Pair Of Weyl Nodes Research Articles

Frequency-independent optical spin injection in Weyl semimetals

We demonstrate that in Weyl semimetals, the momentum-space helical spin texture can couple to the chirality of the Weyl node to generate a frequency-independent optical spin injection. This frequency-independence is rooted in the topology of the Weyl node. Since the helicity and the chirality are always locked for Weyl nodes, the injected spin from a pair of Weyl nodes always add up, implying no symmetry requirements for Weyl semimetals. Finally, we show that such frequency-independent spin injection is robust against multiband corrections and lattice-regularization effect and capable of realizing all-optical magnetization switching in the THz regime.

Existence of nodal-arc and its evolution into Weyl-nodes in the presence of spin-orbit coupling in TaAs & TaP

In this work, we report the existence of nodal-arc, which acts as the building block of all the nodal-rings in TaAs & TaP. This nodal-arc is found to be capable of generating all the nodal-rings in these materials upon the application of space-group symmetry operations including time-reversal symmetry. The arcs are obtained to be dispersive with the energy spread of ∼109 (∼204) meV in TaAs (TaP). Also, the orbitals leading to bands-inversion and thus the formation of nodal-arcs are found to be Ta-5d & As-4p (P-3p) in TaAs (TaP). The area of nodal-rings is found to be highly sensitive to the change in hybridization-strength, where the increase in hybridization-strength leads to the decrease in the area of nodal-rings. In the presence of spin–orbit coupling (SOC), all the points on these arcs get gaped-up and two pairs of Weyl-nodes are found to evolve from them. Out of the two pair, one is found to be situated close to the joining point of the two arcs forming a ring. This causes the evolution of each nodal-ring into three pairs of Weyl-nodes. The coordinates of these Weyl-nodes are found to be robust to the increase in SOC-strength from ∼0.7–3.5 eV. All the results are obtained at the first-principle level. This work provides a clear picture of the existence of nodal-arc due to accidental degeneracy and its evolution into Weyl-nodes under the effect of SOC.

Structure, Magnetotransport, and Theoretical Study on the Layered Antiferromagnet Topological Phase EuCd2As2 under High Pressure

AbstractRich nontrivial topological phases rooted in the interplay between magnetism and topology in the layered antiferromagnet EuCd2As2 have captured vast attention, especially the ideal Weyl semimetal state realized in the spin‐polarized ferromagnetic (FM) structure driven by a moderate external magnetic field. In this work, combining magnetization, magneto‐transport, and structure measurements under high pressure and first principles calculations, this study finds that the pressure can drive the in‐plane antiferromagnetic structure of EuCd2As2 across an intermediate in‐plane FM structure then into the out‐of‐plane FM structure. This study also finds butterfly‐shaped MR and anomalous Hall effect under large pressure, which may support the pressure‐driven FM state. High‐pressure angle‐dispersive X‐ray diffraction and X‐ray absorption near‐edge spectroscopy measurements exclude structure transition and/or change of Eu2+ valence state as sources for the magnetic phase transitions. Alternatively, apparently reduced axial ratio (c/a) and compressed Eu‐layer space distance should play important roles. Interestingly, the calculations unveil that the out‐of‐plane FM structure hosts only one pair of Weyl nodes around the Fermi level, suggesting that pressure can be an alternative way to realize the ideal Weyl semimetal state in EuCd2As2 and will be useful for exploring exotic topological properties in such layered magnetic topological phase with strongly competing magnetic exchanges.

Topological states and topological phase transition in Cu2SnS3 and Cu2SnSe3

Based on the first-principles calculations and model analysis, we propose that the isostructural compounds ${\mathrm{Cu}}_{2}{\mathrm{SnS}}_{3}$ and ${\mathrm{Cu}}_{2}{\mathrm{SnSe}}_{3}$ are both the simplest nodal-line semimetals with only one nodal line in their crystal momentum space when spin-orbit coupling (SOC) is ignored. The inclusion of SOC drives ${\mathrm{Cu}}_{2}{\mathrm{SnS}}_{3}$ into a Weyl semimetal (WSM) state with only two pairs of Weyl nodes, the minimum number required for a WSM with time-reversal symmetry. In contrast, SOC leads ${\mathrm{Cu}}_{2}{\mathrm{SnSe}}_{3}$ to a strong topological insulator (STI) state. This difference can be well understood as there is a topological phase transition (TPT). In it, the Weyl nodes are driven by tunable SOC and annihilate in a mirror plane, resulting in a STI. This TPT, together with the evolution of Weyl nodes, the changing of mirror Chern numbers of the mirror plane, and the ${Z}_{2}$ indices protected by time-reversal symmetry, has been demonstrated by the calculation of ${\mathrm{Cu}}_{2}\mathrm{Sn}{({\mathrm{S}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x})}_{3}$ within virtual crystal approximation and an effective $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ model analysis. Though our first-principles calculations have overestimated the topological states in both compounds, we believe that the theoretical demonstration of controlling the TPT and the evolution of Weyl nodes will stimulate further efforts to explore them.

Visualizing discrete Fermi surfaces and possible nodal-line to Weyl state evolution in ZrSiTe

Topological nodal line semimetals (TNLSMs) represent a quantum state of topological matter. When the crystal/time-reversal symmetry is broken, a nodal line state is expected to evolve into a Dirac semimetal, a Weyl semimetal, or other topological phases according to theoretical studies. Here, we report scanning tunneling microscopy (STM) based quasiparticle interference (QPI) measurements performed on the surface of TNLSM ZrSiTe single crystal. A discrete Fermi surface with multiple electron/hole pockets and the impurity-induced inter-/intra- pockets scatterings are directly visualized from QPI patterns. Moreover, the degenerated Dirac points at X point evolve into the pairs of Weyl nodes when Fe atoms are deposited, suggesting a possible phase transition from the nodal line to the Weyl state. The calculated band structures and the Weyl points by applying Zeeman splitting energies along x-direction, further confirm the existence of Weyl points in the Fe-doped ZrSiTe induced by the broken of time-reversal symmetry.

Emergence of Fermi arcs due to magnetic splitting in an antiferromagnet.

The Fermi surface plays an important role in controlling the electronic, transport and thermodynamic properties of materials. As the Fermi surface consists of closed contours in the momentum space for well-defined energy bands, disconnected sections known as Fermi arcs can be signatures of unusual electronic states, such as a pseudogap1. Another way to obtain Fermi arcs is to break either the time-reversal symmetry2 or the inversion symmetry3 of a three-dimensional Dirac semimetal, which results in formation of pairs of Weyl nodes that have opposite chirality4, and their projections are connected by Fermi arcs at the bulk boundary3,5-12. Here, we present experimental evidence that pairs of hole- and electron-like Fermi arcs emerge below the Neel temperature (TN) in the antiferromagnetic state of cubic NdBi due to a new magnetic splitting effect. The observed magnetic splitting is unusual, as it creates bands of opposing curvature, which change with temperature and follow the antiferromagnetic order parameter. This is different from previous theoretically considered13,14 and experimentally reported cases15,16 of magnetic splitting, such as traditional Zeeman and Rashba, in which the curvature of the bands is preserved. Therefore, our findings demonstrate a type of magnetic band splitting in the presence of a long-range antiferromagnetic order that is not readily explained by existing theoretical ideas.

The effect of size on spin-to-charge conversion in the magnetic Weyl semimetal

A magnetic Weyl semimetal (MWSM), which only has a pair of Weyl nodes, is an ideal platform to study spin-related transport properties, such as the chiral anomaly and the magnetic chiral magnetic effect. This work investigates the sample size and impurity effects on the spin-to-charge conversion in a vertical heterostructure consisting of a ferromagnetic metal and a MWSM, where a spin bias is applied at the interface and a charge current is generated. We find that the two Weyl nodes with opposite chirality generate the same charge current in the y,z directions as a result of the spin injection but opposite in the x direction. The analytic formulas of the conductance in the ballistic and diffusive limits are given. Furthermore, we discuss that the efficiency of spin-to-charge conversion increases and becomes perfect from the ballistic to the diffusive limit. These findings provide new potentials for manipulating the interconversion between spin and charge in the topological semimetals.

Spin-polarized gap in the magnetic Weyl semimetal Co3Sn2S2

We report a unique type of gap in a magnetic Weyl semimetal ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ where the electrons are spin polarized and preserve the spin-momentum locking feature of Weyl fermions. Such spin-polarized gaps are associated with the Weyl node annihilation, where a pair of Weyl nodes with opposite chirality touch each other at \ensuremath{\sim}210 meV above the Fermi energy. These are revealed by both time- and spin-resolved ultrafast spectroscopy experiments, combined with first-principles calculations. The spin-polarized gap opening is accompanied by a topological phase transition, and the gap magnitude exhibits an unconventional temperature dependence originated from the Weyl physics. Furthermore, we propose possible circularly polarized terahertz-midinfrared radiation from such a spin-polarized gap. Our results shed light on exploring the topological properties of excited states and endow application potentials for gapped materials based on chirality.

Nonlinear Hall effect in Weyl semimetals induced by chiral anomaly

We predict a nonlinear Hall effect in certain Weyl semimetals with broken inversion symmetry. When the energy dispersions about pairs of Weyl nodes are skewed -- the Weyl cones are "tilted" -- the concerted actions of the anomalous velocity and the chiral anomaly give rise to the nonlinear Hall effect. This Hall conductivity is linear in both electric and magnetic fields, and depends critically on the tilting of the Weyl cones. We also show that this effect does not rely on a finite Berry curvature dipole, in contrast to the intrinsic quantum nonlinear Hall effect that was recently observed in type-II Weyl semimetals.

Chiral magnetic effect and Maxwell–Chern–Simons electrodynamics in Weyl semimetals

The Weyl semimetal, due to a non-zero energy difference in the pair of Weyl nodes, shows chiral magnetic effect (CME). This leads to a flow of dissipationless electric current along an applied magnetic field. Such a chiral magnetic effect in Weyl semimetals has been studied using the laws of classical electrodynamics. It has been shown that the CME in such a semimetal changes the properties namely, frequency-dependent skin depth, capacitive transport, plasma frequency, etc., in an unconventional way as compared to the conventional metals. In the low-frequency regime, the properties are controlled by a natural length scale due to CME called the chiral magnetic length. Furthermore, unlike the conventional metals, the plasma frequency in this case is shown to be strongly magnetic field-dependent. Since the plasma frequency lies below the optical frequency, the Weyl semimetals will look transparent. Such new and novel observations might help in exploiting these class of materials in potential applications which would completely change the future technology.

Prediction of spin polarized Fermi arcs in quasiparticle interference in CeBi

We predict that CeBi in the ferromagnetic state is a Weyl semimetal. Our calculations within density functional theory show the existence of two pairs of Weyl nodes on the momentum path $(0,0,{k}_{z})$ at $15\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$ above and $100\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$ below the Fermi level. Two corresponding Fermi arcs are obtained on surfaces of mirror-symmetric (010)-oriented slabs at $E=15\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$ and both arcs are interrupted into three segments due to hybridization with a set of trivial surface bands. By studying the spin texture of surface states, we find the two Fermi arcs are strongly spin polarized but in opposite directions, which can be detected by spin-polarized ARPES measurements. Our theoretical study of quasiparticle interference (QPI) for a nonmagnetic impurity at the Bi site also reveals several features related to the Fermi arcs. Specifically, we predict that the spin polarization of the Fermi arcs leads to a bifurcation-shaped feature only in the spin-dependent QPI spectrum, serving as a fingerprint of the Weyl nodes.

Broken symmetries and the related interface-induced effects at Weyl-system TaAs in proximity of noble metals

Weyl semimetal TaAs, congenially accommodating the massless Weyl fermions, furnishes a platform to observe a spontaneous breaking of either the time-reversal or the inversion symmetry and the concurrent genesis of pairs of Weyl nodes with significant topological durability. Former experimental analysis, which reveals that the near-zero spin-polarization of bulk TaAs, experiences a boost in proximity of point-contacts of non-magnetic metals along with the associated tip-induced superconductivity, provides the impetus to study the large-area stacked interfaces of TaAs with noble metals like Au and Ag. The primary outcomes of the present work can be listed as follows: (1) First-principles calculations on the interfacial systems have manifested an increment of the interface-induced spin-polarization and contact-induced transport spin-polarization of TaAs in proximity of noble metals; (2) In contrast to the single interface, for vertically stacked cases, the broken inversion symmetry of the system introduces a z-directional band-dispersion, resulting in an energetically separated series of non-degenerate band crossings. The simultaneous presence of such band-crossings and spin-polarization indicated the coexistence of both broken time reversal and inversion symmetries for metal-semimetal stacked interfaces; (3) quantum transport calculations on different device geometries reveal the importance of contact geometry for spin-transport in TaAs devices. Lateral contacts are found to be more effective in obtaining a uniform spin transport and larger transport spin polarization; (4) the phonon dispersion behaviour of TaAs displays a closure of band-gap with the associated increase of phonon-density of states for the acoustic modes in proximity of lateral contacts of noble metals.

Topological phase transition in the layered magnetic compound MnSb2Te4 : Spin-orbit coupling and interlayer coupling dependence

Based on the first-principles calculations and theoretical analysis, we investigate the electronic structures, topological phase transition (TPT) and topological properties of layered magnetic compound MnSb2Te4. It has the similar crystal and magnetic structure as the magnetic topological insulator MnBi2Te4. We find that when the spin-orbit coupling (SOC) is considered, the band structure of MnSb2Te4 in antiferromagnetic (AFM) state has no band inversion at {\Gamma}. This is due to the SOC strength of Sb is less than that of Bi. The band inversion can be realized by increasing the SOC of Sb by 0.3 times, which drives MnSb2Te4 from a trivial AFM insulator to an AFM topological insulator (TI) or axion insulator. Uniaxial compressive strain along the layer stacking direction is another way to control the band inversion. The interlayer distance shorten by 5% is needed to drive the similar TPT. For the ferromagnetic (FM) MnSb2Te4 with experimental crystal structure, it is a normal FM insulator. The band inversion can happen when SOC is enhanced by 0.1 times or the interlayer distance is decreased by more than 1%. Thus, FM MnSb2Te4 can be tuned to be the simplest type-I Weyl semimetal with only one pair of Weyl nodes on the three-fold rotational axis. These two Weyl nodes are projected onto (1-10) surface with one Fermi arc connecting them.

Weyl fermions in ferromagnetic high-temperature phase of K2Cr8O16

By combining first-principles calculations and symmetry arguments, we propose that the half-metallic phase of K2Cr8O16 presents ferromagnetic Weyl fermions. In particular, K2Cr8O16 possesses two pairs of Weyl nodes, which originate from two groups of nodal lines connected by the mirror reflection symmetry. We show that the non-trivial topological properties of K2Cr8O16 come from the partially occupied t2g states of Cr, and we also demonstrate that such exotic topological feature is robust. The topological surface states and corresponding Fermi arcs are revealed. As K2Cr8O16 is a realistic and widely studied material, our results suggest that K2Cr8O16 is an ideal candidate for studying ferromagnetic Weyl fermions. In addition, K2Cr8O16 possesses several interesting phenomena, such as the co-existence of charge density wave and Weyl fermions, even pairs of FM Weyl points, and tunable distribution of Weyl points, which will attract intensive attentions in this field.

Topological electronic state and anisotropic Fermi surface in half-Heusler GdPtBi

Half-Heusler alloys possess unique and desirable physical properties due to their thermoelectricity, magnetism, superconductivity, and weak antilocalization effects. These properties have become of particular interest since the recent discovery of topological Weyl semimetal state for which the electronic bands are dispersed linearly around one pair of Weyl nodes, with opposite chirality (i.e., chiral anomaly). Here, we report the transport signatures of topological electronic state in a half-Heusler GdPtBi single crystal. We show that the non-trivial π Berry phase, negative magnetoresistance and giant planner Hall effect arise from the chiral anomaly and that the Shubnikov–de Haas oscillation frequency in GdPtBi is angle-dependent with an anisotropic Fermi surface (FS). All transport signatures not only demonstrate the topological electronic state in half-Heusler GdPtBi crystals, but also describe the shape of the anisotropy FS.

Magnetic Semimetals and Quantized Anomalous Hall Effect in EuB_{6}.

Exploration of the novel relationship between magnetic order and topological semimetals has received enormous interest in a wide range of both fundamental and applied research. Here we predict that "soft" ferromagnetic material EuB_{6} can achieve multiple topological semimetal phases by simply tuning the direction of the magnetic moment. Explicitly, EuB_{6} is a topological nodal-line semimetal when the moment is aligned along the [001] direction, and it evolves into a Weyl semimetal with three pairs of Weyl points by rotating the moment to the [111] direction. Interestingly, we identify a composite semimetal phase featuring the coexistence of a nodal line and Weyl points with the moment in the [110] direction. Topological surface states and anomalous Hall conductivity, which are sensitive to the magnetic order, have been computed and are expected to be experimentally observable. Large-Chern-number quantum anomalous Hall effect can be realized in its [111]-oriented quantum-well structures.

Nonlocal annihilation of Weyl fermions in correlated systems

Weyl semimetals (WSMs) are characterized by topologically stable pairs of nodal points in the band structure, that typically originate from splitting a degenerate Dirac point by breaking symmetries such as time reversal or inversion symmetry. Within the independent electron approximation, the transition between an insulating state and a WSM requires the local creation or annihilation of one or several pairs of Weyl nodes in reciprocal space. Here, we show that strong electron-electron interactions may qualitatively change this scenario. In particular, we reveal that the transition to a Weyl semi-metallic phase can become discontinuous, and, quite remarkably, pairs of Weyl nodes with a finite distance in momentum space suddenly appear or disappear in the spectral function. We associate this behavior to the buildup of strong many-body correlations in the topologically non-trivial regions, manifesting in dynamical fluctuations in the orbital channel. We also highlight the impact of electronic correlations on the Fermi arcs.

Zeeman-splitting-induced topological nodal structure and anomalous Hall conductivity in ZrTe5

We investigate the topological nodal structure of three-dimensional (3D) ZrTe$_5$ driven by Zeeman splitting as a function of the direction of external magnetic (B) field by using a Wannier-function-based tight-binding (WFTB) model obtained from first-principles calculations. It is known that small external stimuli can drive 3D ZrTe$_5$ into different topological phases including Dirac semimetal. In order to emphasize the effect of Zeeman splitting, we consider 3D ZrTe$_5$ in a strong TI phase with a small band gap. With Zeeman splitting greater than the band gap, the WFTB model suggests that a type-I nodal ring protected by (glide) mirror symmetry is formed when the B field aligns with the crystal $a$ or $b$ axes, and that a pair of type-I Weyl nodes are formed otherwise, when conduction and valence bands touch. We show that a pair of Weyl nodes can disappear through formation of a nodal ring, rather than requiring two Weyl nodes with opposite chirality to come together. Interestingly, a type-II nodal ring appears from crossings of the top two valence bands when the B field is applied along the $c$ axis. This nodal ring gaps out to form type-II Weyl nodes when the B field rotates in the $bc$ plane. Comparing the WFTB and linearized $k \cdot p$ model, we find inadequacy of the latter at some B field directions. Further, using the WFTB model, we numerically compute the intrinsic anomalous Hall conductivity ${\sigma_{ac}}$ induced by Berry curvature as a function of chemical potential and B field direction. We find that ${\sigma_{ac}}$ increases abruptly when the B field is tilted from the $a$ axis within the $ab$ plane. Our WFTB model also shows significant anomalous Hall conductivity induced by avoided level crossings even in the absence of Weyl nodes.

Magnetic field–induced type II Weyl semimetallic state in geometrically frustrated Shastry-Sutherland lattice GdB4

Weyl semimetal is a topologically non-trivial phase of matter with pairs of Weyl nodes in the k-space, which act as monopole and antimonopole pairs of the Berry curvature. Two hallmarks of the Weyl metallic state are the topological surface state called the Fermi arc and the chiral anomaly. It is known that the chiral anomaly yields anomalous magnetotransport phenomena. In this study, we report the emergence of the type II Weyl semimetallic state in the geometrically frustrated non-collinear antiferromagnetic Shastry-Sutherland lattice (SSL) GdB4 crystal. When we apply magnetic fields perpendicular to the non-collinear moments in the SSL plane, Weyl nodes are created above and below the Fermi energy along the M-A line (τ-band) because the spin tilting breaks the time-reversal symmetry and lifts band degeneracy while preserving C4z or C2z symmetry. The unique electronic structure of GdB4 under magnetic fields applied perpendicular to the SSL gives rise to a non-trivial Berry phase, detected in de Haas-van Alphen experiments, and chiral anomaly–induced negative magnetoresistance. The emergence of the magnetic field–induced Weyl state in the SSL presents a new guiding principle to develop novel types of Weyl semimetals in frustrated spin systems.

Thermodynamic Signatures of Weyl Fermions in NbP

We present a high magnetic field study of NbP—a member of the monopnictide Weyl semimetal (WSM) family. While the monoarsenides (NbAs and TaAs) have topologically distinct left and right-handed Weyl fermi surfaces, NbP is argued to be “topologically trivial” due to the fact that all pairs of Weyl nodes are encompassed by a single Fermi surface. We use torque magnetometry to measure the magnetic response of NbP up to 60 tesla and uncover a Berry paramagnetic response, characteristic of the topological Weyl nodes, across the entire field range. At the quantum limit B* (≈32 T), τ/B experiences a change in slope when the chemical potential enters the last Landau level. Our calculations confirm that this magnetic response arises from band topology of the Weyl pocket, even though the Fermi surface encompasses both Weyl nodes at zero magnetic field. We also find that the magnetic field pulls the chemical potential to the chiral n = 0 Landau level in the quantum limit, providing a disorder-free way of accessing chiral Weyl fermions in systems that are “not quite” WSMs in zero magnetic field.