Weyl Semimetals Research Articles

Nondivergent chiral charge pumping in Weyl semimetals

Recent studies suggest that the nonlinear transport properties in Weyl semimetal may be a measurable consequence of its chiral anomaly. Nonlinear responses in transport are estimated to be substantial, because in real materials such as TaAs or ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$, the Fermi level resides near the Weyl nodes where the chiral charge pumping is said to diverge. However, this work presents semiclassical Boltzmann analysis that indicates that the chiral charge pumping is nondivergent even at the zero-temperature limit. We demonstrate that the divergence in a common semiclassical calculation scheme is not a problem of the scheme itself, but occurs because a commonly used approximation of the change in particle number breaks down near the Weyl nodes. Our result suggests the possibility that the nonlinear properties in Weyl semimetals can be overestimated, and it provides the validity condition for the conventional approximation. We also show the distinct Fermi level dependencies of the chiral magnetic effect and the negative longitudinal magnetoresistance, as a consequence of nondiverging chiral charge pumping.

Connection between topological pumping effect and chiral anomaly in Weyl semimetals

While the semiclassical Boltzmann approach has been widely adopted to study chiral-anomaly-related transport in Weyl semimetals (WSMs), it predicts an unphysical diverging electrical conductivity when ${E}_{F}\ensuremath{\rightarrow}0$, where ${E}_{F}$ is the Fermi energy. Here, we develop a modified semiclassical equation of motion which includes both the diagonal and off-diagonal contributions of the Berry curvature. On this basis, we derive an undivergent classical formula for the positive longitudinal magnetoconductivity in a WSM which resolves the conflict between the classical and ultraquantum approaches. We demonstrate that the chiral anomaly is closely related to the topological pumping effect and it can be realized even in the absence of a magnetic field. With our findings we propose a different perspective to understand the topological properties of WSMs and suggest a way to measure the chiral anomaly using transport.

Directional dependent magnetooptical effect and the photonic spin Hall effect in a magnetic Weyl semimetal-based photonic crystal

The ability to generate and manipulate the directional dependent magnetooptical effect and photonic spin Hall effect is essential toward realistic unidirectional optoelectronic devices, but its exploration remains scarce. Here we theoretically identify that the multilayer structure whose unit cell is composed of a new, to the best of our knowledge, emergent magnetic Weyl semimetal layer and two anisotropic dielectric layers has the capability of creating the propagation direction dependent magnetooptical effect and photonic spin Hall effect simultaneously due to its intrinsic lack of space inversion and time reversal symmetries. Specifically, we also realize the continuous manipulation of the magnetooptical effect and photonic spin Hall effect in this structure under two opposite directions by an electrical means, which is contributed by the control of the optical properties in magnetic Weyl semimetals by Fermi energy. Our work enables an alternative strategy to achieve the directional dependent optical as well as magnetooptical effects simultaneously, which provides new perspectives in the fresh field of unidirectional optoelectronics and spin photonics.

Near-field radiative heat transfer between Weyl semimetal multilayers

Modulation of near-field heat transfer by introducing relative rotation has been previously demonstrated in a two-body system using bulk Weyl semimetals. Here, we first show that, compared with the bulk system, the heat transfer is significantly enhanced by incorporating multilayer Weyl semimetals when the rotation and the material loss are simultaneously modulated. With reduced loss, the multilayer systems having rotation angles of π on both bodies achieve much substantial enhancement than their counterparts in which the rotation angle of one body is 0. In addition, further tuning the off-diagonal components in the permittivity tensor of the Weyl semimetal allows an optimal enhancement. The considerable heat transfer enhancements in the multilayer system over the bulk system are attributed to the vanishing nonreciprocal surface plasmon polariton mode with the rotation of π and appropriately chosen material properties. Our results provide critical understanding on the heat transfer in multilayer Weyl semimetal systems.

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.

Effects of surface potentials on Goos-Hänchen and Imbert-Fedorov shifts in Weyl semimetals

Weyl semimetals exhibit a myriad of exotic transport responses, among which, the Goos-H\"anchen (GH) and Imbert-Fedorov (IF) effects have recently garnered substantial attention. Besides the usual parametric dependence inherited from the underlying Hamiltonian to describe a Weyl system, the IF shift particularly carries a topological identity---it depends on the chirality of the Weyl cones. Observing such signatures following the trail of theoretical predictions applied to clean systems can be severely obfuscated by surface potentials induced by localized impurities that are naturally present in real materials hosting the semimetallic phase. Classifying these potentials, we study their effects on GH and IF shifts to provide useful guidance to experiments that are tuned to the objective of characterizing Weyl semimetals and leveraging them to provide the basis for future technological advances. A transfer matrix-based approach is proposed to study the profile of Weyl wave functions scattering from the impurity potentials. As we unfold, the presence of such potentials can lead to several remarkable effects such as the complete nullification of the IF shift and valley inversion.

Novel Terahertz Properties of Nanostructured Mn3+0.53Sn Films with Different Crystalline Orientations Driven by Ostwald Ripening on (0001) c-Al2O3

The characteristic energies of elementary excitations and collective modes in many quantum materials lie mostly in the terahertz (THz) frequency range, which provides a wide space for the development of THz optical materials and devices. In particular, topological Weyl semimetal Mn3Sn is a noncollinear antiferromagnet with anomalous THz properties, which is strongly affected by thermal energy and external magnetic fields. Despite the explosive growth of the research on magnetic Weyl semimetals recently, its nanoscale structure for applications in THz optical devices remains to be explored. Here, we fabricated nanostructured Mn3+0.53Sn films with different crystal orientations, driven by Ostwald Ripening (OR) on (0001) c-Al2O3. A huge anisotropic THz response manifested a firm link between the optical properties of Weyl antiferromagnet Mn3Sn and its contrivable spin structures. The topological properties of Mn3Sn are robustly protected in its nanostructures. This work can provide a new horizon for the fabrication of a nanostructured magnetic Weyl alloy and for its potential applications in subwavelength high-performance THz devices.

Strain-induced collapse of Landau levels in real Weyl semimetals

The collapse of Landau levels under an electric field perpendicular to the magnetic field is one of the distinctive features of Dirac materials. So is the coupling of lattice deformations to the electronic degrees of freedom in the form of gauge fields which allows the formation of pseudo-Landau levels from strain. We analyze the collapse of Landau levels induced by strain on realistic Weyl semimetals hosting anisotropic, tilted Weyl cones in momentum space. We perform first-principles calculations, to establish the conditions on the external strain for the collapse of Landau levels in TaAs which can be experimentally accessed.

Surface Luttinger arcs in Weyl semimetals

Weyl semimetals famously host a surface topological metal containing open Fermi arcs instead of closed Fermi surfaces. Here, the authors predict another surface feature, Luttinger arcs, that form closed loops with the Fermi arcs in undoped Weyl semimetals. Luttinger arcs are common, albeit experimentally inaccessible, for strongly interacting electrons. Here, they occur even without interactions and switch places with Fermi arcs for different surface terminations -- a property the authors exploit to pinpoint Luttinger arcs for Co and Sn terminations in Co${}_{3}$Sn${}_{2}$S${}_{2}$.

Landau levels and magneto-optical responses in Weyl semimetal quantum wells in a non-uniform magnetic field

We study the Landau level (LL) structure and magneto-optical responses in the Weyl semimetal (WSM) quantum well in the presence of a non-uniform magnetic field (NUMF). The number of LLs in the NUMF is found to be finite, and the LL structure of the system is significantly affected by the inhomogeneity of the magnetic field. The added electric field significantly affects the separation of the two Weyl nodes in momentum space. We investigate the role of the inhomogeneity of the magnetic field, temperature, electron density, and electric field, as well as the doping level on the optical response properties. Both longitudinal and Hall susceptibilities in the $(x,y)$ plane and the longitudinal susceptibility in the $z$ direction display a series of peaks whose height and spacing decrease with the increase of the LL index. At $T\ensuremath{\ne}0$, thermal excitation triggers new transitions, which are forbidden by the Pauli blocked at $T=0$. The optical response spectra are different when the chemical potential lies in different energy regions, which are strongly dependent on the inhomogeneity of the magnetic field, electron density, and electric field. In this paper, we provide a possible way to control the optical response spectrum in WSM materials by changing these parameters.

Near-field radiative heat transfer in three-body Weyl semimetals.

We investigate the near-field radiative heat transfer in a three-body system made of Weyl semimetals. At infinitesimal temperature gradient, the rotation of the middle and the right bodies leads to heat transfer suppression, enabling thermal switching with considerably enhanced heat flux but slightly smaller ratio than two-body system without the middle body, due to stronger cavity surface plasmon polariton modes and their mismatch caused by relative rotation. By further moving the middle body to induce asymmetric cavity sizes, the three-body system can achieve a switching ratio exceeding the two-body counterpart due to asymmetric cavity modes coupling. As the temperature gradient increases to 200 K, the highest switching ratio by optimally tuning the rotation and cavity size asymmetry decreases slightly yet still outperforms the two-body system. Our results provide important understanding of the near-field radiative heat transfer in many-body systems consisting of Weyl semimetals.

Aslamazov Larkin conductivity in layered Dirac/Weyl semimetals

The Aslamazov–Larkin conductivity (ALC) in the layered Dirac/Weyl semi-metals is calculated both for Type-I and Type II for different dimensionality and magnetic fields. The ALC strongly depends on the tilt parameter of the dispersion relation cone. While the 3D and 2D the Aslamazov–Larkin conductivity slightly depends on tilt parameter in Type-I phase and increases in the Type-II phase the 1D ALC decreases in Type-I phase up to zero close to border between Type-I and Type-II phases. Results are discussed in light of the resent experiments on the layered HfTe5 Weyl semi-metals. It is concluded the one dimensional AL conductivity well explained the experimental data.

Strong nonreciprocal thermal radiation by optical Tamm states in Weyl semimetallic photonic multilayers

The almost-complete violation of Kirchhoff's law possesses various potential applications, such as nonreciprocal thermal emitters, thermal routers, and other logic devices. Recently, Weyl semimetal materials have attracted wide attention. It exhibits a very unusual and extremely large gyroscopic optical response within the mid IR without an external magnetic field, which is due to its unique topologically nontrivial electronic state and inherent time-reversal symmetry breaking. Here, we show a planar multilayer structure composed of Weyl semimetals, which can achieve an almost-complete violation of Kirchhoff's law at an incident angle of 18° without applying any external magnetic field. By tuning the thickness of the ITO layer, the angle of incidence, and the axial vector of the WSM, an almost complete violation of Kirchhoff's law can persist over a wide range of angles (18°–52.3°) and wavelengths (6.6 μm–7.2 μm). Furthermore, through the study of the electric field distribution, it is revealed that this enhanced nonreciprocity is due to the local field-enhancing properties of TPPs. Our work may contribute a practical design scheme for constructing strongly nonreciprocal thermal emitters.

Magnetization tunable Weyl states in EuB6

The interplay between magnetism and topological band structure offers extraordinary opportunities to realize rich exotic magnetic topological phases such as axion insulators, Weyl semimetals, and quantum anomalous Hall insulators, and therefore has attracted fast growing research interest. The rare-earth hexaboride $\mathrm{Eu}{\mathrm{B}}_{6}$ represents an interesting magnetic topological phase with tunable magnetizations along different crystallographic directions, while the correlation with the topological properties remains scarcely explored. In this work, combining magnetotransport measurements and first principles calculations, we demonstrate that $\mathrm{Eu}{\mathrm{B}}_{6}$ exhibits versatile magnetic topological phases along different crystallographic directions, which tightly correlate with the varied magnetizations. Moreover, by virtue of the weak magnetocrystalline anisotropy and the relatively strong coupling between the local magnetization and the conduction electrons, we show that the magnetic ground state of the system can be directly probed by the anisotropy in the magnetotransport properties. Our work thus introduces an excellent platform to study the rich topological phases that are tunable by magnetic orders.

All-electrical switching of a topological non-collinear antiferromagnet at room temperature.

Non-collinear antiferromagnetic Weyl semimetals, combining the advantages of a zero stray field and ultrafast spin dynamics, as well as a large anomalous Hall effect and the chiral anomaly of Weyl fermions, have attracted extensive interest. However, the all-electrical control of such systems at room temperature, a crucial step toward practical application, has not been reported. Here, using a small writing current density of around 5×106 A·cm-2, we realize the all-electrical current-induced deterministic switching of the non-collinear antiferromagnet Mn3Sn, with a strong readout signal at room temperature in the Si/SiO2/Mn3Sn/AlOx structure, and without external magnetic field or injected spin current. Our simulations reveal that the switching originates from the current-induced intrinsic non-collinear spin-orbit torques in Mn3Sn itself. Our findings pave the way for the development of topological antiferromagnetic spintronics.

Evolution of Weyl nodes in Ni-doped thallium niobate pyrochlore Tl2−xNixNb2O7

The magnetic Weyl semimetal (WSM) is important for fundamental physics and potential applications due to its spontaneous magnetism, robust band topology, and enhanced Berry curvature. It possesses many unique quantum effects, including a large intrinsic anomalous Hall effect, Fermi arcs, and chiral anomaly. In this work, using ab initio calculations, we propose that Ni-doped pyrochlore Tl2Nb2O7 is a magnetic WSM caused by the exchange field splitting on bands around its quadratic band crossing point. The exchange field tuned by Ni 3d on-site Coulomb interaction parameter U drives the evolution of Weyl nodes and the resulting topological phase transition. As Weyl nodes can exist at generic points in the Brillouin zone and are hard to identify exactly, their creation and annihilation, i.e., the change in their number, chirality, and distribution, have been consistently confirmed with a combined theoretical approach, which employs parity criterion, symmetry indicator analysis, and the Wilson loop of the Wannier center. We find that Weyl nodes remain in a large range of U and are close to the Fermi level, which makes the experimental observation very possible. We think that this method and our proposal of magnetic WSM will be useful in finding more WSMs and add to the understanding of the topological phase transition.

Understanding the three-dimensional quantum Hall effect in generic multi-Weyl semimetals

The quantum Hall effect in three-dimensional Weyl semimetal (WSM) receives significant attention for the emergence of the Fermi loop where the underlying two-dimensional Hall conductivity, namely, sheet Hall conductivity, shows quantized plateaus. In tilt multi-Weyl semimetals (mWSMs) lattice models, we systematically study Landau levels (LLs) and magneto-Hall conductivity both under the parallel and perpendicular magnetic field (referenced to the Weyl node's separation), i.e., $\mathbit{B}\ensuremath{\parallel}z$ and $\mathbit{B}\ensuremath{\parallel}x$, to explore the impact of tilting and nonlinearity in the dispersion. We make use of two (single) node low-energy models to qualitatively explain the emergence of mid-gap chiral (linear crossing of chiral) LLs on the lattice for $\mathbit{B}\ensuremath{\parallel}z$ $(\mathbit{B}\ensuremath{\parallel}x)$. Remarkably, we find that the sheet Hall conductivity becomes quantized for $\mathbit{B}\ensuremath{\parallel}z$ even when two Weyl nodes project onto a single Fermi point in two opposite surfaces, forming a Fermi loop with ${k}_{z}$ as the good quantum number. On the other hand, the Fermi loop, connecting two distinct Fermi points on two opposite surfaces, with ${k}_{x}$ being the good quantum number, causes the quantization in sheet Hall conductivity for $\mathbit{B}\ensuremath{\parallel}x$. The quantization is almost lost (perfectly remained) in the type-II phase for $\mathbit{B}\ensuremath{\parallel}x$ $(\mathbit{B}\ensuremath{\parallel}z)$. Interestingly, the jump profiles between the adjacent quantized plateaus change with the topological charge for both cases. The momentum-integrated three-dimensional Hall conductivity is not quantized; however, it bears the signature of chiral LLs resulting in the linear dependence on $\ensuremath{\mu}$ for small $\ensuremath{\mu}$. The linear zone (its slope) reduces (increases) as the tilt (topological charge) of the underlying WSM increases.

Non-adiabatic corrections to chiral charge pumping in topological nodal semimetals

Studying many-body versions of Landau-Zener-like problems of non-interacting electrons in the Slater formalism for several $k \cdot p$ models representing Weyl and Dirac semimetals, we systematically include non-adiabatic corrections to a quantum limit of chiral charge pumping in these models. In this paper, we show that relative homotopy invariant [Sun et al., Phys. Rev. Lett. 121, 106402 (2018)] and Euler class invariant [Bouhon et al., Nat. Phys. 16, 1137 (2020)] non-trivially manifest in the non-adiabatic corrections to the quantum limit of chiral charge pumping. These corrections could affect conductivity channels connected with the presence of chiral anomaly. Moreover, we show that, for non-symmorphic systems, this contribution is sensitive to the direction of the applied magnetic field (in respect to the so-called non-symmorphic nodal loop), suggesting that the conjectured direction-selective chiral anomaly in non-symmorphic systems [Bzdu\v{s}ek et al., Nature (London) 538, 75 (2016)] could lead to a strongly anisotropic longitudinal magnetoresistance. The presented approach can be easily applied to other $k \cdot p$ or tight-binding models.

Hidden Local Symmetry Breaking in a Kagome-Lattice Magnetic Weyl Semimetal.

Exploring the relationship between intriguing physical properties and structural complexity is a central topic in studying modern functional materials. Co3Sn2S2, a newly discovered kagome-lattice magnetic Weyl semimetal, has triggered intense interest owing to the intimate coupling between topological semimetallic states and peculiar magnetic properties. However, the origins of the magnetic phase separation and spin glass state below TC in this ordered compound are two unresolved yet important puzzles in understanding its magnetism. Here, we report the discovery of local symmetry breaking surprisingly co-emerges with the onset of ferromagnetic order in Co3Sn2S2, by a combined use of neutron total scattering and half-polarized neutron diffraction. An anisotropic distortion of the cobalt kagome lattice at the atomic/nano level is also found, with distinct distortion directions among the two Co1 and four Co2 atoms. The mismatch of local and average symmetries occurs below TC, indicating that Co3Sn2S2 evolves to an intrinsically lattice disordered system when the ferromagnetic order is established. The local symmetry breaking with intrinsic lattice disorder provides new understanding of the puzzling magnetic properties. Our density functional theory (DFT) calculation indicates that the local symmetry breaking is expected to reorient local ferromagnetic moments, unveiling the existence of the ferromagnetic instability associated with the lattice instability. Furthermore, DFT calculation unveils that the local symmetry breaking could affect the Weyl property by breaking the mirror plane. Our findings highlight the fundamentally important role that the local symmetry breaking plays in advancing our understanding on the magnetic and topological properties in Co3Sn2S2, which may draw attention to explore the overlooked local symmetry breaking in Co3Sn2S2, its derivatives and more broadly in other topological Dirac/Weyl semimetals and kagome-lattice magnets.

Antisymmetric Seebeck Effect in a Tilted Weyl Semimetal.

Tilting the Weyl cone breaks the Lorentz invariance and enriches the Weyl physics. Here, we report the observation of a magnetic-field-antisymmetric Seebeck effect in a tilted Weyl semimetal, Co_{3}Sn_{2}S_{2}. Moreover, it is found that the Seebeck effect and the Nernst effect are antisymmetric in both the in-plane magnetic field and the magnetization. We attribute these exotic effects to the one-dimensional chiral anomaly and phase space correction due to the Berry curvature. The observation is further reproduced by a theoretical calculation, taking into account the orbital magnetization.