type-II Weyl Research Articles

Two types of three-dimensional quantum Hall effects in multilayer WTe2

Interplay between topological surface states and bulk states gives rise to diverse exotic transport phenomena in topological materials. The recently proposed Weyl orbit in topological semimetals in the presence of magnetic field is a remarkable example. This novel closed magnetic orbit consists of Fermi arcs on two spatially separated sample surfaces which are connected by the bulk chiral zero mode, which can contribute to transport. Here we report Shubnikov--de Haas oscillation and its evolution into quantum Hall effect (QHE) in multilayered type-II Weyl semimetal $\mathrm{W}{\mathrm{Te}}_{2}$. We observe both the three-dimensional (3D) QHE from bulk states by parallel stacking of confined two-dimensional layers in the low magnetic field region and the 3D QHE in the quantized surface transport due to Weyl orbits in the high magnetic field region. Our study of the two types of QHEs controlled by magnetic field and our demonstration of the crossover between quantized bulk and surface transport provide an essential platform for the future quantized transport studies in topological semimetals.

Large anomalous Hall effect and intrinsic Berry curvature in magnetic Weyl semimetal NdAlGe

Weyl semimetals driven by both time-reversal (TRS) and inversion symmetries (IS) are rare and be a good platform to investigate the relationship between chiral current and magnetic order. NdAlGe compound, grown in a single crystalline form by the flux method, has a noncentrosymmetric I41md crystal structure, which breaks inversion symmetry. The magnetic susceptibility χ(T) shows anisotropic behavior; ferromagnetic with divergence of field cooling (FC) and zero field cooling (ZFC) in H∥c, and antiferromagnetic transition for magnetic field H⊥c. The band structure calculation has revealed that NdAlGe is the type-II Weyl semimetal with four types of Weyl nodes in the ab-plane with a probable Fermi surface nesting vector. The ferromagnetic spin alignment gives a significant anomalous Hall coefficient Rs and large anomalous Hall conductivity σxyA, for H∥c. The giant anomalous Hall conductivity σxyA, constant SH=σxyA/M (H = 50 kOe) value, and their Karplus and Luttinger (KL) analysis support that the giant AHE is associated with the intrinsic Berry curvature in NdAlGe compound. The intrinsic Berry curvature is also confirmed by the planar Hall effect over a wide temperature range, implying that the Weyl semimetallic property is not relevant with the magnetic order.

Ab initio study of the nonlinear optical properties and dc photocurrent of the Weyl semimetal TaIrTe4

The type-II Weyl semimetal TaIrTe${}_{4}$ exhibits one of the largest nonlinear photoresponses measured to date [Ma $e\phantom{\rule{0}{0ex}}t$ $a\phantom{\rule{0}{0ex}}l$., Nature Materials 18, 476 (2019)]. The present work provides theoretical calculations on several competing candidate effects that can account for it. The third-order contribution known as the jerk current matches the measured magnitude of the photocurrent as well as its angular distribution. The origin of the large photoresponse is traced back to a constructive interference between the effective mass and the dipole matrix element of the Weyl bands crossing the Fermi level.

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.

Tetragonal Mexican-hat dispersion and switchable half-metal state with multiple anisotropic Weyl fermions in penta-graphene

Due to the paired valence electrons configuration, all known two-dimensional (2D) carbon allotropes are intrinsically nonmagnetic. Based on the reported 2D carbon structure database and first-principles calculations, herein we demonstrate that inherent ferromagnetism can be obtained in the prominent allotrope, penta-graphene, which has a unique Mexican-hat valence band edge, giving rise to van Hove singularities and electronic instability. Induced by modest hole-doping that is achievable in electrolyte gate, the semiconducting penta-graphene can be transformed into different ferromagnetic half-metals with room-temperature stability and switchable spin directions. In particular, multiple anisotropic Weyl states, including type-I and type-II Weyl cones and hybrid quasi Weyl nodal loop, can be found in a sizable energy window of spin-down half-metal under proper strains. These findings not only identify a promising carbon allotrope to obtain the inherent magnetism for carbon-based spintronic devices, but highlight the possibility to realize different Weyl states by combining the electronic and mechanical means as well.

Drastic enhancement of the superconducting temperature in type-II Weyl semimetal candidate MoTe2 via biaxial strain

A type-II Weyl semimetal candidate MoTe2, which superconducts at Tc ∼0.1 K, is one of the promising candidates for realizing topological superconductivity. However, the exceedingly low Tc is associated with a small upper critical field (Hc2), implying a fragile superconducting phase that only exists on a small region of the H–T phase diagram. Here, we describe a simple and versatile approach based on the differential thermal expansion between dissimilar materials to subject a thin single crystalline MoTe2 to biaxial strain. With this approach, we successfully enhance the Tc of MoTe2 by fivefold and consequently expand the superconducting region on the H–T phase diagram significantly. To demonstrate the relative ease of studying the superconductivity in the biaxially strained MoTe2, we further present the magnetotransport data, enabling the study of the temperature-dependent Hc2 and the anisotropy of the superconducting state, which would otherwise be difficult to obtain in a free-standing MoTe2. Our work shows that biaxial strain is an effective knob to tune the electronic properties of MoTe2. Due to the simplicity of our methodology to apply biaxial strain, we anticipate its direct applicability to a wider class of quantum materials.

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.

Phase-controlled van der Waals growth of wafer-scale 2D MoTe2 layers for integrated high-sensitivity broadband infrared photodetection

Being capable of sensing broadband infrared (IR) light is vitally important for wide-ranging applications from fundamental science to industrial purposes. Two-dimensional (2D) topological semimetals are being extensively explored for broadband IR detection due to their gapless electronic structure and the linear energy dispersion relation. However, the low charge separation efficiency, high noise level, and on-chip integration difficulty of these semimetals significantly hinder their further technological applications. Here, we demonstrate a facile thermal-assisted tellurization route for the van der Waals (vdW) growth of wafer-scale phase-controlled 2D MoTe2 layers. Importantly, the type-II Weyl semimetal 1T′-MoTe2 features a unique orthorhombic lattice structure with a broken inversion symmetry, which ensures efficient carrier transportation and thus reduces the carrier recombination. This characteristic is a key merit for the well-designed 1T′-MoTe2/Si vertical Schottky junction photodetector to achieve excellent performance with an ultrabroadband detection range of up to 10.6 µm and a large room temperature specific detectivity of over 108 Jones in the mid-infrared (MIR) range. Moreover, the large-area synthesis of 2D MoTe2 layers enables the demonstration of high-resolution uncooled MIR imaging capability by using an integrated device array. This work provides a new approach to assembling uncooled IR photodetectors based on 2D materials.

Evolution of extremely large magnetoresistance in a Weyl semimetal, WTe2 with Ni-doping

${\mathrm{WTe}}_{2}$, a type-II Weyl semimetal, exhibits extremely large magnetoresistance (XMR) that is attributed to perfect electron-hole compensation. Here, we studied the evolution of the electronic properties of ${\mathrm{WTe}}_{2}$ with Ni substitution at W sites. Transport measurements exhibit a metal-to-insulator transition at low temperatures with the application of magnetic field; the field-induced effect is significantly reduced in the doped sample. The XMR of about ${10}^{6}$% at 2 K in ${\mathrm{WTe}}_{2}$ is reduced to ${10}^{4}$% in the 10% Ni-doped sample. The magnetoresistance shows an ${H}^{2}$ dependence and follows the temperature dependence of classical carrier mobility. We observe a deviation from Kohler's rule in both cases, indicating the presence of multiple types of charge carriers. Quantum oscillation data exhibit a signature of four Fermi pockets (two electron and two hole pockets) in both cases, and the nontrivial nature of the electron and hole bands. Interestingly, the electron-hole compensation is nearly perfect even in the doped compound, although the size of the Fermi pockets and the charge-carrier interaction parameters are slightly changed with doping. These results reveal intriguing insight into the XMR behavior of this class of materials and the possibilities of tuning the properties of charge carriers within the XMR regime.

Topologically protected dynamics in three-dimensional nonlinear antisymmetric Lotka-Volterra systems

Studies of topological bands and their associated low-dimensional boundary modes have largely focused on linear systems. This work reports robust dynamical features of three-dimensional (3D) nonlinear systems in connection with intriguing topological bands in 3D. Specifically, for a 3D setting of coupled rock-paper-scissors cycles governed by the antisymmetric Lotka-Volterra equation (ALVE) that is inherently nonlinear, we unveil distinct characteristics and robustness of surface-polarized masses and analyze them in connection with the dynamics and topological bands of the linearized Lotka-Volterra equation. Our results show that insights learned from Weyl semimetal phases with type-I and type-II Weyl singularities based on a linearized version of the ALVE are still remarkably useful, even though the system dynamics is far beyond the linear regime. This work indicates the relevance and importance of the concept of topological boundary modes in analyzing high-dimensional nonlinear systems and hopes to stimulate further topological studies where various topological gapless phases of matter may emerge in higher-dimensional nonlinear systems.

Observation of a single pair of type-III Weyl points in sonic crystals

In electronics systems, the Weyl points can be classified into three types based on the geometry of the Fermi surface, and each type exhibits various unique and intriguing phenomena. While the type-I and type-II Weyl points have been achieved in both spinful and spinless systems, the realization of type-III Weyl points remains challenging, and has not been reported in artificial periodic systems. Here, we for the first time report the experimental observation of the type-III Weyl points in a sonic crystal. Remarkably, a single pair of type-III Weyl points are observed as the only band crossings in a frequency range, experimentally disproving a common belief in the field, namely, the minimal number of Weyl points in nonmagnetic systems is four. The consistency between experimental results and theoretical predictions confirms the existence of type-III Weyl points, noncontractible Fermi arc surface states, and chiral edge states. Our work not only fill the gap of the type-III Weyl point in sonic crystal but also stimulate related researches in other systems, such as photonic, mechanical and cold atom systems.

Understanding bulk photovoltaic effect in type-II Weyl semimetal Td-WTe2 using polarization dependent photocurrent measurement

Topological effects in a Weyl semimetal are explored in developing self-powered photodetectors at room temperature. The observed photocurrent is attributed to a combined effect of photothermoelectric effect and bulk photovoltaic phenomenon and is found to be a non-linear optical effect that converts light into electrical current. The self-powered photoresponse at 640 nm excitation wavelength reveals the presence of a diverging Berry curvature of tungsten ditelluride (Td-WTe2) at room temperature. The different perspective of polarization dependent photocurrent spectroscopy is used to separate the photothermal current from the shift current and the circular photo galvanic response from the linear photo galvanic response.

Anomalous symmetry breaking in the Weyl semimetal CeAlGe

CeAlGe, a proposed type-II Weyl semimetal, orders antiferromagnetically below 5 K. At 2 K, spin-flop and a spin-flip transitions to less than 1 $\mu_B$/Ce are observed in the $M(H)$ data below 30 kOe, ($\bf{H}\|\bf{a}$ and $\bf{b}$, and 4.3 kOe, $\bf{H}\|\langle110\rangle$, respectively, indicating a four-fold symmetry of the $M(H)$ data along the principal directions in the tetragonal $\it{ab}$ plane with $\langle110\rangle$ set of easy directions. However, anomalously robust and complex twofold symmetry is observed in the angular dependence of resistivity and magnetic torque data in the magnetically ordered state once the field is swept in the $\it{ab}$ plane. This twofold symmetry is independent of temperature and field hystereses and suggests a magnetic phase transition that separates two different magnetic structures in the $\it{ab}$ plane. The boundary of this magnetic phase transition and possibly the type of low-field magnetic structure can be tuned by an Al deficiency.

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.

Photonic Weyl semimetals in pseudochiral metamaterials

We investigate the photonic topological phases in pseudochiral metamaterials characterized by the magnetoelectric tensors with symmetric off-diagonal chirality components. The underlying medium is considered a photonic analogue of the type-II Weyl semimetal featured with two pairs of tilted Weyl cones in the frequency-wave vector space. As the ’spin’-degenerate condition is satisfied, the photonic system consists of two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in terms of the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between vacuum and the pseudochiral metamaterial exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, the surface modes are tangent to both the vacuum light cone and the Weyl cones, which form two pairs of crossing surface sheets that are symmetric about the transverse axes. At the Weyl frequency, the surface modes that connect the Weyl points form four Fermi arc-like states as line segments. Topological features of the pseudochiral metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.

Lifshitz transitions and hybrid Weyl points in RbAg5Se3

We explore the topological phase transitions of RbAg5Se3 using first-principles calculations in combination with the maximally localized Wannier function method. Our computations reveal that the type-II Dirac cone in RbAg5Se3 protected by the inversion and time-inversion (PT) symmetry in addition to the C4z rotation symmetry can be regulated to type-III and type-I Dirac points by applying strain along the [001] direction. More interestingly, when the inversion symmetry is lifted by intercalating a Pt atom into the unit cell, sixteen hybrid Weyl points emerge accompanied by the Fermi arcs connecting the adjacent Brillouin zones and surface states on the (010) surface. The type-II Weyl point has the chirality of 1, while the type-I Weyl point has the chirality of −1. Our work suggests that RbAg5Se3 serves as a promising platform for study of topological phases transitions with curious transport phenomena.

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.

High-order harmonic generations in tilted Weyl semimetals

We investigate high-order harmonic generations (HHGs) under comparison of Weyl cones in two types. Due to the hyperboloidal electron pocket structure, strong noncentrosymmetrical generations in high orders are observed around a single type-II Weyl point, especially at zero frequency. Such a remarkable DC signal is proved to have attributions from the intraband transition after spectral decomposition. Under weak pulse electric field, the linear optical response of a non-tilted Weyl cone is consistent with the Kubo theory. With extensive numerical simulations, we conclude that the non-zero chemical potential can enhance the even-order generations, from the slightly tilted system to the over-tilted systems. In consideration of dynamical symmetries, type-I and type-II Weyl cones also show different selective responses under the circularly polarized light. Finally, using a more realistic model containing two pairs of Weyl points, we demonstrate that paired Weyl points with opposite chirality can suppress the overall even-order generations.

Dissipation and geometry in nonlinear quantum transports of multiband electronic systems

Nonlinear responses in condensed matters attract recent intensive interest because they provide rich information about the materials and hold the possibility of being applied in diodes or high-frequency optical devices. Nonlinear responses are often closely related to the multiband nature of the system which can be taken into account by the geometric quantities such as the Berry curvature as shown in the nonlinear Hall effect. Theoretically, the semi-classical Boltzmann treatment or the reduced density matrix method have been often employed, in which the effect of dissipation is included through the relaxation time approximation. In the diagrammatic method, the relaxation is treated through the imaginary part of the self-energy of the Green function and the consequent broadening of the spectral function for the integration over the real frequency. Therefore, the poles of the Green function do not play explicit pole when there is finite dissipation. In this paper, in stark contrast to this conventional picture, we show that the poles of the Green function determine mostly the nonlinear response functions with dissipation, which leads to the terms with the Fermi distribution function of complex argument and results in the dissipation-induced geometric term. We elucidate the geometric origin of the nonreciprocal conductivity, which is related to the Berry curvature generalized to the higher derivative. Finally, we derive the analytical results on the geometric terms of the nonlinear conductivities in the type-I and type-II Weyl Hamiltonian to demonstrate their crucial roles.

Detection of Weyl fermions and the metal to Weyl-semimetal phase transition in WTe2 via broadband high resolution NMR

Weyl fermions (WFs) in the type-II Weyl semimetal (WSM) ${\mathrm{WTe}}_{2}$ are difficult to resolve experimentally because the Weyl bands disperse in an extremely narrow region of the ($E\text{\ensuremath{-}}k$) space. Here, by using DFT-assisted high-resolution $^{125}\mathrm{Te}$ solid-state nuclear magnetic resonance (ssNMR) in the temperature range 50--700 K, we succeeded in detecting low energy WF excitations and monitoring their evolution with temperature. Remarkably, WFs are observed to emerge at $T\ensuremath{\sim}120$ K, while at lower temperatures ${\mathrm{WTe}}_{2}$ behaves as a trivial metal. This intriguing phenomenon is induced by the rapid raise of the Fermi level upon heating, which crosses the Weyl bands only for $T>120$ K. The abrupt change of the NMR parameters at this temperature is signature of a topological Lifshitz transition instead of a cursive energy-bands crossing.