Search

The nonlinear Hall effect (NLHE) is a phenomenon which could produce a transverse Hall voltage in a time-reversal-invariant material. Here, we report the real space characterization of NLHE evaluated through quantum transport in TaIrTe4 nanoribbon without the explicit Berry curvature dipole (BCD) information. We first characterize the NLHE in both transverse confined directions in global-level measurement. The impact of quantum confinement in NLHE is evaluated by adjusting the width of nanoribbons. Then, the probing area is trimmed to the atomic scale to evaluate the local texture, where we discover its unique patterns among the probed atomic groups for the first time. The analysis of charge distribution reveals the connections between NLHE's local patterns and its non-centrosymmetric nature, rendering nearly an order of Hall voltage enhancement through probe positioning. Our work paves the way to expand the range of NLHE study and unveil its physics in more versatile material systems.

Nontrivial band topologies in semimetals lead to robust surface states that can contribute dominantly to the total conduction. This may result in reduced resistivity with decreasing feature size contrary to conventional metals, which may highly impact the semiconductor industry. Here we study the resistivity scaling of a representative topological semimetal CoSi using realistic band structures and Green's function methods. We show that there exists a critical thickness d_c dividing different scaling trends. Above d_c, when the defect density is low such that surface conduction dominates, resistivity reduces with decreasing thickness; when the defect density is high such that bulk conduction dominates, resistivity increases in as conventional metals. Below d_c, the persistent remnants of the surface states give rise to decreasing resistivity down to the ultrathin limit, unlike in topological insulators. The observed CoSi scaling can apply to broad classes of topological semimetals, providing guidelines for materials screening and engineering. Our study shows that topological semimetals bear the potential of overcoming the resistivity scaling challenges in back-end-of-line interconnect applications.

MnBi2Te4 (MBT) is the first intrinsic magnetic topological insulator with the interaction of spin-momentum locked surface electrons and intrinsic magnetism, and it exhibits novel magnetic and topological phenomena. Recent studies suggested that the interaction of electrons and magnetism can be affected by the Mn-doped Bi2Te3 phase at the surface due to inevitable structural defects. Here we report an observation of nonreciprocal transport, i.e. current-direction-dependent resistance, in a bilayer composed of antiferromagnetic MBT and nonmagnetic Pt. The emergence of the nonreciprocal response below the N\'eel temperature confirms a correlation between nonreciprocity and intrinsic magnetism in the surface state of MBT. The angular dependence of the nonreciprocal transport indicates that nonreciprocal response originates from the asymmetry scattering of electrons at the surface of MBT mediated by magnon. Our work provides an insight into nonreciprocity arising from the correlation between magnetism and Dirac surface electrons in intrinsic magnetic topological insulators.

A charge density wave (CDW) of a nonzero ordering vector $\mathbf{q}$ couple electronic states at $\mathbf{k}$ and $\mathbf{k}+\mathbf{q}$ statically, giving rise to a reduced Brillouin zone (RBZ) due to the band folding effect. Its structure, in terms of an irreducible representation of the little group of $\mathbf{q}$, would change the symmetry of the system and electronic structure accompanying possible change of band inversion, offering a chance of the topological phase transition. Monolayer 1\textit{T}-TiSe$_2$ is investigated for it shows an unconventional CDW phase having a triple-$q$ $M_1^-$ structure. Moreover, the coupling between the triple-$q$ component of the $M_1^-$ CDW will inevitably produce a small $M_1^+$ CDW. The CDW yields a band inversion in 1\textit{T}-TiSe$_2$ but different types of CDW can affect the electronic structure and system topology differently. The impact of CDW of different types was studied by utilizing a symmetrization-antisymmetrization technique to extract the $M_1^-$ and $M_1^+$ CDW contributions in the DFT-based tight-binding model and study their effects. The results are consistent with the parity consideration, improving understanding of topology for a CDW system with and without parity., Comment: 8 pages, 6 figures. Accepted by New. J. Phys

Weyl semimetal Td-phase WTe2 possesses the spin-resolved band structure with strong spin-orbit coupling, holding promises as a useful spin source material. The noncentrosymmetric crystalline structure of Td-WTe2 endows the generation of the out-of-plane polarized spin, which is of great interest in magnetic memory applications. Previously, WTe2 was explored in spin devices based on mechanically exfoliated single crystal flakes with a size of micrometers. For practical spintronics applications, it is highly desirable to implement wafer-scale thin films. In this work, we utilize centimeter-scale chemical vapor deposition (CVD)-grown Td-WTe2 thin films and study the spin current generation by the spin torque ferromagnetic resonance technique. We find the in-plane and out-of-plane spin conductivities of 7.36 x 10^3 (h/2e) (ohm-m)^-1 and 1.76 x 10^3 (h/2e) (ohm-m)^-1, respectively, in CVD-growth 5 nm-WTe2. We further demonstrate the current-induced magnetization switching in WTe2/NiFe at room temperature in the domain wall motion regime, which may invigorate potential spintronic device innovations based on Weyl semimetals.

The resistance bottleneck in metal-interconnect scaling calls for new interconnect materials. This paper explores topological semimetals as a potential solution. After reviewing the desirable properties of topological semimetals for back-end-of-line (BEOL) interconnects, we use CoSi as an example to demonstrate the decreasing resistance-area product with scaling and provide material-search guidelines., Comment: 4 pages, 12 figures

The nonlinear Hall effect (NLHE), which can produce a transverse voltage without any magnetic field, is a potential alternative for rectification or frequency doubling. However, the low temperature detection of NLHE limits its applications. Here, we report the room-temperature NLHE in a type-II Weyl semimetal TaIrTe4, which hosts a robust NLHE due to substantial broken inversion symmetry and large band overlapping at the Fermi level. We also observe a temperature-induced sign inversion of NLHE in TaIrTe4. Our theoretical calculations suggest that the observed sign inversion is a result of temperature-induced shift in the chemical potential indicating a direct correlation of NLHE with the electronic structure at the Fermi surface. Finally, the room-temperature NLHE in TaIrTe4 is exploited to demonstrate the wireless RF rectification with zero external bias and magnetic field. This work opens a door to realizing room temperature applications based on the NLHE in Weyl semimetals.

The nonlinear Hall effect due to Berry curvature dipole (BCD) induces frequency doubling, which was recently observed in time-reversal-invariant materials. Here we report novel electric frequency doubling in the absence of BCD on a surface of the topological insulator Bi2Se3 under zero magnetic field. We observe that the frequency-doubling voltage transverse to the applied ac current shows a threefold rotational symmetry, whereas it forbids BCD. One of the mechanisms compatible with the symmetry is skew scattering, arising from the inherent chirality of the topological surface state. We introduce the Berry curvature triple, a high-order moment of the Berry curvature, to explain skew scattering under the threefold rotational symmetry. Our work paves the way to obtain a giant second-order nonlinear electric effect in high mobility quantum materials, as the skew scattering surpasses other mechanisms in the clean limit.

We report an unconventional quantum spin Hall phase in the monolayer T$_\text{d}$-WTe$_2$, which exhibits hitherto unknown features in other topological materials. The low-symmetry of the structure induces a canted spin texture in the $yz$ plane, which dictates the spin polarization of topologically protected boundary states. Additionally, the spin Hall conductivity gets quantized ($2e^2/h$) with a spin quantization axis parallel to the canting direction. These findings are based on large-scale quantum simulations of the spin Hall conductivity tensor and nonlocal resistances in multi-probe geometries using a realistic tight-binding model elaborated from first-principle methods. The observation of this canted quantum spin Hall effect, related to the formation of topological edge states with nontrivial spin polarization, demands for specific experimental design and suggests interesting alternatives for manipulating spin information in topological materials., Comment: For comments please contact josehugo.garcia@icn2.cat

The spin polarization induced by the spin Hall effect (SHE) in thin films typically points out of the plane. This is rooted on the specific symmetries of traditionally studied systems, not in a fundamental constraint. Recently, experiments on few-layer ${\rm MoTe}_2$ and ${\rm WTe}_2$ showed that the reduced symmetry of these strong spin-orbit coupling materials enables a new form of {\it canted} spin Hall effect, characterized by concurrent in-plane and out-of-plane spin polarizations. Here, through quantum transport calculations on realistic device geometries, including disorder, we predict a very large gate-tunable SHE figure of merit $\lambda_s\theta_{xy}\sim 1\text{--}50$ nm in ${\rm MoTe}_2$ and ${\rm WTe}_2$ monolayers that significantly exceeds values of conventional SHE materials. This stems from a concurrent long spin diffusion length ($\lambda_s$) and charge-to-spin interconversion efficiency as large as $\theta_{xy} \approx 80$\%, originating from momentum-invariant (persistent) spin textures together with large spin Berry curvature along the Fermi contour, respectively. Generalization to other materials and specific guidelines for unambiguous experimental confirmation are proposed, paving the way towards exploiting such phenomena in spintronic devices. These findings vividly emphasize how crystal symmetry and electronic topology can govern the intrinsic SHE and spin relaxation, and how they may be exploited to broaden the range and efficiency of spintronic materials and functionalities., Comment: Published version, Phys. Rev. Reserach

The ability to switch magnetic elements by spin-orbit-induced torques has recently attracted much attention for a path towards high-performance, non-volatile memories with low power consumption. Realizing efficient spin-orbit-based switching requires harnessing both new materials and novel physics to obtain high charge-to-spin conversion efficiencies, thus making the choice of spin source crucial. Here we report the observation of spin-orbit torque switching in bilayers consisting of a semimetallic film of 1T'-MoTe2 adjacent to permalloy. Deterministic switching is achieved without external magnetic fields at room temperature, and the switching occurs with currents one order of magnitude smaller than those typical in devices using the best-performing heavy metals. The thickness dependence can be understood if the interfacial spin-orbit contribution is considered in addition to the bulk spin Hall effect. Further threefold reduction in the switching current is demonstrated with resort to dumbbell-shaped magnetic elements. These findings foretell exciting prospects of using MoTe2 for low-power semimetal material based spin devices.

Topological electrons in semimetals are usually vulnerable to chemical doping and environment change, which restricts their potential application in future electronic devices. In this paper we report that the type-II Dirac semimetal $\mathbf{VAl_3}$ hosts exceptional, robust topological electrons which can tolerate extreme change of chemical composition. The Dirac electrons remain intact even after a substantial part of V atoms have been replaced in the $\mathbf{V_{1-x}Ti_xAl_3}$ solid solutions. This Dirac semimetal state ends at $x=0.35$ where a Lifshitz transition to $p$-type trivial metal occurs. The V-Al bond is completely broken in this transition as long as the bonding orbitals are fully depopulated by the holes donated from Ti substitution. In other words, the Dirac electrons in $\mathbf{VAl_3}$ are protected by the V-Al bond whose molecular orbital is their bonding gravity center. Our understanding on the interrelations among electron count, chemical bond and electronic properties in topological semimetals suggests a rational approach to search robust, chemical-bond-protected topological materials.

Most topological insulators discovered today in spinful systems can be transformed from topological semimetals (TSMs) with vanishing bulk gap via introducing the spin-orbit coupling (SOC), which manifests the intrinsic links between the gapped TI phases and the gapless TSMs. Recently, we have proposed a new family of TSMs in time-reversal invariant {\it spinless} systems, which host butterfly-like nodal-lines (NLs) consisting of a pair of identical concentric intersecting coplanar ellipses (CICE). In this Communication, we unveil the intrinsic link between this exotic class of nodal-line semimetals (NLSMs) and a $\mathbb{Z}_{4}$ = 2 topological crystalline insulator (TCI), by including substantial SOC. We demonstrate that in three space groups ({\it i.e.} $Pbam$ (No.55), $P4/mbm$ (No.127) and $P4_2/mbc$ (No.135)), the TCI supports a fourfold Dirac fermion on the (001) surface protected by two glide symmetries, which originates from the intertwined drumhead surface states of the CICE NLs. The higher order topology is further demonstrated by the emergence of one-dimensional helical hinge states, indicating a new higher order topological insulator protected by a glide symmetry., Comment: 6 pages, 3 figures

In recent years, the exotic properties of topological semimetals (TSMs) have attracted great attention and significant efforts have been made in seeking for new topological phases and material realization. In this work, we propose a new family of TSMs which harbors an unprecedented nodal line (NL) landscape consisting of a pair of concentric intersecting coplanar ellipses (CICE) at half-filling. Meanwhile, the CICE at half-filling guarantees the presence of a second pair of CICE beyond half-filling. Both CICEs are linked at four-fold degenerate points (FDPs) at zone boundaries. In addition, we identify the generic criteria for the existence of the CICE in a time reversal invariant {\it spinless} fermion system or a spinfull system with negligible spin-orbital coupling (SOC). Consequently, 9 out of 230 space groups (SGs) are feasible for hosting CICE whose location centers in the first Brillouin zone (BZ) are identified. We provide a simplest model with SG $Pbam$ (No. 55) which exhibits CICE, and the exotic intertwined drumhead surface states, induced by double-band-inversions. Finally, we propose a series of material candidates that host butterfly-like CICE NLs, such as, ZrX$_2$ (X=P,As), GeTe$_5$Tl$_2$, CYB$_2$ and Al$_2$Y$_3$., Comment: 6 pages, 3 figures

The observation of chirality is ubiquitous in nature. Contrary to intuition, the population of opposite chiralities is surprisingly asymmetric at fundamental levels. Examples range from parity violation in the subatomic weak force to the homochirality in essential biomolecules. The ability to achieve chirality-selective synthesis (chiral induction) is of great importance in stereochemistry, molecular biology and pharmacology. In condensed matter physics, a crystalline electronic system is geometrically chiral when it lacks any mirror plane, space inversion center or roto-inversion axis. Typically, the geometrical chirality is predefined by a material's chiral lattice structure, which is fixed upon the formation of the crystal. By contrast, a particularly unconventional scenario is the gyrotropic order, where chirality spontaneously emerges across a phase transition as the electron system breaks the relevant symmetries of an originally achiral lattice. Such a gyrotropic order, proposed as the quantum analogue of the cholesteric liquid crystals, has attracted significant interest. However, to date, a clear observation and manipulation of the gyrotropic order remain challenging. We report the realization of optical chiral induction and the observation of a gyrotropically ordered phase in the transition-metal dichalcogenide semimetal $1T$-TiSe$_2$. We show that shining mid-infrared circularly polarized light near the critical temperature leads to the preferential formation of one chiral domain. As a result, we are able to observe an out-of-plane circular photogalvanic current, whose direction depends on the optical induction. Our study provides compelling evidence for the spontaneous emergence of chirality in the correlated semimetal TiSe$_2$. Such chiral induction provides a new way of optical control over novel orders in quantum materials., Comment: 22 pages, 5 figures

Recent theoretical advances have proposed a new class of topological crystalline insulator (TCI) phases protected by rotational symmetries. Distinct from topological insulators (TIs), rotational symmetry-protected TCIs are expected to show unique topologically protected boundary modes: First, the surface normal to the rotational axis features unpinned Dirac surface states whose Dirac points are located at generic k points. Second, due to the higher-order bulk boundary correspondence, a 3D TCI also supports 1D helical edge states. Despite the unique topological electronic properties, to date, purely rotational symmetry-protected TCIs remain elusive in real materials. Using first-principles band calculations and theoretical modeling, we identify the van der Waals material $\alpha$-Bi4Br4 as a TCI purely protected by rotation symmetry. We show that the Bi4Br4's (010) surface exhibits a pair of unpinned topological Dirac fermions protected by the two-fold rotational axis. These unpinned Dirac fermions show an exotic spin texture highly favorable for spin transport and a band structure consisting of van Hove singularities due to Lifshitz transition. We also identify 1D topological hinge states along the edges of an $\alpha$-Bi4Br4 rod. We further discuss how the proposed topological electronic properties in $\alpha$-Bi4Br4 can be observed by various experimental techniques.

The nature of Fermi surface defines the physical properties of conductors and many physical phenomena can be traced to its shape. Although the recent discovery of a current-dependent nonlinear magnetoresistance in spin-polarized non-magnetic materials has attracted considerable attention in spintronics, correlations between this phenomenon and the underlying fermiology remain unexplored. Here, we report the observation of nonlinear magnetoresistance at room temperature in a semimetal WTe2, with an interesting temperature-driven inversion. Theoretical calculations reproduce the nonlinear transport measurements and allow us to attribute the inversion to temperature-induced changes in Fermi surface convexity. We also report a large anisotropy of nonlinear magnetoresistance in WTe2, due to its low symmetry of Fermi surfaces. The good agreement between experiments and theoretical modeling reveals the critical role of Fermi surface topology and convexity on the nonlinear magneto-response. These results lay a new path to explore ramifications of distinct fermiology for nonlinear transport in condensed-matter.

The electrical Hall effect is the production of a transverse voltage under an out-of-plane magnetic field. Historically, studies of the Hall effect have led to major breakthroughs including the discoveries of Berry curvature and the topological Chern invariants. In magnets, the internal magnetization allows Hall conductivity in the absence of external magnetic field. This anomalous Hall effect (AHE) has become an important tool to study quantum magnets. In nonmagnetic materials without external magnetic fields, the electrical Hall effect is rarely explored because of the constraint by time-reversal symmetry. However, strictly speaking, only the Hall effect in the linear response regime, i.e., the Hall voltage linearly proportional to the external electric field, identically vanishes due to time-reversal symmetry. The Hall effect in the nonlinear response regime, on the other hand, may not be subject to such symmetry constraints. Here, we report the observation of the nonlinear Hall effect (NLHE) in the electrical transport of the nonmagnetic 2D quantum material, bilayer WTe2. Specifically, flowing an electrical current in bilayer WTe2 leads to a nonlinear Hall voltage in the absence of magnetic field. The NLHE exhibits unusual properties sharply distinct from the AHE in metals: The NLHE shows a quadratic I-V characteristic; It strongly dominates the nonlinear longitudinal response, leading to a Hall angle of about 90 degree. We further show that the NLHE directly measures the "dipole moment" of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe2. Our results demonstrate a new Hall effect and provide a powerful methodology to detect Berry curvature in a wide range of nonmagnetic quantum materials in an energy-resolved way.

The charge density wave (CDW) in 1T-TiSe2 accompanied by the periodic lattice distortion has a nontrivial symmetry configuration. The symmetry is important as an indication of the mechanism and a cue for experimental probes. We examine the symmetry of the system and clear up the connection of electronic structures between the normal and the CDW states. Especially, we unravel the consequential irreducible representations (IRs) of electronic states and, more ahead, those of gap functions among bands when the CDW occurs. Normally symmetry-related topology will be achieved directly, so we assert that the theory is valuable and practical for the search of topological CDW insulators., Comment: 13 pages, 5 figures

Topological crystalline insulators (TCI) are insulating electronic phases of matter with nontrivial topology originating from crystalline symmetries. Recent theoretical advances have provided powerful guidelines to search for TCIs in real materials. Using density functional theory, we identify a class of new TCI states in the tetragonal lattice of the Ca$_2$As material family. On both top and side surfaces, we observe topological surface states protected independently by rotational and mirror symmetries. We show that a particular lattice distortion can single out the newly proposed topological protection by the rotational symmetry. As a result, the Dirac points of the topological surface states are moved to generic locations in momentum space away from any high symmetry lines. Such topological surface states have not been seen before. Moreover, the other family members, including Ca$_2$Sb, Ca$_2$Bi and Sr$_2$Sb, feature different topological surface states due to their distinct topological invariants. We thus further propose topological phase transitions in the pseudo-binary systems such as (Ca$_{1-x}$Sr$_x$)$_2$As and Ca$_2$As$_x$Sb$_{1-x}$. Our work reveals rich and exotic TCI physics across the Ca$_2$As family of materials, and suggests the feasibility of materials database search methods to discover new TCIs., Comment: 5 pages, 4 figures

The Weyl semimetal WTe2 and MoTe2 show great potential in generating large spin currents since they possess topologically-protected spin-polarized states and can carry a very large current density. In addition, the intrinsic noncentrosymmetry of WTe2 and MoTe2 endows with a unique property of crystal symmetry-controlled spin-orbit torques. An important question to be answered for developing spintronic devices is how spins relax in WTe2 and MoTe2. Here, we report a room-temperature spin relaxation time of 1.2 ns (0.4 ns) in WTe2 (MoTe2) thin film using the time-resolved Kerr rotation (TRKR). Based on ab initio calculation, we identify a mechanism of long-lived spin polarization resulting from a large spin splitting around the bottom of the conduction band, low electron-hole recombination rate and suppression of backscattering required by time-reversal and lattice symmetry operation. In addition, we find the spin polarization is firmly pinned along the strong internal out-of-plane magnetic field induced by large spin splitting. Our work provides an insight into the physical origin of long-lived spin polarization in Weyl semimetals which could be useful to manipulate spins for a long time at room temperature.

We propose that the quasi-one-dimensional molybdenum selenide compound Tl2-xMo6Se6 is a time-reversal-invariant topological superconductor induced by inter-sublattice pairing, even in the absence of spin-orbit coupling (SOC). No noticeable change in superconductivity is observed in Tl-deficient (0<=x<=0.1) compounds. At weak SOC, the superconductor prefers the triplet d vector lying perpendicular to the chain direction and two-dimensional E2u symmetry, which is driven to a nematic order by spontaneous rotation symmetry breaking. The locking energy of the d vector is estimated to be weak and hence the proof of its direction would rely on tunnelling or phase-sensitive measurements., Comment: 6 pages, 3 figures, 1 table

Charge density wave (CDW) phases are symmetry-reduced states of matter in which a periodic modulation of the electronic charge frequently leads to drastic changes of the electronic spectrum, including the emergence of energy gaps. We analyze the CDW state in a 1T-TiSe$_2$ monolayer within a density functional theory framework and show that, similarly to its bulk counterpart, the monolayer is unstable towards a commensurate $2{\times}2$ periodic lattice distortion (PLD) and CDW at low temperatures. Analysis of the electron and phonon spectrum establishes the PLD as the stable $T=0$ K configuration with a narrow bandgap, whereas the undistorted and semi-metalic state is stable only above a threshold temperature. The lattice distortions as well as the unfolded and reconstructed band structure in the CDW phase agree well with experimental results. We also address evidence in our results for the role of electron-electron interactions in the CDW instability of 1T-TiSe$_2$ monolayers., Comment: 5 pages, 4 figures

We introduce the first multiorbital effective tight-binding model to describe the effect of electron-electron interactions in this system. Upon fixing all the effective hopping parameters in the normal state against an ab initio band structure, and with only the overall scale of the interactions as the sole adjustable parameter, we find that a self-consistent Hartree-Fock solution reproduces extremely well the experimental behavior of the charge density wave (CDW) order parameter in the full range $0

The discoveries of Dirac and Weyl semimetal states in spin-orbit compounds led to the realizations of elementary particle analogs in table-top experiments. In this paper, we propose the concept of a three-dimensional type-II Dirac fermion and identify a new topological semimetal state in the large family of transition-metal icosagenides, MA3 (M=V, Nb, Ta; A=Al, Ga, In). We show that the VAl3 family features a pair of strongly Lorentz-violating type-II Dirac nodes and that each Dirac node consists of four type-II Weyl nodes with chiral charge +/-1 via symmetry breaking. Furthermore, we predict the Landau level spectrum arising from the type-II Dirac fermions in VAl3 that is distinct from that of known Dirac semimetals. We also show a topological phase transition from a type-II Dirac semimetal to a quadratic Weyl semimetal or a topological crystalline insulator via crystalline distortions. The new type-II Dirac fermions, their novel magneto-transport response, the topological tunability and the large number of compounds make VAl3 an exciting platform to explore the wide-ranging topological phenomena associated with Lorentz-violating Dirac fermions in electrical and optical transport, spectroscopic and device-based experiments., Comment: 28 pages, 7 Figures

Atomically thin transitional metal ditellurides like WTe2 and MoTe2 have triggered tremendous research interests because of their intrinsic nontrivial band structure. They are also predicted to be 2D topological insulators and type-II Weyl semimetals. However, most of the studies on ditelluride atomic layers so far rely on the low-yield and time-consuming mechanical exfoliation method. Direct synthesis of large-scale monolayer ditellurides has not yet been achieved. Here, using the chemical vapor deposition (CVD) method, we demonstrate controlled synthesis of high-quality and atom-thin tellurides with lateral size over 300 {\mu}m. We found that the as-grown WTe2 maintains two different stacking sequences in the bilayer, where the atomic structure of the stacking boundary is revealed by scanning transmission electron microscope (STEM). The low-temperature transport measurements revealed a novel semimetal-to-insulator transition in WTe2 layers and an enhanced superconductivity in few-layer MoTe2. This work paves the way to the synthesis of atom-thin tellurides and also quantum spin Hall devices.

Topological metals and semimetals (TMs) have recently drawn significant interest. These materials give rise to condensed matter realizations of many important concepts in high-energy physics, leading to wide-ranging protected properties in transport and spectroscopic experiments. The most studied TMs, i.e., Weyl and Dirac semimetals, feature quasiparticles that are direct analogues of the textbook elementary particles. Moreover, the TMs known so far can be characterized based on the dimensionality of the band crossing. While Weyl and Dirac semimetals feature zero-dimensional points, the band crossing of nodal-line semimetals forms a one-dimensional closed loop. In this paper, we identify a TM which breaks the above paradigms. Firstly, the TM features triply-degenerate band crossing in a symmorphic lattice, hence realizing emergent fermionic quasiparticles not present in quantum field theory. Secondly, the band crossing is neither 0D nor 1D. Instead, it consists of two isolated triply-degenerate nodes interconnected by multi-segments of lines with two-fold degeneracy. We present materials candidates. We further show that triplydegenerate band crossings in symmorphic crystals give rise to a Landau level spectrum distinct from the known TMs, suggesting novel magneto-transport responses. Our results open the door for realizing new topological phenomena and fermions including transport anomalies and spectroscopic responses in metallic crystals with nontrivial topology beyond the Weyl/Dirac paradigm., Comment: 24 pages, 4 figures, and 1 table

Weyl semimetals are novel topological conductors that host Weyl fermions as emergent quasiparticles. While the Weyl fermions in high-energy physics are strictly defined as the massless solution of the Dirac equation and uniquely fixed by Lorentz symmetry, there is no such constraint for a topological metal in general. Specifically, the Weyl quasiparticles can arise by breaking either the space-inversion ($\mathcal{I}$) or time-reversal ($\mathcal{T}$) symmetry. They can either respect Lorentz symmetry (type-I) or strongly violate it (type-II). To date, different types of Weyl fermions have been predicted to occur only in different classes of materials. In this paper, we present a significant materials breakthrough by identifying a large class of Weyl materials in the RAlX (R=Rare earth, Al, X=Ge, Si) family that can realize all different types of emergent Weyl fermions ($\mathcal{I}$-breaking, $\mathcal{T}$-breaking, type-I or type-II), depending on a suitable choice of the rare earth elements. Specifically, RAlX can be ferromagnetic, nonmagnetic or antiferromagnetic and the electronic band topology and topological nature of the Weyl fermions can be tuned. The unparalleled tunability and the large number of compounds make the RAlX family of compounds a unique Weyl semimetal class for exploring the wide-ranging topological phenomena associated with different types of emergent Weyl fermions in transport, spectroscopic and device-based experiments., Comment: This paper reports theoretical prediction of Weyl semimetal (type-I and type-II) states in the R-Al-X family. For the experimental discovery, see our earlier paper at http://arxiv.org/abs/1603.07318

We theoretically investigate the development of unconventional superconductivity in the Sb(111) thin film when its Fermi level is tuned to near type-II Van Hove singularities (VHS), which locate at non-time-reversal invariant momenta. Via patch renormalization group analysis, we show that the leading instability is a chiral p + ip-wave superconducting order. The origin of such pairing relies on the hexagonal structure of the VHS and strong spin-orbit coupling, resulting in the anisotropy of the electron-electron scattering to provide an attractive channel. Our study hence suggests that superconducting Sb thin films originated from VHS physics may host Majorana zero modes in the magnetic vortices and provides another application perspective to such material., Comment: 7 pages, 5 figures, accepted by Physical Review B

We report theoretical and experimental discovery of Lorentz-violating Weyl fermion semimetal type-II state in the LaAlGe class of materials. Previously type-II Weyl state was predicted in WTe2 materials which remains unrealized in surface experiments. We show theoretically and experimentally that LaAlGe class of materials are the robust platforms for the study of type-II Weyl physics., Comment: This paper reports theoretical prediction and experimental discovery together. A detailed theoretical paper describing the topology of the full family of X(Lanthanides)AlGe materials will follow. Other related papers can be found at http://physics.princeton.edu/zahidhasangroup/index_WS.html

Topological semimetals (TSMs) including Weyl semimetals and nodal-line semimetals are expected to open the next frontier of condensed matter and materials science. Although the first inversion breaking Weyl semimetal was recently discovered in TaAs, its magnetic counterparts, i.e., the time-reversal breaking Weyl and nodal line semimetals, remain elusive. They are predicted to exhibit exotic properties distinct from the inversion breaking TSMs including TaAs. In this paper, we identify the magnetic topological semimetal state in the ferromagnetic half-metal compounds Co$_2$TiX (X=Si, Ge, or Sn) with Curie temperatures higher than 350 K. Our first-principles band structure calculations show that, in the absence of spin-orbit coupling, Co$_2$TiX features three topological nodal lines. The inclusion of spin-orbit coupling gives rise to Weyl nodes, whose momentum space locations can be controlled as a function of the magnetization direction. Our results not only open the door for the experimental realization of topological semimetal states in magnetic materials at room temperatures, but also suggest potential applications such as unusual anomalous Hall effects in engineered monolayers of the Co$_2$TiX compounds at high temperatures., Comment: 16 pages, 4 figures, and 1 table

The recent discovery of the first Weyl semimetal in TaAs provides the first observation of a Weyl fermion in nature. Such a topological semimetal features a novel type of anomalous surface state, the Fermi arc, which connects a pair of Weyl nodes through the boundary of the crystal. Here, we present theoretical calculations of the quasi-particle interference (QPI) patterns that arise from the surface states including the topological Fermi arcs in the Weyl semimetals TaAs and NbP. Most importantly, we discover that the QPI exhibits termination-points that are fingerprints of the Weyl nodes in the interference pattern. Our results, for the first time, propose an interference signature of the topological Fermi arcs in TaAs, which provides important guidelines for STM measurements on this prototypical Weyl semimetal compound. The scattering channels presented here is relevant to transport phenomena on the surface of the TaAs class of Weyl semimetals. Our work is also the first systematic calculation of the quantum interferences from the Fermi arc surface states, which is in general useful for future STM studies on other Weyl semimetals., Comment: 15pages, 6 figures

A Weyl semimetal is a new state of matter that host Weyl fermions as quasiparticle excitations. The Weyl fermions at zero energy correspond to points of bulk band degeneracy, Weyl nodes, which are separated in momentum space and are connected only through the crystal's boundary by an exotic Fermi arc surface state. We experimentally measure the spin polarization of the Fermi arcs in the first experimentally discovered Weyl semimetal TaAs. Our spin data, for the first time, reveal that the Fermi arcs' spin polarization magnitude is as large as 80% and possesses a spin texture that is completely in-plane. Moreover, we demonstrate that the chirality of the Weyl nodes in TaAs cannot be inferred by the spin texture of the Fermi arcs. The observed non-degenerate property of the Fermi arcs is important for the establishment of its exact topological nature, which reveal that spins on the arc form a novel type of 2D matter. Additionally, the nearly full spin polarization we observed (~80%) may be useful in spintronic applications., Comment: 4 figures, 15 pages

Weyl semimetals are expected to open up new horizons in physics and materials science because they provide the first realization of Weyl fermions and exhibit protected Fermi arc surface states. However, they had been found to be extremely rare in nature. Recently, a family of compounds, consisting of TaAs, TaP, NbAs and NbP was predicted as Weyl semimetal candidates. Here, we experimentally realize a Weyl semimetal state in TaP. Using photoemission spectroscopy, we directly observe the Weyl fermion cones and nodes in the bulk and the Fermi arcs on the surface. Moreover, we find that the surface states show an unexpectedly rich structure, including both topological Fermi arcs and several topologically-trivial closed contours in the vicinity of the Weyl points, which provides a promising platform to study the interplay between topological and trivial surface states on a Weyl semimetal's surface. We directly demonstrate the bulk-boundary correspondence and hence establish the topologically nontrivial nature of the Weyl semimetal state in TaP, by resolving the net number of chiral edge modes on a closed path that encloses the Weyl node. This also provides, for the first time, an experimentally practical approach to demonstrating a bulk Weyl fermion from a surface state dispersion measured in photoemission., Comment: Theoretical discovery of TaP as a Weyl Fermion material (November 2014) was made in http://www.nature.com/ncomms/2015/150612/ncomms8373/full/ncomms8373.html

Weyl nodes are topological objects in three-dimensional metals. Their topological property can be revealed by studying the high-field transport properties of a Weyl semimetal. While the energy of the lowest Landau band (LLB) of a conventional Fermi pocket always increases with magnetic field due to the zero point energy, the LLB of Weyl cones remains at zero energy unless a strong magnetic field couples the Weyl fermions of opposite chirality. In the Weyl semimetal TaP, we achieve such a magnetic coupling between the electron-like Fermi pockets arising from the W1 Weyl fermions. As a result, their LLBs move above chemical potential, leading to a sharp sign reversal in the Hall resistivity at a specific magnetic field corresponding to the W1 Weyl node separation. By contrast, despite having almost identical carrier density, the annihilation is unobserved for the hole-like pockets because the W2 Weyl nodes are much further separated. These key findings, corroborated by other systematic analyses, reveal the nontrivial topology of Weyl fermions in high-field measurements., Comment: the Fig2 and Fig 3 are not compatible with this version