type-II Weyl Semimetals Research Articles

Robust edge photogalvanic effect in thin-film WTe2

The photogalvanic effect (PGE) in Weyl semimetals, such as WTe2 and MoTe2, has been widely observed and is considered a promising phenomenon for advancing Weyl semimetal-based optoelectronic devices. However, as device dimensions continue to shrink, edge effects on photocurrent generation and modulation become increasingly significant and cannot be overlooked. Herein, we have discovered a locally enhanced edge linear photogalvanic effect at the edge of WTe2 thin-film devices using a home-built polarization-modulated scanning photocurrent system, which arises from symmetry breaking. Furthermore, the magnitude and direction of this edge photocurrent are modulated by the polarization direction of the incident light. This research provides valuable insights for the development of polarization-sensitive photodetectors based on layered type-II Weyl semimetals.

Revealing Fermi surface evolution and Berry curvature in an ideal type-II Weyl semimetal

In type-II Weyl semimetals (WSMs), the tilting of the Weyl cones leads to the coexistence of electron and hole pockets that touch at the Weyl nodes. These electrons and holes experience the Berry curvature generated by the Weyl nodes, leading to an anomalous Hall effect that is highly sensitive to the Fermi level position. Here we have identified field-induced ferromagnetic MnBi2-xSbxTe4 as an ideal type-II WSM with a single pair of Weyl nodes. By employing a combination of quantum oscillations and high-field Hall measurements, we have resolved the evolution of Fermi-surface sections as the Fermi level is tuned across the charge neutrality point, precisely matching the band structure of an ideal type-II WSM. Furthermore, the anomalous Hall conductivity exhibits a heartbeat-like behavior as the Fermi level is tuned across the Weyl nodes, a feature of type-II WSMs that was long predicted by theory. Our work uncovers a large free carrier contribution to the anomalous Hall effect resulting from the unique interplay between the Fermi surface and diverging Berry curvature in magnetic type-II WSMs.

Anisotropic positive linear and sub-linear magnetoresistivity in the cubic type-II Dirac metal Pd3In7

We report a transport study on Pd3In7 which displays multiple Dirac type-II nodes in its electronic dispersion. Pd3In7 is characterized by low residual resistivities and high mobilities, which are consistent with Dirac-like quasiparticles. For an applied magnetic field (μ0H) having a non-zero component along the electrical current, we find a large, positive, and linear in μ0H longitudinal magnetoresistivity (LMR). The sign of the LMR and its linear dependence deviate from the behavior reported for the chiral-anomaly-driven LMR in Weyl semimetals. Interestingly, such anomalous LMR is consistent with predictions for the role of the anomaly in type-II Weyl semimetals. In contrast, the transverse or conventional magnetoresistivity (CMR for electric fields E⊥μ0H) is large and positive, increasing by 103−104 % as a function of μ0H while following an anomalous, angle-dependent power law {rho }_{{{{rm{xx}}}}}propto {({mu }_{0}H)}^{n} with n(θ) ≤ 1. The order of magnitude of the CMR, and its anomalous power-law, is explained in terms of uncompensated electron and hole-like Fermi surfaces characterized by anisotropic carrier scattering likely due to the lack of Lorentz invariance.

Proximity-induced superconductivity in type-II Weyl semimetal NbIrTe4

Heterostructures between conventional superconductors and materials with different electronic ground states have emerged as a powerful method for exploring the exotic superconducting properties induced by the proximity effect. Here, we investigate Andreev transport through the interface between an s-wave superconductor Nb and a type-II Wely semimetal NbIrTe4. The differential conductance measurement reveals an anomalous zero-bias conductance peak and prominent subgap structures at low temperatures. Furthermore, we found that these subgap structures are not only related to the interface coupling strength but also influenced by the thickness of the NbIrTe4 flake. For thin devices (≤100 nm), the differential conductance spectra only exhibit a single-gap structure. While in thicker devices (∼150 nm), we observed the distinct double-gap structure, which is likely to originate from the proximity-induced superconductivity gap on the bulk and surface of the NbIrTe4 flakes. These results can provide a good reference for understanding the superconducting phase in type-II Weyl semimetals and take a step toward its future application in the field of superconducting electronics.

Faraday rotation enhancement and characteristic of the Weyl node separation and tilt degree by resonant tunneling

The 8 × 8 magneto-optical matrix has been derived to discuss the Faraday rotation (FR) effect, which is induced by the linear polarization wave passing through a sandwich structure composed of a dielectric layer and two identical Weyl semimetals (WSMs). The giant enhanced FR angle about 45° can be realized at the resonant tunneling wavelength of right hand circularly polarization (RCP) waves by enlarging the difference of the resonant tunneling wavelength of RCP and left hand circularly polarization waves suitably. It is shown that the resonant wavelengths depend on the Weyl node separation and tilt degree of Weyl cones in both type-I and type-II WSMs. More importantly, there exists a tunable one-to-one relationship between the Weyl node separation and the wavelength of the resonant FR angle, as well as the tilt degree and the wavelength of the resonant FR angle, which enables the characteristic of the Weyl node separation and tilt degree. Our research reveals an available method to determine the Weyl node separation and tilt degree of Weyl cones in both type-I and type-II WSMs.

A Centimeter-Scale Type-II Weyl Semimetal for Flexible and Fast Ultra-Broadband Photodetection from Ultraviolet to Sub-Millimeter Wave Regime.

Flexible photodetectors with ultra-broadband sensitivities, fast response, and high responsivity are crucial for wearable applications. Recently, van der Waals (vdW) Weyl semimetals have gained much attention due to their unique electronic band structure, making them an ideal material platform for developing broadband photodetectors from ultraviolet (UV) to the terahertz (THz) regime. However, large-area synthesis of vdW semimetals on a flexible substrate is still a challenge, limiting their application in flexible devices. In this study, centimeter-scale type-II vdW Weyl semimetal, Td -MoTe2 films, are grown on a flexible mica substrate by molecular beam epitaxy. A self-powered and flexible photodetector without an antenna demonstrated an outstanding ability to detect electromagnetic radiation from UV to sub-millimeter (SMM) wave at room temperature, with a fast response time of ≈20 µs, a responsivity of 0.53mA W-1 (at 2.52 THz), and a noise-equivalent power (NEP) of 2.65 nW Hz-0.5 (at 2.52 THz). The flexible photodetectors are also used to image shielded items with high resolution at 2.52 THz. These results can pave the way for developing flexible and wearable optoelectronic devices using direct-grown large-area vdW semimetals.

Visualization of bulk and edge photocurrent flow in anisotropic Weyl semimetals

Materials that rectify light into current in their bulk are desired for optoelectronic applications. In inversion-breaking Weyl semimetals, bulk photocurrents may arise due to nonlinear optical processes that are enhanced near the Weyl nodes. However, the photoresponse of these materials is commonly studied by scanning photocurrent microscopy (SPCM), which convolves the effects of photocurrent generation and collection. Here, we directly image the photocurrent flow inside the type-II Weyl semimetals WTe2 and TaIrTe4 using high-sensitivity quantum magnetometry with nitrogen-vacancy center spins. We elucidate an unknown mechanism for bulk photocurrent generation termed the anisotropic photothermoelectric effect (APTE), where unequal thermopowers along different crystal axes drive intricate circulations of photocurrent around the photoexcitation. Using simultaneous SPCM and magnetic imaging at the sample's interior and edges, we visualize how the APTE stimulates the long-range photocurrent collected in our Weyl semimetal devices through the Shockley-Ramo theorem. Our results highlight an overlooked, but widely relevant source of current flow and inspire novel photodetectors using homogeneous materials with anisotropy.

In-plane magnetotransport phenomena in tilted Weyl semimetals

The nontrivial Berry curvature and chiral anomaly result in plenty of interesting magnetotransport and magneto-thermoelectric transport phenomena in Weyl semimetals, two of which are the planar Hall effect and planar Nernst effect. Based on the semi-classical Boltzmann theory, we theoretically study the in-plane magnetotransport coefficients (including electric conductivity, thermoelectric conductivity and Nernst thermopower) for both type-I and type-II Weyl semimetals using a linearized low-energy Hamiltonian. We find that for tilt-coplanar setup where the electric field (or temperature gradient) is applied along the tilted direction of the Weyl nodes, the planar Hall conductivity (or planar Nernst thermopower) shows a magnetic field linear dependence. And these linear responses do no obey the reported dependence on the angle θ between the magnetic and electric field for planar Hall effect. For tilt-perpendicular setup where the applied field (E or ) and magnetic field are perpendicular to the tilted direction, the planar Hall conductivity (or planar Nernst thermopower) mainly follows a magnetic field quadratic dependence, and it satisfies the characteristic. There are also anomalous Hall effect and anomalous Nernst effect in the plane perpendicular to the tilted direction of the two oppositely tilted Weyl nodes. These findings can be verified experimentally by changing the direction and magnitude of the in-plane magnetic field.

Colossal Room-Temperature Terahertz Topological Response in Type-II Weyl Semimetal NbIrTe4.

The electromagnetic spectrum between microwave and infrared light is termed the "terahertz (THz) gap," of which there is an urgent lack of feasible and efficient room-temperature (RT) THz detectors. Type-II Weyl semimetals (WSMs) have been predicted to host significant RT topologicalphotoresponses in low-frequency regions, especially in the THz gap, well addressing the shortcomings of THz detectors. However, such devices havenotbeenexperimentally realized yet. Herein, a type-II WSM (NbIrTe4 ) is selected to fabricate THz detector, which exhibits a photoresponsivity of 5.7×104 VW-1 and a one-year air stability at RT. Such excellent THz-detection performance can be attributed to the topological effect of type-II WSM in which the effective mass of photogenerated electrons can be reduced by the large tilting angle of Weyl nodes to further improve mobility and photoresponsivity. Impressively, this device shows a giant intrinsic anisotropic conductance (σmax /σmin =339) and THz response (Iph-max /Iph-min = 40.9), both of which are record values known. The findings open a new avenue for the realization of uncooled and highly sensitive THz detectors by exploring type-II WSM-based devices.

A Weyl semimetal WTe2/GaAs 2D/3D Schottky diode with high rectification ratio and unique photocurrent behavior

Since the discovery of Dirac semimetal graphene, two-dimensional (2D) Weyl semimetals (WSMs) have been widely used in low-energy photon detection, polarization imaging, and other systems due to their rich physical characteristics, such as unique nonlinear optical structure, topological nontrivial electronic structure, thickness-tunable bandgap, high electric conductivity, and so on. However, it is difficult to detect the photocurrent signal at room temperature because of its large intrinsic background current. Fortunately, the fabrication of a van der Waals (vdW) heterojunction based on WSM can effectively suppress the background current, greatly extend the detection range, improve the light absorption efficiency, and increase the response speed. Herein, the 2D type-II WSM 1T′-WTe2/bulk GaAs vdW vertical Schottky diode is investigated. Benefiting from the lateral built-in electric field of 260 meV and zero-bandgap structure of 52 nm 1T′-WTe2, it delivers a rectifying ratio over 103 and can respond to the wavelength range of 400–1100 nm. Particularly, when the light power density is 0.02 mW/cm2, the maximum photoresponsivity (R) and specific detectivity (D*) under 808 nm are 298 mA/W and 1.70 × 1012 Jones, respectively. Meanwhile, the Ilight/Idark ratio and response time are 103 and 520/540 μs, respectively. Moreover, an abnormal negative response behavior can be observed with thin WTe2 (11 nm) under 1064 nm illumination because of the open surface bandgap. It is suggested that such 2D WTe2/GaAs mixed-dimensional vdW structure can be extended to other WSM/3D semiconductor junctions and used in fast response and wide broadband spectrum photodetectors' arrays.

Origin of the type-II Weyl state in topological antiferromagnetic YbMnBi2

Recently, the topological nature of an antiferromagnet YbMnBi2 has been controversial. YbMnBi2 is regarded as a candidate of Type-II Weyl semimetals with magnetic moments of Mn atoms canting about 10{\deg} in some studies but as a Dirac semimetal without canting in others. By means of systematical density functional theory calculations, we show the perfect YbMnBi2 bulk has a collinear antiferromagnetic ordering and, naturally, it is a Dirac semimetal. Considering the vital role of magnetic moment canting in generating the Type-II Weyl state, we artificially cant the magnetic moments of Mn atoms and find that YbMnBi2 enters into the Type-II Weyl state from about 2{\deg}. Inspired by this and taking into account the possible defects in experiments, we suggest that Bi vacancies in Mn-Bi-Mn bonds, which produce sizable Dzyaloshinskii-Moriya interactions and thereby cant the magnetic moments of Mn atoms, can tune the topological nature of YbMnBi2 from Dirac semimetals to Type-II Weyl semimetals. Our work unveils the possible underlying mechanism for the Type-II Weyl state in YbMnBi2, providing insights into the Weyl state in other magnetic topological materials.

Type-II Weyl Excitation in Vortex Arrays

Weyl-like magnon excitations in ordered magnets have attracted significant recent attention. Despite the tantalizing physics and application prospects, the experimental observation of Weyl magnons is still challenging owing to their extraordinarily high frequency that is not accessible to the microstrip antenna technique. Here we predict gigahertz Weyl excitations in the collective dynamics of dipolar-coupled magnetic vortices arranged in a three-dimensional stacked honeycomb lattice. It is found that inversion symmetry breaking leads to the emergence of the type-II Weyl semimetal (WSM) state with tilted dispersion. We derive the full phase diagram of the vortex arrays that support WSMs with both single and double pairs of Weyl nodes, and the topological insulator phase. We observe robust arc surface states in a dual-segment fashion due to the tilted nature of type-II WSMs. Our findings uncover the low-frequency WSM phase in magnetic-texture-based crystals that are indispensable for future Weyltronic applications.

Hydrostatic pressure-induced magnetic and topological phase transitions in the MnBi2Te4 family of materials

The recent discovery of intrinsic magnetic topological insulator (TI) $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ has inspired enormous research interest to explore emergent physics created by the interplay of magnetism and topology. Here we systematically investigated the influence of hydrostatic pressure on structural, magnetic, and topological electronic properties of the $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ family of materials by first-principles calculations. Our results indicate that properties of these layered materials can be effectively tuned by pressure, leading to various kinds of magnetic and topological phase transitions. These include magnetic transitions from $A$-type antiferromagnetism to novel magnetic states, such as frustrated magnetism and intralayer ferromagnetism in conditions of antiferromagnetic intralayer coupling. Moreover, rich topological phase transitions can be driven by pressure in these materials, including trivial insulator to antiferromagnetic TI, type-I or type-II Weyl semimetals, or high-order TI phases. The findings call for in-depth experimental investigations of magnetic and topological physics in these intriguing material systems under high pressure.

Goos–Hänchen and Imbert–Fedorov shifts in tiltedWeyl semimetals

We establish the beam models of Goos–Hänchen (GH) and Imbert–Fedorov (IF) effects in tilted Weyl semimetals (WSMs), and systematically study the influences of Weyl cone tilting and chemical potential on the GH and IF shifts at a certain photon energy 1.96 eV. It is found that the GH and IF shifts in tilted type-I and type-II WSMs are both almost symmetric about the Weyl cone tilting. Meanwhile, the GH and IF shifts in type-I WSMs almost do not change with the tilt degree of Weyl cones, while those in type-II WSMs are extremely dependent on tilt degree. These trends are mainly due to the nearly symmetric distribution of WSMs conductivities, where the conductivities keep stable in type-I WSMs and gradually decrease with tilt degree in type-II WSMs. By adjusting the chemical potential, the boundary between type-I and type-II WSMs widens, and the dependence of the beam shifts on the tilt degree can be manipulated. Furthermore, by extending the relevant discussions to a wider frequency band, the peak fluctuation of GH shifts and the decrease of IF shifts occur gradually as the frequency increases, and the performance of beam shifts at photon energy 1.96 eV is equally suitable for other photon frequencies. The above findings provide a new reference for revisiting the beam shifts in tilted WSMs and determining the types of WSMs.

Investigation on crystal structure, electrical and magnetic properties of CeAl(Si1-xGex)

The discovery of Weyl and Dirac fermions has greatly encouraged the study of topological aspects in condensed matter physics, especially the discovery of ferromagnetic type-II Weyl semimetals such as CeAlX (X ​= ​Si, Ge). However, the evolution process of the physical characteristics of CeAlX during the Ge/Si substitution has not been studied in detail, and the relevant researches were mostly based on their polycrystalline samples. Herein, the millimeter level single crystals of CeAl(Si1-xGex) were prepared and studied systemically. It can be concluded that the higher Ge content leads to the bigger lattice constants and electrical resistivity, but the lower magnetic transition temperature (TC) and magnetoresistance (MR). The electrical conductivity at room temperature and the MR at 2 ​K of CeAl(Si0.9Ge0.1) can even reach up to 6.35 and 6.55 times bigger than that of CeAl(Si0.1Ge0.9), respectively. In addition, CeAl(Si1-xGex) would change from n-type to p-type after “x” exceeds 0.5. The continuously tunable isoelectronic Ge/Si substitution makes CeAl(Si1-xGex) an excellent platform for exploring the exotic electromagnetic responses of topological materials.

Anisotropic Shubnikov-de Haas effect in topological Weyl semimetal MoTe2

Newly emergent type-II Weyl semimetals with topological surface states so-called Fermi arcs have attracted much attention for their novel physical properties and potential application in quantum devices. Here, we investigate the in-plane anisotropic structure and inversion symmetry breaking by angle-resolved polarized Raman and second harmonic generation and observe the anisotropic Shubnikov-de Haas effect in Weyl Semimetal MoTe2, which is only present in the b-axis (armchair chain) direction. First-principles calculation depicts the type-II Weyl points and clear topological Fermi arcs. A nontrivial π Berry's phase from Landau quantization and an extra-quantum oscillation frequency arising by Weyl orbit are obtained, which provide evidence for the existence of an anisotropic type-II Weyl state in MoTe2. This work reveals the nontrivial topological surface state of Weyl semimetal MoTe2 in both theory and experiment, providing a promising platform for unique physical properties and applications in quantum information processing.

Frequency manipulation of topological surface states by Weyl phase transitions.

By creating a synthetic frequency dimension with dynamic modulation in a 2D honeycomb waveguide array, we construct both Type-I and Type-II Weyl semimetals (WSMs) and utilize the WSM phase transition to control the frequency evolutions of topological surface states. We show that Type-I WSMs and Type-II WSMs manifest opposite and same band slopes for the two surface states, which give rise to the bidirectional and unidirectional frequency shifts, respectively. Moreover, by cascading Type-I Weyl lattices and Type-II Weyl lattices together, we also achieve the time-reversed evolution of frequency, such as frequency negative refraction, bandwidth expansion-compression, and perfect imaging. The Letter may find applications in robust signal transmission and processing with synthesized topological states.

General formula of chiral anomaly for type-I and type-II Weyl semimetals

Weyl semimetals (WSMs) are classified into type-I and type-II, depending on the magnitudes of the inclination of Weyl cones. It is known that these WSMs show negative longitudinal magnetoresistance originating from chiral anomaly. Moreover, we have recently revealed that type-II WSMs show positive longitudinal magnetoresistance originating from chiral anomaly. The negative longitudinal magnetoresistance in type-I WSMs can be explained utilizing the conventional formula of the chiral anomaly, which does not have the term related to the inclination of the Weyl cones. However, we cannot explain both the positive and the negative longitudinal magnetoresistance in type-II WSMs utilizing it. Therefore, in this paper, we derive the general formula including the term related to the inclination of the Weyl cones in order to explain straightforwardly the positive and the negative longitudinal magnetoresistance in type-II WSMs. Also, we consider both cases where a pair of the Weyl cones are tilted in the same direction (positive tilt chirality) and toward (or against) each other (negative tilt chirality) in order to investigate the influence of the direction to which the Weyl cones are tilted. As a result, we find that in the negative tilt chirality, the general formula is strongly affected by the inclination. These results suggest that we can estimate whether the WSMs show the positive or the negative longitudinal magnetoresistance using the general formula from the information of their tilt chirality and the magnitudes of the inclination of the Weyl cones.

Spin susceptibilities in magnetic type-I and type-II Weyl semimetals

We investigate interacting spin susceptibilities in lattice models for $\mathcal{T}$-reversal symmetry-broken Weyl semimetals. We employ a random phase approximation (RPA) method for the spin-SU(2)-symmetry-broken case that includes mixtures of ladder and bubble diagrams, beyond a SU(2)-symmetric case. Within this approach, the relations between the tendency towards magnetic order and the band structure tilt parameter $\gamma$ under different temperatures are explored. The critical interaction strength $U_c$ for magnetic ordering decreases as the tilt term changes from type-I Weyl semimetals to type-II. The lower temperature, the sharper is the drop in $U_c$ at the critical point between them. The variation of $U_c$ with a slight doping near half-filling is also studied. It is generally found that these Weyl systems show a strongly anisotropic spin response with an enhanced doubly degenerate transverse susceptibility perpendicular to tilt direction, inherited from $\mathcal{C}_{4z}$ rational symmetry of bare Hamiltonian, but with the longitudinal response suppressed with respect to that. For small tilts $\gamma$ and strong enough interaction, we find two degenerate ordering patterns with spin order orthogonal to the tilt direction but much shorter spin correlation length parallel to the spin direction. With increasing the tilt, the system develops instabilities with respect to in-plane magnetic orders with wavevector $(0,\pi, q_z)$ and $(\pi,0, q_z)$, with $q_z$ increasing from 0 to $\pi$ before the transition to a type-II Weyl semimetal is reached. These results indicate a greater richness of magnetic phases in correlated Weyl semimetals that also pose challenges for precise theoretical descriptions.

Dimensionality-dependent type-II Weyl semimetal state in Mo0.25W0.75Te2

Weyl nodes and Fermi arcs in type-II Weyl semimetals (WSMs) have led to lots of exotic transport phenomena. Recently, Mo$_{0.25}$W$_{0.75}$Te$_{2}$ has been established as a type-II WSM with Weyl points located near Fermi level, which offers an opportunity to study its intriguing band structure by electrical transport measurements. Here, by selecting a special sample with the thickness gradient across two- (2D) and three-dimensional (3D) regime, we show strong evidences that Mo$_{0.25}$W$_{0.75}$Te$_{2}$ is a type-II Weyl semimetal by observing the following two dimensionality-dependent transport features: 1) A chiral-anomaly-induced anisotropic magneto-conductivity enhancement, proportional to the square of in-plane magnetic field (B$_{in}$$^{2}$); 2) An additional quantum oscillation with thickness-dependent phase shift. Our theoretical calculations show that the observed quantum oscillation originates from a Weyl-orbit-like scenario due to the unique band structure of Mo$_{0.25}$W$_{0.75}$Te$_{2}$. The in situ dimensionality-tuned transport experiment offers a new strategy to search for type-II WSMs.