating nodal lines in phonon spectra

Catalog of maximally charged Weyl points hosting nearly emanating nodal lines in phonon spectra

Antiferromagnetic second-order topology in two-dimensional NiRuCl6

In recent years, 2D second-order topological insulators (SOTIs) have garnered considerable interest because of their unique properties. However, only the FeSe monolayer with four corner states (two occupied and two unoccupied states) near the Fermi level has been reported to be a candidate for 2D intrinsic antiferromagnetic SOTIs in theory. The limited amount of antiferromagnetic SOTIs has hindered future research, and corner states should be at the Fermi level in order to manifest interesting physics. Herein, we propose NiRuCl6 as a candidate for 2D antiferromagnetic SOTIs with corner states strictly at the Fermi level. Without spin–orbit coupling (SOC), NiRuCl6 is an antiferromagnetic half-metal with a compensating magnetic moment and decoupled spin bands. In the spin-up channel, NiRuCl6 hosts a nontrivial gap of 1.11 eV, where zero-dimensional corner states appear. In the spin-down channels, NiRuCl6 hosts metallically behaved bands, where a spin-polarized quadratic Weyl point emerges. With SOC, two spin bands are coupled, and NiRuCl6 becomes an antiferromagnetic SOTI with three degenerate corner states at the Fermi level inside the SOC-induced gap with a value of 0.11 eV. Remarkably, the corner states in NiRuCl6 are resistant to changes in SOC strength and magnetization orientation. We also reveal that the phononic second-order topology and corner vibrational modes appear in the phonon dispersion curves of NiRuCl6. The presented results improve the general understanding of antiferromagnetic SOTIs and contribute to the prediction of materials with ideal corner states at the Fermi level, thereby advancing the field of topological antiferromagnetic spintronics.

Interplay of magnetism and band topology in Eu[formula omitted]Ca[formula omitted]Mg[formula omitted]Bi[formula omitted] (x=0, 0.5, 0.67) from first principles study

Recent discovery of the time reversal symmetry breaking magnetic Weyl semimetals (WSMs) has created a huge surge of activities in the field of quantum topological materials. In this work, we have studied systematically various magnetic orders, electronic structure and the interplay between the magnetic order and band topology in one such material, EuMg2Bi2 (EMB) and its Ca doped variant using first principle methods within the framework of density functional theory (DFT). Our thorough investigation reveals the existence of various magnetic order driven topological phases (for example, topological insulator in the A-type antiferromagnetic (A-AFM) phase with Eu moments aligned along the crystallographic a or b direction, Dirac semimetal in the A-AFM phase when Eu moments are parallel to c direction and Weyl semimetal in the ferromagnetic (FM) phase with Eu moments pointing along the c direction) in this material. These phases are found to be energetically very close and hence are expected to be tunable from one to the other by an external handle such as magnetic field or chemical substitution. Most importantly, we observe the existence of a single pair of Weyl points (WPs) connecting valence and conduction band very close to the Fermi level (FL) along Γ-A direction in the FM state of EuMg2Bi2 with Eu moments aligned along the c direction making it an ideal Weyl semimetal in its FM state exactly similar to EuCd2As2. On doping 50% and 67% Ca at Eu sites, we observe the single pair of WPs to move even closer to the FL which is highly desirable for application purposes. Further, we observe that the separation between the WPs in the pair decreases in doped compounds compared to that in the parent compound which has direct consequence on anomalous Hall conductivity (AHC). Our first principles calculation of AHC shows high peak values exactly at these WPs and the peak height decreases when we dope the system with Ca. Therefore, Ca doping can be a good external handle to tune AHC in this system.

Detection of chirality imbalance in photonic Weyl metamaterials with mirror symmetry-breaking

In condensed systems, Weyl quasiparticles have a massless nature and exhibit various relativistic chiral phenomena such as Klein tunneling, chiral anomaly, and Fermi arc surface states. However, in photonic systems, Weyl points (WPs) are protected by the D2d symmetry, often leading to multiple chiral WPs at the same energy level, which makes generating chirality-related effects challenging. To overcome this hinderance, a perturbation that breaks mirror symmetry in the metallic saddle structure was introduced. This perturbation effectively separates the energies of distinct chiral WPs, enabling the experimental measurement of the spectral intensity for each Weyl band and the assessment of chirality imbalance among the WPs. By maintaining time-reversal symmetry, the present study offers an approach for investigating the imbalance in the chirality of pseudo-fermionic fields in photonic materials.

Phononic Weyl pair, phononic Weyl complex, phononic real Chern insulator state, and phononic corner modes in 2D Kekulé-order graphene

The conceptual framework of topological states has recently been extended to bosonic systems, particularly phononic systems. In this work, we chose the recently experimentally prepared two-dimensional (2D) Kekulé-order graphene as a target to propose the coexistence of gapless and gapped topological phonon states in its phonon curves. This is the first work to investigate rich gapped and gapless topological phonon states in experimentally feasible 2D materials. For the gapped topological phonons, 2D Kekulé-order graphene hosts phononic real Chern insulator states, i.e., second-order topological states, and corner vibrational modes inside frequency gaps at 27.96 and 37.065 THz. For the gapless topological phonons, 2D Kekulé-order graphene hosts a phononic Weyl pair [comprising two linear Weyl points (LWPs)] and a phononic Weyl complex [comprising one quadratic nodal point (QNP) and two LWPs] around 7.54 and 47.3 THz (39.2 THz), respectively. Moreover, the difference between the phononic Weyl pair and the phononic Weyl complex was investigated in detail. Our study not only promotes 2D Kekulé-order graphene as a concrete material platform for exploring the intriguing physics of phononic second-order topology but also proposes the coexistence of different categories of Weyl phonons, i.e., a Weyl complex that comprises two LWPs and one QNP, in two dimensions. Our work paves the way for new advancements in topological phononics comprising gapless and gapped topological phonons.

Observation of Termination-Dependent Topological Connectivity in a Magnetic Weyl Kagome Lattice.

Engineering surfaces and interfaces of materials promises great potential in the field of heterostructures and quantum matter designers, with the opportunity to drive new many-body phases that are absent in the bulk compounds. Here, we focus on the magnetic Weyl kagome system Co3Sn2S2 and show how for the terminations of different samples the Weyl points connect differently, still preserving the bulk-boundary correspondence. Scanning tunneling microscopy has suggested such a scenario indirectly, and here, we probe the Fermiology of Co3Sn2S2 directly, by linking it to its real space surface distribution. By combining micro-ARPES and first-principles calculations, we measure the energy-momentum spectra and the Fermi surfaces of Co3Sn2S2 for different surface terminations and show the existence of topological features depending on the top-layer electronic environment. Our work helps to define a route for controlling bulk-derived topological properties by means of surface electrostatic potentials, offering a methodology for using Weyl kagome metals in responsive magnetic spintronics.

Realization of charge-four Weyl point in fermionic systems

Realization of charge-four Weyl point in fermionic systems

Anomalous Landau quantization in intrinsic magnetic topological insulators

The intrinsic magnetic topological insulator, Mn(Bi1−xSbx)2Te4, has been identified as a Weyl semimetal with a single pair of Weyl nodes in its spin-aligned strong-field configuration. A direct consequence of the Weyl state is the layer dependent Chern number, C. Previous reports in MnBi2Te4 thin films have shown higher C states either by increasing the film thickness or controlling the chemical potential. A clear picture of the higher Chern states is still lacking as data interpretation is further complicated by the emergence of surface-band Landau levels under magnetic fields. Here, we report a tunable layer-dependent C = 1 state with Sb substitution by performing a detailed analysis of the quantization states in Mn(Bi1−xSbx)2Te4 dual-gated devices—consistent with calculations of the bulk Weyl point separation in the doped thin films. The observed Hall quantization plateaus for our thicker Mn(Bi1−xSbx)2Te4 films under strong magnetic fields can be interpreted by a theory of surface and bulk spin-polarised Landau level spectra in thin film magnetic topological insulators.

P6322-type SrNiIO6: An ideal half-metallic candidate with a fully spin-polarized Weyl complex

Researchers are interested in magnetic topological materials because they can integrate magnetic and topological properties. Using the first-principles calculations, we identify the P6322-type SrNiIO6 as a dynamically stable half-metallic candidate with a completely spin-polarized Weyl complex formed by two hourglass charge-3 and six charge-1 Weyl points. Furthermore, distinct surface arcs linked the projections of two spin-polarized charge-3 Weyl points and six spin-polarized charge-1 Weyl points, resulting in a fully spin-polarized sextuple-helicoid surface arc mode on the (001) surface of P6322-type SrNiIO6. P6322-type SrNiIO6 with fully spin-polarized charge-3 and charge-1 Weyl points and a fully spin-polarized sextuple-helicoid surface arc mode is, without a doubt, a promising candidate for applications in spintronic and topological physics.

Spectral localization for semimetals and Callias operators

A semiclassical argument is used to show that the low-lying spectrum of a self-adjoint operator, the so-called spectral localizer, determines the number of Dirac or Weyl points of an ideal semimetal. Apart from the ion-mobility spectrometer localization procedure, an explicit computation for the local toy models given by a Dirac or Weyl point is the key element of proof. The argument has numerous similarities to Witten’s reasoning leading to the strong Morse inequalities. The same techniques allow to prove a spectral localization for Callias operators associated with potentials with isolated gap-closing points.

Nodal-line symmetry breaking induced colossal anomalous Hall and Nernst effects in Cu2CoSn Heusler compound

The presence of topological band crossings near the Fermi energy is essential for the realization of large anomalous transport properties in the materials. The topological semimetals host such properties owing to their unique topological band structure, such as Weyl points or nodal lines (NLs), those are protected by certain symmetries of the crystal. When the NLs break out in the system, a large Berry curvature arises in the surrounding area of the gapped NL. In the present work, we studied anomalous transport properties of Cu2CoSn compound, which has a cubic Heusler crystal structure (space group: Fm3¯m). Cu2CoSn full Heusler compound possesses NLs at the Fermi level that is protected by mirror reflection symmetries of the lattice. Upon introducing the spin–orbit coupling in the Hamiltonian and by setting the magnetization axis along the [001] direction, we found that the NLs are gapped out and large Berry curvature arises in the system. The integral of Berry curvature gives the intrinsic anomalous Hall conductivity (AHC) about 1003 S/cm and the anomalous Nernst conductivity (ANC) about 3.98 A/m K at the Fermi level. These values of AHC and ANC are comparable to the largest reported values for the Co2MnGa Heusler compound. Therefore, Cu2CoSn becomes a newborn member of the family of full Heusler compounds, which possesses giant AHC and ANC that can be useful for the spintronics application.

Magnetic quadratic nodal line with spin–orbital coupling in CrSb

Quadratic nodal lines (QNLs) with quadratic band splitting in the Brillouin zone have different properties from conventional linear nodal lines. In this study, based on symmetry analysis and first-principles calculation, we prove that magnetic quadratic nodal line (MQNL) exists in antiferromagnetic configurations of one single realistic solid-state material CrSb with the P63′/m′m′c structure that breaks the time-reversal symmetry. In magnetic systems with the non-negligible spin–orbit coupling effect, we show that nodal lines with a quadratic leading order dispersion can be realized around Fermi level. Moreover, CrSb shows four long Fermi arcs near Fermi energy level resulting from six pairs of Weyl points with opposite chirality. Our results reveal a promising platform for exploring the topological states with intriguing effects. We hope that the proposed realistic material can be viewed as ideal candidate to realize the MQNL in solid-state materials.

Two-dimensional Dirac phonons without/with inversion symmetry

In a recent study, two-dimensional Dirac phonons that are protected by nonsymmorphic symmetries in spinless systems were systematically investigated. However, the focus of this study was on the classification of Dirac phonons. To address the gap in the research on the topological features of 2D Dirac phonons based on their effective models, we classified the 2D Dirac phonons into two classes: without or with inversion symmetry, thereby clarifying the minimal symmetry requirements for enforcing 2D Dirac points. Based on symmetry analysis, we discovered that screw symmetries, together with time-reversal symmetry, play an essential role in the existence of Dirac points. To validate this result, we constructed the k·p model to describe the Dirac phonons and discussed their topological features accordingly. We found that a 2D Dirac point could be considered as a composition of two 2D Weyl points with opposite chirality. Furthermore, we provided two concrete materials to demonstrate our findings. Overall, our work provides a more detailed study of 2D Dirac points in spinless systems and clarifies their topological features.

Giant spin-splitting and tunable spin-momentum locked transport in room temperature collinear antiferromagnetic semimetallic CrO monolayer

In this work, we present theoretical predictions of a two-dimensional collinear antiferromagnetic semimetal, CrO, which exhibits a giant spin-split band structure, spin-momentum locked transport properties, and a high Néel temperature. Specifically, CrO features two pairs of spin-polarized anisotropic Weyl points at the Fermi level. By manipulating the position of these Weyl points with strain, we demonstrate that four different antiferromagnetic spintronic states with zero net magnetic moments can be achieved, including semimetals with two spin-polarized transport channels, half-semimetals, semiconductors with two spin-polarized transport channels, and half-semiconductors. The strain-induced semiconducting state also preserves the ultra-high carrier mobility of Weyl points, and the bandgap can be easily tuned. These findings offer a good avenue in spintronics without net magnetic moment or strong spin–orbit coupling and could lead to the development of antiferromagnetic materials for spintronic applications.