Symmetry-protected ideal Weyl semimetal in HgTe-class materials

Dai X., Lu H., Shen S., Yao H.

Topological Weyl semimetals can host Weyl nodes with monopole charges in momentum space. How to detect the signature of the monopole charges in quantum transport remains a challenging topic. Here, we reveal the connection between the parity of monopole charge in topological semimetals and the quantum interference corrections to the conductivity. We show that the parity of monopole charge determines the sign of the quantum interference correction, with odd and even parity yielding the weak anti-localization and weak localization effects, respectively. This is attributed to the Berry phase difference between time-reversed trajectories circulating the Fermi sphere that encloses the monopole charges. From standard Feynman diagram calculations, we further show that the weak-field magnetoconductivity at low temperatures is proportional to $+\sqrt{B}$ in double-Weyl semimetals and $-\sqrt{B}$ in Weyl semimetals, respectively, which could be verified experimentally.

Ming W., Wang Z.F., Zhou M., Yoon M., Liu F.

Spin splitting of Rashba states in two-dimensional electron system provides a promising mechanism of spin manipulation for spintronics applications. However, Rashba states realized experimentally to date are often outnumbered by spin-degenerated substrate states at the same energy range, hindering their practical applications. Here, by density functional theory calculation, we show that Au one monolayer film deposition on a layered semiconductor surface beta-InSe(0001) can possess "ideal" Rashba states with large spin splitting, which are completely situated inside the large band gap of the substrate. The position of the Rashba bands can be tuned over a wide range with respect to the substrate band edges by experimentally accessible strain. Furthermore, our nonequilibrium Green's function transport calculation shows that this system may give rise to the long-sought strong current modulation when made into a device of Datta-Das transistor. Similar systems may be identified with other metal ultrathin films and layered semiconductor substrates to realize ideal Rashba states.

Soluyanov A.A., Gresch D., Wang Z., Wu Q., Troyer M., Dai X., Bernevig B.A.

Fermions—elementary particles such as electrons—are classified as Dirac, Majorana or Weyl. Majorana and Weyl fermions had not been observed experimentally until the recent discovery of condensed matter systems such as topological superconductors and semimetals, in which they arise as low-energy excitations. Here we propose the existence of a previously overlooked type of Weyl fermion that emerges at the boundary between electron and hole pockets in a new phase of matter. This particle was missed by Weyl because it breaks the stringent Lorentz symmetry in high-energy physics. Lorentz invariance, however, is not present in condensed matter physics, and by generalizing the Dirac equation, we find the new type of Weyl fermion. In particular, whereas Weyl semimetals—materials hosting Weyl fermions—were previously thought to have standard Weyl points with a point-like Fermi surface (which we refer to as type-I), we discover a type-II Weyl point, which is still a protected crossing, but appears at the contact of electron and hole pockets in type-II Weyl semimetals. We predict that WTe2 is an example of a topological semimetal hosting the new particle as a low-energy excitation around such a type-II Weyl point. The existence of type-II Weyl points in WTe2 means that many of its physical properties are very different to those of standard Weyl semimetals with point-like Fermi surfaces.

Xiong J., Kushwaha S.K., Liang T., Krizan J.W., Hirschberger M., Wang W., Cava R.J., Ong N.P.

Breaking chiral symmetry in a solid Dirac semimetals have graphene-like electronic structure, albeit in three rather than two dimensions. In a magnetic field, their Dirac cones split into two halves, one supporting left-handed and the other right-handed fermions. If an electric field is applied parallel to the magnetic field, this “chiral” symmetry may break: a phenomenon called the chiral anomaly. Xiong et al. observed this anomaly in the Dirac semimetal Na3Bi (see the Perspective by Burkov). Transport measurements lead to the detection of the predicted large negative magnetoresistance, which appeared only when the two fields were nearly parallel to each other. Science, this issue p. 413, see also p. 378 Transport measurements in a magnetic field indicate the breaking of chiral symmetry. [Also see Perspective by Burkov] In a Dirac semimetal, each Dirac node is resolved into two Weyl nodes with opposite “handedness” or chirality. The two chiral populations do not mix. However, in parallel electric and magnetic fields (E||B), charge is predicted to flow between the Weyl nodes, leading to negative magnetoresistance. This “axial” current is the chiral (Adler-Bell-Jackiw) anomaly investigated in quantum field theory. We report the observation of a large, negative longitudinal magnetoresistance in the Dirac semimetal Na3Bi. The negative magnetoresistance is acutely sensitive to deviations of the direction of B from E and is incompatible with conventional transport. By rotating E (as well as B), we show that it is consistent with the prediction of the chiral anomaly.

Yang L.X., Liu Z.K., Sun Y., Peng H., Yang H.F., Zhang T., Zhou B., Zhang Y., Guo Y.F., Rahn M., Prabhakaran D., Hussain Z., Mo S.-., Felser C., Yan B., et. al.

Experiments show that TaAs is a three-dimensional topological Weyl semimetal. Three-dimensional (3D) topologicalWeyl semimetals (TWSs) represent a state of quantum matter with unusual electronic structures that resemble both a ‘3D graphene’ and a topological insulator. Their electronic structure displays pairs of Weyl points (through which the electronic bands disperse linearly along all three momentum directions) connected by topological surface states, forming a unique arc-like Fermi surface (FS). Each Weyl point is chiral and contains half the degrees of freedom of a Dirac point, and can be viewed as a magnetic monopole in momentum space. By performing angle-resolved photoemission spectroscopy on the non-centrosymmetric compound TaAs, here we report its complete band structure, including the unique Fermi-arc FS and linear bulk band dispersion across the Weyl points, in agreement with the theoretical calculations1,2. This discovery not only confirms TaAs as a 3DTWS, but also provides an ideal platform for realizing exotic physical phenomena (for example, negative magnetoresistance, chiral magnetic effects and the quantum anomalous Hall effect) which may also lead to novel future applications.

Xu S., Alidoust N., Belopolski I., Yuan Z., Bian G., Chang T., Zheng H., Strocov V.N., Sanchez D.S., Chang G., Zhang C., Mou D., Wu Y., Huang L., Lee C., et. al.

Three types of fermions play a fundamental role in our understanding of nature: Dirac, Majorana and Weyl. Whereas Dirac fermions have been known for decades, the latter two have not been observed as any fundamental particle in high-energy physics, and have emerged as a much-sought-out treasure in condensed matter physics. A Weyl semimetal is a novel crystal whose low-energy electronic excitations behave as Weyl fermions. It has received worldwide interest and is believed to open the next era of condensed matter physics after graphene and three-dimensional topological insulators. However, experimental research has been held back because Weyl semimetals are extremely rare in nature. Here, we present the experimental discovery of the Weyl semimetal state in an inversion-symmetry-breaking single-crystalline solid, niobium arsenide (NbAs). Utilizing the combination of soft X-ray and ultraviolet photoemission spectroscopy, we systematically study both the surface and bulk electronic structure of NbAs. We experimentally observe both the Weyl cones in the bulk and the Fermi arcs on the surface of this system. Our ARPES data, in agreement with our theoretical band structure calculations, identify the Weyl semimetal state in NbAs, which provides a real platform to test the potential of Weyltronics. Experiments show that niobium arsenide is a Weyl semimetal.

Lv B.Q., Xu N., Weng H.M., Ma J.Z., Richard P., Huang X.C., Zhao L.X., Chen G.F., Matt C.E., Bisti F., Strocov V.N., Mesot J., Fang Z., Dai X., Qian T., et. al.

Experiments show that TaAs is a three-dimensional topological Weyl semimetal. In 1929, H. Weyl proposed that the massless solution of the Dirac equation represents a pair of a new type of particles, the so-called Weyl fermions1. However, their existence in particle physics remains elusive after more than eight decades. Recently, significant advances in both topological insulators and topological semimetals have provided an alternative way to realize Weyl fermions in condensed matter, as an emergent phenomenon: when two non-degenerate bands in the three-dimensional momentum space cross in the vicinity of the Fermi energy (called Weyl nodes), the low-energy excitations behave exactly as Weyl fermions. Here we report the direct observation in TaAs of the long-sought-after Weyl nodes by performing bulk-sensitive soft X-ray angle-resolved photoemission spectroscopy measurements. The projected locations at the nodes on the (001) surface match well to the Fermi arcs, providing undisputable experimental evidence for the existence of Weyl fermionic quasiparticles in TaAs.

Xu S., Belopolski I., Alidoust N., Neupane M., Bian G., Zhang C., Sankar R., Chang G., Yuan Z., Lee C., Huang S., Zheng H., Ma J., Sanchez D.S., Wang B., et. al.

Weyl physics emerges in the laboratory Weyl fermions—massless particles with half-integer spin—were once mistakenly thought to describe neutrinos. Although not yet observed among elementary particles, Weyl fermions may exist as collective excitations in so-called Weyl semimetals. These materials have an unusual band structure in which the linearly dispersing valence and conduction bands meet at discrete “Weyl points.” Xu et al. used photoemission spectroscopy to identify TaAs as a Weyl semimetal capable of hosting Weyl fermions. In a complementary study, Lu et al. detected the characteristic Weyl points in a photonic crystal. The observation of Weyl physics may enable the discovery of exotic fundamental phenomena. Science , this issue p. 613 and 622

Huang S., Xu S., Belopolski I., Lee C., Chang G., Wang B., Alidoust N., Bian G., Neupane M., Zhang C., Jia S., Bansil A., Lin H., Hasan M.Z.

Weyl fermions are massless chiral fermions that play an important role in quantum field theory but have never been observed as fundamental particles. A Weyl semimetal is an unusual crystal that hosts Weyl fermions as quasiparticle excitations and features Fermi arcs on its surface. Such a semimetal not only provides a condensed matter realization of the anomalies in quantum field theories but also demonstrates the topological classification beyond the gapped topological insulators. Here, we identify a topological Weyl semimetal state in the transition metal monopnictide materials class. Our first-principles calculations on TaAs reveal its bulk Weyl fermion cones and surface Fermi arcs. Our results show that in the TaAs-type materials the Weyl semimetal state does not depend on fine-tuning of chemical composition or magnetic order, which opens the door for the experimental realization of Weyl semimetals and Fermi arc surface states in real materials. Proposals for the realization of Weyl semimetals, topologically non-trivial materials which host Weyl fermion quasiparticles, have faced demanding experimental requirements. Here, the authors predict such a state in stoichiometric TaAs, arising due to the breaking of inversion symmetry.

Jian S., Jiang Y., Yao H.

Supersymmetry (SUSY) interchanges bosons and fermions but no direct evidence of it has been revealed in nature yet. In this Letter, we observe that fluctuating pair density waves (PDW) consist of two complex order parameters which can be superpartners of the unavoidably doubled Weyl fermions in three-dimensional lattice models. We construct explicit fermionic lattice models featuring 3D Weyl fermions and show that PDW is the leading instability via a continuous phase transition as short-range interactions exceed a critical value. Using a renormalization group, we theoretically show that N=2 space-time SUSY emerges at the continuous PDW transitions in 3D Weyl semimetals, which we believe is the first realization of emergent (3+1)D space-time SUSY in microscopic lattice models. We further discuss possible routes to realize such lattice models and experimental signatures of emergent SUSY at the PDW criticality.

Hirayama M., Okugawa R., Ishibashi S., Murakami S., Miyake T.

We study Weyl nodes in materials with broken inversion symmetry. We find based on first-principles calculations that trigonal Te and Se have multiple Weyl nodes near the Fermi level. The conduction bands have a spin splitting similar to the Rashba splitting around the H points, but unlike the Rashba splitting the spin directions are radial, forming a hedgehog spin texture around the H points, with a nonzero Pontryagin index for each spin-split conduction band. The Weyl semimetal phase, which has never been observed in real materials without inversion symmetry, is realized under pressure. The evolution of the spin texture by varying the pressure can be explained by the evolution of the Weyl nodes in k space.

Liu J., Vanderbilt D.

We study the problem of phase transitions from 3D topological to normal insulators without inversion symmetry. In contrast with the conclusions of some previous work, we show that a Weyl semimetal always exists as an intermediate phase regardless of any constriant from lattice symmetries, although the interval of the critical region is sensitive to the choice of path in the parameter space and can be very narrow. We demonstrate this behavior by carrying out first-principles calculations on the noncentrosymmetric topological insulators LaBiTe$_3$ and LuBiTe$_3$ and the trivial insulator BiTeI. We find that a robust Weyl-semimetal phase exists in the solid solutions LaBi$_{1-x}$Sb$_x$Te$_3$ and LuBi$_{1-x}$Sb$_x$Te$_3$ for $x\!\approx\!38.5-41.9$\% and $x\!\approx\!40.5-45.1$\% respectively. A low-energy effective model is also constructed to describe the critical behavior in these two materials. In BiTeI, a Weyl semimetal also appears with applied pressure, but only within a very small pressure range, which may explain why it has not been experimentally observed.

Zhang H., Wang J., Xu G., Xu Y., Zhang S.

Based on ab initio calculations, we demonstrate that the ferromagnetic CdO/EuO superlattice is a simple Weyl semimetal with two linear Weyl nodes in the Brillouin zone, and the corresponding CdO/EuO quantum well realizes the stichometric quantum anomalous Hall state without random magnetic doping. In addition, a simple effective model is presented to describe the basic mechanism of spin polarized band inversion in this system.

Hosur P., Qi X.

The last decade has witnessed great advancements in the science and engineering of systems with unconventional band structures, seeded by studies of graphene and topological insulators. While the band structure of graphene simulates massless relativistic electrons in two dimensions, topological insulators have bands that wind non-trivially over momentum space in a certain abstract sense. Over the last couple of years, enthusiasm has been burgeoning in another unconventional and topological (although, not quite in the same sense as topological insulators) phase -- the Weyl Semimetal. In this phase, electrons mimic Weyl fermions that are well-known in high-energy physics, and inherit many of their properties, including an apparent violation of charge conservation known as the Chiral Anomaly. In this review, we recap some of the unusual transport properties of Weyl semimetals discussed in the literature so far, focusing on signatures whose roots lie in the anomaly. We also mention several proposed realizations of this phase in condensed matter systems, since they were what arguably precipitated activity on Weyl semimetals in the first place.

Son D.T., Spivak B.Z.

We consider the classical magnetoresistance of a Weyl metal in which the electron Fermi surface possesses nonzero fluxes of the Berry curvature. Such a system may exhibit large negative magnetoresistance with unusual anisotropy as a function of the angle between the electric and magnetic fields. In this case the system can support an additional type of plasma wave. These phenomena are consequences of the chiral anomaly in electron transport theory.

Kong W., Xiao X., Wei J., Wang R., Wu X.

Yin C., Jiang H., Lv Y., Yao S., Zhou J., Chen Y.B., Chen Y.

Aglagul D., Shi J.

We present theoretical observations on the topological nature of strained III–V semiconductors. By k·p perturbation, it can be shown that the strain-engineered conduction band hosts a Kramers–Weyl node at the Γ point. It is theoretically shown that a curated strain can create and then tune the sign of the topological charge. Furthermore, we outline experimental methods for both the realization and detection of strain-induced topological phase transitions.

Yadav S., Ptok A.

Zhu T., Ni H., Wei B., Wang H.

Wang Z., Wang M., Zhou Y., Wang G., Zhong H.

Zhu P., Zhang R.

Pandey V., Pandey S.K.

This work establishes the existence of dispersive nodal-arcs and their evolution into Weyl nodes under the effect of spin-orbit coupling (SOC) in NbAs and NbP. The obtained features mimic the observations as reported for TaAs and TaP in our previous work (Pandey in J Phys Condens Matter 35:455501, 2023). In addition, this work reports that the number of nodes in the TaAs class of Weyl semimetals (WSMs) can be altered by creating strain along a or c direction of the crystals. For instance, the number of nodes in NbAs under SOC-effect along with 2% (3%) tensile-strain in a direction is found to be 40 (56) in its full Brillouin zone (BZ). Besides the nodes, such strain are found to have considerable impact on the nodal-lines of these WSMs when effect of SOC is ignored. In the absence of SOC, a 3% tensile (compressive) strain along the a (c) direction leads to the partially merging of nodal-lines in the extended BZ of NbAs and NbP, which is not observed in TaAs and TaP within the range of – 3% to 3% strain. Apart from this, the work discusses the role of Weyl physics in affecting the Seebeck coefficient (S) of any WSM. In this direction, it is discussed that how a symmetric Weyl cone, even if tilted, will have no contribution to the S of WSMs. Furthermore, the work highlights the conditions under which a Weyl cone can contribute to the S of a given WSM. Next, the discussion of Weyl contribution to S is validated over TaAs class of WSMs via investigating the features of their Weyl cones and calculating the contributions of such cones to the S of these semimetals. Weyl-cone contributed S in these WSMs is found to be anisotropic within the temperature range of 0–100 K. The value of S contributed from Weyl cone is found to be as large as $$\sim $$ 70 $$\mu $$ V/K below 25 K in case of NbP. Lastly, the expected effect of axial strain and change in SOC-strength on S of TaAs class of WSMs is discussed. The findings of this work present a possibility of engineering the topological properties of TaAs class of WSMs via creating strain in their crystal. It also makes the picture of Weyl physics’  impact on the S of WSMs a more clear.

Medel L., Ghosh R., Martín-Ruiz A., Mandal I.

We continue our investigation of the response tensors in planar Hall (or planar thermal Hall) configurations where a three-dimensional Weyl/multi-Weyl semimetal is subjected to the combined influence of an electric field $${\textbf{E}}$$ (and/or temperature gradient $$\nabla _{{\textbf{r}} } T$$ ) and an effective magnetic field $${\textbf{B}}_\chi$$ , generalizing the considerations of Phys. Rev. B 108 (2023) 155132 and Physica E 159 (2024) 115914. The electromagnetic fields are oriented at a generic angle with respect to each other, thus leading to the possibility of having collinear components, which do not arise in a Hall set-up. The net effective magnetic field $${\textbf{B}}_\chi$$ consists of two parts—(a) an actual/physical magnetic field $${\textbf{B}}$$ applied externally; and (b) an emergent magnetic field $${\textbf{B}}_5$$ which quantifies the elastic deformations of the sample. $${\textbf{B}}_5$$ is an axial pseudomagnetic field because it couples to conjugate nodal points with opposite chiralities with opposite signs. Using a semiclassical Boltzmann formalism, we derive the generic expressions for the response tensors, including the effects of the Berry curvature (BC) and the orbital magnetic moment (OMM), which arise due to a nontrivial topology of the bandstructures. We elucidate the interplay of the BC-only and the OMM-dependent parts in the longitudinal and transverse (or Hall) components of the electric, thermal, and thermoelectric response tensors. Especially, for the co-planar transverse components of the response tensors, the OMM part acts exclusively in opposition (sync) with the BC-only part for the Weyl (multi-Weyl) semimetals.

Yang A.Z., Liu Z.

Cheng Y., Liu D., Liu X., Zhang R., Cui X., Liu Z., Song T.

Fan Y., Wang H., Tang P., Murakami S., Wan X., Zhang H., Xing D.

Liang Y., Lin X., Wan B., Guo Z., Cao X., Shao D., Sun J., Gou H.

Topological electrides have attracted extensive attention, not only serving as good platforms for studying Dirac fermion, Weyl fermion, and diverse quasiparticles beyond the Dirac and Weyl fermions, but also hosting rich physical and chemical properties such as low work function, high conductivity, and high electron mobility. Motivated by the synthesized YCl and Y2Cl3 electrides with nontrivial topology, we have explored the Y-Cl binary system under pressure. Based on the first-principles calculations and crystal-structure prediction techniques, we find a t-YCl phase with the space group of P4/ that is both thermodynamically and lattice dynamically stable, and also recoverable to the ambient condition. Based on the k·p method and irreducible representation analyses, we propose that t-YCl has a topological nodal chain surrounding the Z point in the Brillouin zone without spin-orbit coupling (SOC), and evolves into a Dirac semimetal phase with two Dirac points protected by R4z symmetry when taking SOC into consideration. In addition, based on the band representation (BR) analyses, we find the highest occupied bands belong to A1@2a BR. Since both the Y and Cl atoms occupy the 2c Wyckoff positions, i.e., no atom in t-YCl system locates at the 2a Wyckoff positions, it thus suggests the unconventional nature of an uncompensated state at the 2a Wyckoff position. Remembering the ionic compound nature, the unconventional t-YCl phase hosts great potential to be an electride material, which has been further verified by our electron localization function calculations, with the uncompensated state at 2a Wyckoff position contributed by the interstitial quasiatoms. Our work provides a good theoretical and experimental platform for the study of pressure-induced topological electride states. Published by the American Physical Society 2024

Li M., Wang Z., Ding Z., Tao Y., Huang F.

We investigate the quantum interference of the electron–hole conversions from the two interfaces in a Weyl semimetal (WSM)-based hybrid structure, in which a superconducting WSM is sandwiched in between two normal ones. The quantum interference is characterized by the chirality-anomaly-manipulation (CAM). It is found that only low energy is in favor for s-wave BCS pairing states. The Andreev reflection (AR) chirality blockade can be tuned by the stagger angle α for the relative orientation of paired Weyl points, accompanied by an AR bipolar chirality diode. Thus, a strong CAM is indicated for the electron–hole conversion. However, the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) pairing states have no energy preference, with the weak and strong CAMs being near and far away from the zero energy, respectively. More interestingly, a perfect AR with the normal reflection suppressed thoroughly can be obtained at any α as a result of the FFLO paring with the same chirality. In addition, the conductance or noise power, which incorporates the contributions of the two paired Weyl nodes, not only, in turn, embodies the respective features of their contributions but also can be experimentally measured to discern between the BCS and FFLO paring states.

Ponomarenko Vladimir P., Popov Victor, Shuklov Ivan, Ivanov Victor V., Razumov Vladimir F.

Photosensing based on colloidal quantum dots (CQDs) is a rapidly developing area of infrared photoelectronics. The use of colloidal quantum dots markedly simplifies the manufacture, decreases the restrictions to the pixel pitch of the photosensitive elements, and reduces the production cost, which facilitates the wide use of IR sensors in various technological systems. This paper is the first exhaustive overeview of the architectures, methods of manufacturing and basic properties of photonic sensors based on colloidal quantum dots of compounds of Group II, IV and VI elements. Characteristic features of the synthesis and roles of the ligands and CQD morphology in the design of photosensors are considered in detail. The structures of photoresistive, photodiode and phototransistor elements based on HgTe, HgSe, PbS and PbSe CQDs, which are sensitive in various spectral ranges, are described. The main parameters of the most advanced optoelectronic devices based on colloidal quantum dot structures are presented. The key trends in the development of this area are analyzed.The bibliography includes 361 references.