type-II Weyl Semimetals Research Articles

Tilting dependence and anisotropy of anomaly-related magnetoconductance in type-II Weyl semimetals

We theoretically study chiral magnetic effect in type-II Weyl semimetals based on a concise formalism for the magnetoconductance in the semiclassical limit. Using the formula, we find that the anomaly-related current is generally dominated by the contribution from the Weyl nodes when the Fermi level is sufficiently close to the nodes. This is related to the fact that the current is proportional to the square of the Berry curvature, which enhances the contribution from the electrons around the Weyl nodes. The increase and the anisotropy of magnetoconductance induced by the tilting is also explained in a comprehensive way.

Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe_{2} (X=Mo,W).

In recent years, transition metal dichalcogenides (TMDs) have garnered great interest as topological materials. In particular, monolayers of centrosymmetric β-phase TMDs have been identified as 2D topological insulators (TIs), and bulk crystals of noncentrosymmetric γ-phase MoTe_{2} and WTe_{2} have been identified as type-II Weyl semimetals. However, angle-resolved photoemission spectroscopy and STM probes of these semimetals have revealed huge, arclike surface states that overwhelm, and are sometimes mistaken for, the much smaller topological surface Fermi arcs of bulk type-II Weyl points. In this Letter, we calculate the bulk and surface electronic structure of both β- and γ-MoTe_{2}. We find that β-MoTe_{2} is, in fact, a Z_{4}-nontrivial higher-order TI (HOTI) driven by double band inversion and exhibits the same surface features as γ-MoTe_{2} and γ-WTe_{2}. We discover that these surface states are not topologically trivial, as previously characterized by the research that differentiated them from the Weyl Fermi arcs but, rather, are the characteristic split and gapped fourfold Dirac surface states of a HOTI. In β-MoTe_{2}, this indicates that it would exhibit helical pairs of hinge states if it were bulk insulating, and in γ-MoTe_{2} and γ-WTe_{2}, these surface states represent vestiges of HOTI phases without inversion symmetry that are nearby in parameter space. Using nested Wilson loops and first-principles calculations, we explicitly demonstrate that, when the Weyl points in γ-MoTe_{2} are annihilated, which may be accomplished by symmetry-preserving strain or lattice distortion, γ-MoTe_{2} becomes a nonsymmetry-indicated, noncentrosymmetric HOTI. We also show that, when the effects of spin-orbit coupling are neglected, β-MoTe_{2} is a nodal-line semimetal with Z_{2}-nontrivial monopole nodal lines (MNLSM). This finding confirms that MNLSMs driven by double band inversion are the weak-spin-orbit coupling limit of HOTIs, implying that MNLSMs are higher-order topological semimetals with flat-band-like hinge states, which we find to originate from the corner modes of 2D "fragile" TIs.

Strong and Tunable Electrical Anisotropy in Type-II Weyl Semimetal Candidate WP2 with Broken Inversion Symmetry.

A transition metal diphosphide, WP2 , is a candidate for type-II Weyl semimetals (WSMs) in which spatial inversion symmetry is broken and Lorentz invariance is violated. As one of the prerequisites for the presence of the WSM state in WP2 , spatial inversion symmetry breaking in this compound has rarely been investigated. Furthermore, the anisotropy of the WP2 electrical properties and whether its electrical anisotropy can be tuned remain elusive. Angle-resolved polarized Raman spectroscopy, electrical transport, optical spectroscopy, and first-principle studies of WP2 are reported. The energies of the observed Raman-active phonons and the angle dependences of the detected phonon intensities are consistent with results obtained by first-principle calculations and analysis of the proposed crystal symmetry without spatial inversion, showing that spatial inversion symmetry is broken in WP2 . Moreover, the measured ratio (Rc /Ra ) between the crystalline c-axis and a-axis electrical resistivities exhibits a weak dependence on temperature (T) in the temperature range from 100 to 250 K, but increases abruptly at T ≤ 100 K, and then reaches the value of ≈8.0 at T = 10 K, which is by far the strongest in-plane electrical resistivity anisotropy among the reported type-II WSM candidates with comparable carrier concentrations. Optical spectroscopy study, together with the first-principle calculations on the electronic band structure, reveals that the abrupt enhancement of the electrical resistivity anisotropy at T ≤ 100 K mainly arises from a sharp increase in the scattering rate anisotropy at low temperatures. More interestingly, the Rc /Ra of WP2 at T = 10 K can be tuned from 8.0 to 10.6 as the magnetic field increases from 0 to 9 T. The so-far-strongest and magnetic-field-tunable electrical resistivity anisotropy found in WP2 can serve as a degree of freedom for tuning the electrical properties of type-II WSMs, which paves the way for the development of novel electronic applications based on type-II WSMs.

Giant optical activity and Kerr effect in type-I and type-II Weyl semimetals

We explore optical activity in thin films and bulk of type-I and type II Weyl semimetals (WSM), and demonstrate the existence of a giant Kerr effect in both. In time-reversal symmetry broken WSM thin films, the polarization rotation is caused by the optical Hall conductivity including the anomalous Hall term. The Kerr angle is found to be $\propto Q/\omega$, with $Q$ and $\omega$ being the Weyl node separation and the optical frequency, respectively. In contrast, the optical activity in the bulk WSM is dominated by axion electrodynamics, which persists even in the Pauli blocked regime of no optical transitions. In bulk WSM, $Q$ acts analogous to the magnetization in magnetic materials, leading to large `polar Kerr effect' (linear in $Q$) when light is incident on WSM surface without Fermi arc states, and the `Voigt effect' (quadratic in $Q$), when light is incident on surface with Fermi arc states.

Nonlocal transport in superconducting heterostructures based on Weyl semimetals

We investigate the nonlocal transport properties in normal/superconducting/normal (NSN) junctions based on time-reversal symmetric type-$\mathrm{I}$ and type-$\mathrm{II}$ Weyl semimetals (WSMs). In the type-$\mathrm{I}$ WSM-based NSN junction, we show that a crossed-Andreev-reflection-dominated nonlocal transport can be realized within wide ranges of related parameters, which is favorable for the Cooper-pair splitting. For the type-$\mathrm{II}$ WSM-based NSN junction, we focus on the manifestations of the anisotropic aspects of type-II WSMs in the nonlocal transport. Owing to the hyperboloidlike Fermi surfaces of type-II WSMs, the scattering configurations and nonlocal differential conductance are strongly anisotropic, differing from the scenarios in similar NSN junctions based on other Dirac materials. These results enrich the understanding of the correlated transport in time-reversal symmetric WSM-based superconducting heterostructures.

Berry curvature induced thermopower in type-I and type-II Weyl semimetals

Berry curvature acts analogous to a magnetic field in the momentum-space, and it modifies the flow of charge carriers and entropy. This induces several intriguing magnetoelectric and magnetothermal transport phenomena in Weyl semimetals. %, including the planar Hall and planar Nernst effect. Here, we explore the impact of the Berry curvature and orbital magnetization on the thermopower in tilted type-I and type-II Weyl semimetals, using semiclassical Boltzmann transport formalism. We analytically calculate the full magnetoconductivity matrix and use it to obtain the thermopower matrix for different orientations of the magnetic field $(B)$, with respect to the tilt axis. We find that that the tilt of the Weyl nodes induces linear magnetic field terms in the conductivity matrix, as well as in the thermopower matrix. The linear-$B$ term appears in the Seebeck coefficients, when the $B$-field is applied along the tilt axis. Applying the magnetic field in a plane perpendicular to the tilt axis results in a quadratic-$B$ planar Nernst effect, linear-$B$ out-of-plane Nernst effect and quadratic-$B$ correction in the Seebeck coefficient.

Nernst thermopower of time-reversal breaking type-II Weyl semimetals

Weyl semimetals host linear energy dispersions around Weyl nodes, as well as monopoles of Berry curvature in momentum space around these points. These features give rise to unique transport signatures in a Weyl semimetal, such as transverse transport without an applied magnetic field, known as anomalous transport. The type-II Weyl semimetal, recently experimentally demonstrated in several materials, is classified by a tilting of the Weyl nodes. This paper provides a theoretical study on thermoelectric transport in time-reversal breaking type-II Weyl semimetals. Our results examine the balance between anomalous and non-anomalous contributions to the Nernst effect when subject to an external magnetic field. We also show how increasing scattering times have on enhancing effect on thermoelectric transport in these materials. Since a temperature-dependent chemical potential has been theoretically shown to be paramount when considering anomalous transport, we also study how similar considerations impact the Nernst thermopower in the non-anomalous case.

Spatial anisotropy of the Kondo screening cloud in a type-II Weyl semimetal

We theoretically study the Kondo screening of a spin-1/2 magnetic impurity in the bulk of a type-II Weyl semimetal (WSM) by use of the variational wave function method. We consider a type-II WSM model with two Weyl nodes located on the $k_z$-axis, and the tilting of the Weyl cones are along the $k_x$ direction. Due to co-existing electron and hole pockets, the density of states at the Fermi energy becomes finite, leading to a significant enhancement of Kondo effect. Consequently, the magnetic impurity and the conduction electrons always form a bound state, this behavior is distinct from that in the type-I WSMs, where the bound state is only formed when the hybridization exceeds a critical value. Meanwhile, the spin-orbit coupling and unique geometry of the Fermi surface lead to strongly anisotropic Kondo screening cloud in coordinate space. The tilting terms break the rotational symmetry of the type-II WSM about the $k_z$-axis, but the system remains invariant under a combined transformation $\mathcal{T}R^{y}(\pi)$, where $\mathcal{T}$ is the time-reversal operation and $R^{y}(\pi)$ is the rotation about the $y$-axis by $\pi$. Largely modified diagonal and off-diagonal components of the spin-spin correlation function on three principal planes reflect this change in band symmetry. Most saliently, the tilting terms trigger the emergence of non-zero off-diagonal components of spin-spin correlation function on the $x$-$z$ principal plane.

Disorder and magnetic transport in tilted Weyl semimetals

We investigate the effect of disorder on the Landau levels (LLs) in tilted three-dimensional Weyl semimetals (WSMs) when a magnetic field is present. Based on the minimum lattice model and by using the exact diagonalization and Kubo's formula, we numerically calculate the Hall conductivity and the density of states (DOS), from which several striking signatures are found to distinguish type-I WSMs from type-II WSMs: the first is the response of the Hall conductivity to the Fermi energy around the band center in clean limit, the second is the performance of the Hall conductivity to disorder, where in type-I WSMs, the robustness of the low-energy LLs is broken successively from the higher LLs to the lower ones and can be understood with the sink down picture, and the third is the behavior of the DOS at zero energy to disorder. The implications of our results are discussed.

Optical evidence of the type-II Weyl semimetals MoTe2 and WTe2

The carrier dynamics and electronic structures of type-II Weyl semimetal candidates ${\mathrm{MoTe}}_{2}$ and ${\mathrm{WTe}}_{2}$ have been investigated by using temperature-dependent optical conductivity $[\ensuremath{\sigma}(\ensuremath{\omega})]$ spectra. Two kinds of Drude peaks (narrow and broad) have been separately observed. The width of the broad Drude peak increases with elevating temperature above the Debye temperature of about 130 K in the same way as those of normal metals, on the other hand, the narrow Drude peak becomes visible below 80 K and the width is rapidly suppressed with decreasing temperature. Because the temperature dependence of the narrow Drude peak is similar to that of a type-I Weyl semimetal TaAs, it was concluded to originate from Dirac carriers of Weyl bands. The result suggests that the conductance has the contribution of two kinds of carriers, normal semimetallic and Dirac carriers, and this observation is evidence of the type-II Weyl semimetals ${\mathrm{MoTe}}_{2}$ and ${\mathrm{WTe}}_{2}$. The obtained carrier mass of the semimetallic bands and the interband transition spectra suggest the weak electron correlation effect in both materials.

Observation of Weyl Nodes in Robust Type-II Weyl Semimetal WP_{2}.

Distinct to type-I Weyl semimetals (WSMs) that host quasiparticles described by the Weyl equation, the energy dispersion of quasiparticles in type-II WSMs violates Lorentz invariance and the Weyl cones in the momentum space are tilted. Since it was proposed that type-II Weyl fermions could emerge from (W,Mo)Te_{2} and (W,Mo)P_{2} families of materials, a large number of experiments have been dedicated to unveiling the possible manifestation of type-II WSMs, e.g., surface-state Fermi arcs. However, the interpretations of the experimental results are very controversial. Here, using angle-resolved photoemission spectroscopy supported by the first-principles calculations, we probe the tilted Weyl cone bands in the bulk electronic structure of WP_{2} directly, which are at the origin of Fermi arcs at the surfaces and transport properties related to the chiral anomaly in type-II WSMs. Our results ascertain that, due to the spin-orbit coupling, the Weyl nodes originate from the splitting of fourfold degenerate band-crossing points with Chern numbers C=±2 induced by the crystal symmetries of WP_{2}, which is unique among all the discovered WSMs. Our finding also provides a guiding line to observe the chiral anomaly that could manifest in novel transport properties.

Origin of planar Hall effect in type-II Weyl semimetal MoTe2

Besides the negative longitudinal magnetoresistance (MR), planar Hall effect (PHE) is a newly emerging experimental tool to test the chiral anomaly or nontrivial Berry curvature in Weyl semimetals (WSMs). However, the origins of PHE in various systems are not fully distinguished and understood. Here we perform a systematic study on the PHE and anisotropic MR (AMR) of Td-MoTe2, a type-II WSM. Although the PHE and AMR curves can be well fitted by the theoretical formulas, we demonstrate that the anisotropic resistivity arises from the orbital MR (OMR), instead of the negative MR as expected in the chiral anomaly effect. In contrast, the positive MR indicates that the large OMR dominates over the chiral anomaly effect. This explains why it is difficult to measure negative MR in type-II WSMs. We argue that the measured PHE can be related with the chiral anomaly only when the negative MR is simultaneously observed.

Signature of indirect magnetic interaction in the crossover from type-I to type-II Weyl semimetals

We have theoretically investigated the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in Weyl semimetals (WSMs) with tilted dispersion in the framework of the Matsubara Green's function. It is shown that there emerges a sharp peak or dip of the RKKY interaction at the phase boundary, which can unambiguously characterize the phase transition from type-I to type-II WSMs. Distinct responses of the RKKY interaction to the tilted parameter $A$ in two phases are revealed to distinguish different Weyl phases. Moreover, we find that a nonzero Dzyaloshinskii-Moriya term survives even for Fermi energy at the Weyl points, which is completely contributed by the tilting effect and is distinguished from the previous mechanism. Consequently, the RKKY interaction provides richer signatures superior to usual conductivity to probe Weyl phases with tilted dispersion since it involves a contribution from both the Fermi surface and the Fermi sea. We have performed an analysis with both the analytical formula and numerical calculations.

Experimental Realization of Type-II Weyl Points and Fermi Arcs in Phononic Crystal.

Weyl points (WPs), as the doubly degenerate points in three-dimensional momentum band structures, carry quantized topological charges and give rise to a variety of extraordinary properties, such as robust surface wave and chiral anomaly. Type-II Weyl semimetals, which have conical dispersions in Fermi surfaces and a strongly tilted dispersion with respect to type I, have recently been proposed in condensed-matter systems and photonics. Although the type-II WPs have been theoretically predicted in acoustics, the experimental realization in phononic crystals has not been reported so far. Here, we experimentally realize a type-II Weyl phononic crystal. We demonstrate the topological transitions observed at the WP frequencies and the topological surface acoustic waves between the Weyl frequencies. The experiment results are in good accordance with our theoretical analyses. Due to the violation of the Lorentz symmetry, the type-II WPs only exist in low energy systems. As the analog counterpart in classical waves, the phononic crystal brings a platform for the research of type-II WPs in macroscopic systems.

Linear magnetochiral transport in tilted type-I and type-II Weyl semimetals

Berry curvature in Weyl semimetals results in very intriguing magneto-electric and magneto-thermal transport properties. In this paper, we explore the impact of the tilting of the Weyl nodes, which breaks the time-reversal symmetry, on the magneto-electric conductivity of type-I and type-II Weyl semimetals. Using the Berry curvature connected Boltzmann transport formalism, we find that in addition to the quadratic-B corrections induced by the tilt, there are also anisotropic and B-linear corrections in several elements of the conductivity matrix. For the case of magnetic field applied perpendicular to the tilt direction, we show the existence of finite B-linear transverse conductivity components. For the other case of magnetic field applied parallel to the tilt axis, the B-linear corrections appear in the longitudinal conductivity and will result in asymmetric lineshape in the magneto-resistence measurements. Unlike the quadratic-B corrections, these linear corrections are independent of the chemical potential, and are sensitive to the direction of the tilt axis and the applied magnetic field. Our systematic analysis of the full magneto-electric conductivity matrix, predicts several specific experimental signatures related to the tilting of the Weyl nodes in both type-I and type-II Weyl semimetals.

Proximity-Induced Superconductivity with Subgap Anomaly in Type II Weyl Semi-Metal WTe2.

Due to the nontrivial topological band structure in type II Weyl semi-metal tungsten ditelluride (WTe2), unconventional properties may emerge in its superconducting phase. While realizing intrinsic superconductivity has been challenging in the type II Weyl semi-metal WTe2, the proximity effect may open an avenue for the realization of superconductivity. Here, we report the observation of proximity-induced superconductivity with a long coherence length along the c axis in WTe2 thin flakes based on a WTe2/NbSe2 van der Waals heterostructure. Interestingly, we also observe anomalous oscillations of the differential resistance during the transition from the superconducting to the normal state. Theoretical calculations show excellent agreement with experimental results, revealing that such a subgap anomaly is the intrinsic property of WTe2 in superconducting state induced by the proximity effect. Our findings enrich the understanding of the superconducting phase of type II Weyl semi-metals and pave the way for their future applications in topological quantum computing.

Photoinduced tunable anomalous Hall and Nernst effects in tilted Weyl semimetals using Floquet theory

In this paper, we discuss the effect of a periodically driving circularly polarized laser beam in the high frequency limit, on the band structure and thermal transport properties of type-I and type-II Weyl semimetals (WSMs). We develop the notion of an effective Fermi surface stemming from the time-averaged Floquet Hamiltonian and discuss its effects on the steady-state occupation numbers of electrons and holes in the linearized model. In order to compute the transport coefficients averaged over a period of the incident laser source, we employ the Kubo formalism for Floquet states and show that the Kubo formula for the conductivity tensor retains its well known form with the difference that the eigenstates and energies are replaced by the Floquet states and their quasi-energies. We find that for type-I WSMs the anomalous thermal Hall conductivity grows quadratically with the amplitude $A_{0}$ of the U(1) gauge field for low tilt, while the Nernst conductivity remains unaffected. For type-II WSMs, the Hall conductivity decreases non-linearly with $A_{0}$ due to the contribution from the physical momentum cutoff, required to keep finite electron and hole pocket sizes, and the Nernst conductivity falls of logarithmically with $A_{0}^2$. These results may serve as a diagnostic for material characterization and transport parameter tunability in WSMs, which are currently the subject of a wide range of experiments.

Quantum oscillations and magnetoresistance in type-II Weyl semimetals: Effect of a field-induced charge density wave

Recent experiments on type-II Weyl semimetals such as WTe$_2$, MoTe$_2$, Mo$_x$W$_{1-x}$Te$_2$ and WP$_2$ reveal remarkable transport properties in presence of a strong magnetic field, including an extremely large magnetoresistance and an unusual temperature dependence. Here, we investigate magnetotransport via the Kubo formula in a minimal model of a type-II Weyl semimetal taking into account the effect of a charge density wave (CDW) transition, which can arise even at weak coupling in the presence of a strong magnetic field because of the special Landau level dispersion of type-II Weyl systems. Consistent with experimental measurements we find an extremely large magnetoresistance with close to $B^2$ scaling at particle-hole compensation, while in the extreme quantum limit there is a transition to a qualitatively new scaling with approximately $B^{0.75}$. We also investigate the Shubnikov-de Haas effect and find that the amplitude of the resistivity quantum oscillations are greatly enhanced below the CDW transition temperature which is accompanied by an unusual non-monotonous (non-Lifshitz-Kosevich) temperature dependence.

Epsilon-near-zero response and tunable perfect absorption in Weyl semimetals

We theoretically study the electromagnetic response of type-I and type-II centrosymmetric Weyl semimetals. We derive an anisotropic permittivity tensor with off-diagonal elements to describe such gyrotropic media. Our findings reveal that for appropriate Weyl cones tilts, the real part of the transverse component of the permittivity can exhibit an epsilon-near-zero response. The tilt parameter can also control the amount of loss in the medium, ranging from lossless to dissipative when transitioning from type-I to type-II. Similarly, by tuning either the frequency of the electromagnetic field or the chemical potential in the system, an epsilon-near-zero response can appear as the permittivity of the Weyl semimetal transitions between positive and negative values. Employing the obtained permittivity tensor, we consider a setup where the Weyl semimetal is deposited on a perfect conductive substrate and study the refection and absorption characteristics of this layered configuration. We show that by choosing the proper geometrical and material parameters, devices can be created that perfectly absorb electromagnetic energy over a wide angular range of incident electromagnetic waves.

Planar Hall effect in the type-II Weyl semimetal Td−MoTe2

Topological Weyl semimetals (WSMs), a new quantum state of matter, provide the realization of relativistic Weyl fermions in solid-state physics. The appearance of the Weyl nodes will demonstrate novel transport phenomena related to the chiral anomaly. Theoretical prediction hints that the giant planar Hall effect (PHE) can be induced by the chiral anomaly in the WSMs. In this work, we performed PHE measurements to probe chiral charge in type-II WSM ${T}_{d}\text{\ensuremath{-}}\mathrm{MoT}{\mathrm{e}}_{2}$. Robust transverse voltage can be acquired when the magnetic field and electric current is coplanar. Subsequently, the amplitude of intrinsic PHE increased sharply at $T=50\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ with the decreasing temperature. The increasing trend in the temperature dependence is attributed to coupling effect between the chiral charge and the electric one, which drives the system into intermediate-coupling states at higher field. Our work confirms that the PHE measurement is a practical transport tool to probe chiral charge pumping effect in the WSMs systems.