Topological chiral crystals with helicoid-arc quantum states.

The quantum behaviour of electrons in materials is the foundation of modern electronics and information technology1-11, and quantum materials with topological electronic and optical properties are essential for realizing quantized electronic responses that can be used for next generation technology. Here we report the first observation of topological quantum properties of chiral crystals6,7 in the RhSi family. We find that this material class hosts a quantum phase of matter that exhibits nearly ideal topological surface properties originating from the crystals' structural chirality. Electrons on the surface of these crystals show a highly unusual helicoid fermionic structure that spirals around two high-symmetry momenta, indicating electronic topological chirality. The existence of bulk multiply degenerate band fermions is guaranteed by the crystal symmetries; however, to determine the topological invariant or charge in these chiral crystals, it is essential to identify and study the helicoid topology of the arc states. The helicoid arcs that we observe on the surface characterize the topological charges of ±2, which arise from bulk higher-spin chiral fermions. These topological conductors exhibit giant Fermi arcs of maximum length (π), which are orders of magnitude larger than those found in known chiral Weyl fermion semimetals5,8-11. Our results demonstrate an electronic topological state of matter on structurally chiral crystals featuring helicoid-arc quantum states. Such exotic multifold chiral fermion semimetal states could be used to detect a quantized photogalvanic optical response, the chiral magnetic effect and other optoelectronic phenomena predicted for this class of materials6.

New type of Weyl semimetal with quadratic double Weyl fermions.

Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs.

Mirror Protected Dirac Fermions on a Weyl Semimetal NbP Surface.

The first Weyl semimetal was recently discovered in the NbP class of compounds. Although the topology of these novel materials has been identified, the surface properties are not yet fully understood. By means of scanning tunneling spectroscopy, we find that NbP's (001) surface hosts a pair of Dirac cones protected by mirror symmetry. Through our high-resolution spectroscopic measurements, we resolve the quantum interference patterns arising from these novel Dirac fermions and reveal their electronic structure, including the linear dispersions. Our data, in agreement with our theoretical calculations, uncover further interesting features of the Weyl semimetal NbP's already exotic surface. Moreover, we discuss the similarities and distinctions between the Dirac fermions here and those in topological crystalline insulators in terms of symmetry protection and topology.

Atomic-Scale Visualization of Quasiparticle Interference on a Type-II Weyl Semimetal Surface.

We combine quasiparticle interference simulation (theory) and atomic resolution scanning tunneling spectromicroscopy (experiment) to visualize the interference patterns on a type-II Weyl semimetal Mo_{x}W_{1-x}Te_{2} for the first time. Our simulation based on first-principles band topology theoretically reveals the surface electron scattering behavior. We identify the topological Fermi arc states and reveal the scattering properties of the surface states in Mo_{0.66}W_{0.34}Te_{2}. In addition, our result reveals an experimental signature of the topology via the interconnectivity of bulk and surface states, which is essential for understanding the unusual nature of this material.

Signatures of Fermi Arcs in the Quasiparticle Interferences of the Weyl Semimetals TaAs and NbP.

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 quasiparticle 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 a universal interference signature of the topological Fermi arcs in TaAs, which is fundamental for scanning tunneling microscope (STM) measurements on this prototypical Weyl semimetal compound. More generally, our work provides critical guideline and methodology for STM studies on new Weyl semimetals. Further, the scattering channels revealed by our QPIs are broadly relevant to surface transport and device applications based on Weyl semimetals.

Criteria for Directly Detecting Topological Fermi Arcs in Weyl Semimetals.

The recent discovery of the first Weyl semimetal in TaAs provides the first observation of a Weyl fermion in nature and demonstrates a novel type of anomalous surface state, the Fermi arc. Like topological insulators, the bulk topological invariants of a Weyl semimetal are uniquely fixed by the surface states of a bulk sample. Here we present a set of distinct conditions, accessible by angle-resolved photoemission spectroscopy (ARPES), each of which demonstrates topological Fermi arcs in a surface state band structure, with minimal reliance on calculation. We apply these results to TaAs and NbP. For the first time, we rigorously demonstrate a nonzero Chern number in TaAs by counting chiral edge modes on a closed loop. We further show that it is unreasonable to directly observe Fermi arcs in NbP by ARPES within available experimental resolution and spectral linewidth. Our results are general and apply to any new material to demonstrate a Weyl semimetal.

Spin Polarization and Texture of the Fermi Arcs in the Weyl Fermion Semimetal TaAs.

A Weyl semimetal is a new state of matter that hosts Weyl fermions as quasiparticle excitations. The Weyl fermions at zero energy correspond to points of bulk-band degeneracy, called 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 lies completely in the plane of the surface. 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 nondegenerate property of the Fermi arcs is important for establishing its exact topological nature, which reveals 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.

Gigantic surface lifetime of an intrinsic topological insulator.

The interaction between light and novel two-dimensional electronic states holds promise to realize new fundamental physics and optical devices. Here, we use pump-probe photoemission spectroscopy to study the optically excited Dirac surface states in the bulk-insulating topological insulator Bi_{2}Te_{2}Se and reveal optical properties that are in sharp contrast to those of bulk-metallic topological insulators. We observe a gigantic optical lifetime exceeding 4 µs (1 µs=10^{-6} s) for the surface states in Bi_{2}Te_{2}Se, whereas the lifetime in most topological insulators, such as Bi_{2}Se_{3}, has been limited to a few picoseconds (1 ps=10^{-12} s). Moreover, we discover a surface photovoltage, a shift of the chemical potential of the Dirac surface states, as large as 100 mV. Our results demonstrate a rare platform to study charge excitation and relaxation in energy and momentum space in a two-dimensional system.

Non-Kondo-like electronic structure in the correlated rare-earth hexaboride YbB(6).

We present angle-resolved photoemission studies on the rare-earth-hexaboride YbB(6), which has recently been predicted to be a topological Kondo insulator. Our data do not agree with the prediction and instead show that YbB(6) exhibits a novel topological insulator state in the absence of a Kondo mechanism. We find that the Fermi level electronic structure of YbB(6) has three 2D Dirac cone like surface states enclosing the Kramers's points, while the f orbital that would be relevant for the Kondo mechanism is ∼1 eV below the Fermi level. Our first-principles calculation shows that the topological state that we observe in YbB(6) is due to an inversion between Yb d and B p bands. These experimental and theoretical results provide a new approach for realizing novel correlated topological insulator states in rare-earth materials.

Observation of Weyl fermions in a magnetic non-centrosymmetric crystal.

The absence of inversion symmetry in non-centrosymmetric materials has a fundamental role in the emergence of a vast number of fascinating phenomena, like ferroelectricity, second harmonic generation, and Weyl fermions. The removal of time-reversal symmetry in such systems further extends the variety of observable magneto-electric and topological effects. Here we report the striking topological properties in the non-centrosymmetric spin-orbit magnet PrAlGe by combining spectroscopy and transport measurements. By photoemission spectroscopy below the Curie temperature, we observe topological Fermi arcs that correspond to projected topological charges of ±1 in the surface Brillouin zone. In the bulk, we observe the linear energy-dispersion of the Weyl fermions. We further observe a large anomalous Hall response in our magneto-transport measurements, which is understood to arise from diverging bulk Berry curvature fields associated with the Weyl band structure. These results establish a novel Weyl semimetal phase in magnetic non-centrosymmetric PrAlGe.

Demonstration of universal parametric entangling gates on a multi-qubit lattice.

We show that parametric coupling techniques can be used to generate selective entangling interactions for multi-qubit processors. By inducing coherent population exchange between adjacent qubits under frequency modulation, we implement a universal gate set for a linear array of four superconducting qubits. An average process fidelity of ℱ = 93% is estimated for three two-qubit gates via quantum process tomography. We establish the suitability of these techniques for computation by preparing a four-qubit maximally entangled state and comparing the estimated state fidelity with the expected performance of the individual entangling gates. In addition, we prepare an eight-qubit register in all possible bitstring permutations and monitor the fidelity of a two-qubit gate across one pair of these qubits. Across all these permutations, an average fidelity of ℱ = 91.6 ± 2.6% is observed. These results thus offer a path to a scalable architecture with high selectivity and low cross-talk.

Nexus fermions in topological symmorphic crystalline metals.

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. It has been well-established that the known TMs can be classified by the dimensionality of the topologically protected band degeneracies. 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 that goes beyond the above paradigms. It shows an exotic configuration of degeneracies without a well-defined dimensionality. Specifically, it consists of 0D nexus with triple-degeneracy that interconnects 1D lines with double-degeneracy. We show that, because of the novel form of band crossing, the new TM cannot be described by the established results that characterize the topology of the Dirac and Weyl nodes. Moreover, triply-degenerate nodes realize emergent fermionic quasiparticles not present in relativistic quantum field theory. We present materials candidates. 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.

Discovery of Lorentz-violating type II Weyl fermions in LaAlGe.

In quantum field theory, Weyl fermions are relativistic particles that travel at the speed of light and strictly obey the celebrated Lorentz symmetry. Their low-energy condensed matter analogs are Weyl semimetals, which are conductors whose electronic excitations mimic the Weyl fermion equation of motion. Although the traditional (type I) emergent Weyl fermions observed in TaAs still approximately respect Lorentz symmetry, recently, the so-called type II Weyl semimetal has been proposed, where the emergent Weyl quasiparticles break the Lorentz symmetry so strongly that they cannot be smoothly connected to Lorentz symmetric Weyl particles. Despite some evidence of nontrivial surface states, the direct observation of the type II bulk Weyl fermions remains elusive. We present the direct observation of the type II Weyl fermions in crystalline solid lanthanum aluminum germanide (LaAlGe) based on our photoemission data alone, without reliance on band structure calculations. Moreover, our systematic data agree with the theoretical calculations, providing further support on our experimental results.

A novel artificial condensed matter lattice and a new platform for one-dimensional topological phases.

Engineered lattices in condensed matter physics, such as cold-atom optical lattices or photonic crystals, can have properties that are fundamentally different from those of naturally occurring electronic crystals. We report a novel type of artificial quantum matter lattice. Our lattice is a multilayer heterostructure built from alternating thin films of topological and trivial insulators. Each interface within the heterostructure hosts a set of topologically protected interface states, and by making the layers sufficiently thin, we demonstrate for the first time a hybridization of interface states across layers. In this way, our heterostructure forms an emergent atomic chain, where the interfaces act as lattice sites and the interface states act as atomic orbitals, as seen from our measurements by angle-resolved photoemission spectroscopy. By changing the composition of the heterostructure, we can directly control hopping between lattice sites. We realize a topological and a trivial phase in our superlattice band structure. We argue that the superlattice may be characterized in a significant way by a one-dimensional topological invariant, closely related to the invariant of the Su-Schrieffer-Heeger model. Our topological insulator heterostructure demonstrates a novel experimental platform where we can engineer band structures by directly controlling how electrons hop between lattice sites.

A strongly robust type II Weyl fermion semimetal state in Ta3S2.

Weyl semimetals are of great interest because they provide the first realization of the Weyl fermion, exhibit exotic quantum anomalies, and host Fermi arc surface states. The separation between Weyl nodes of opposite chirality gives a measure of the robustness of the Weyl semimetal state. To exploit the novel phenomena that arise from Weyl fermions in applications, it is crucially important to find robust separated Weyl nodes. We propose a methodology to design robust Weyl semimetals with well-separated Weyl nodes. Using this methodology as a guideline, we search among the material parameter space and identify by far the most robust and ideal Weyl semimetal candidate in the single-crystalline compound tantalum sulfide (Ta3S2) with new and novel properties beyond TaAs. Crucially, our results show that Ta3S2 has the largest k-space separation between Weyl nodes among known Weyl semimetal candidates, which is about twice larger than the measured value in TaAs and 20 times larger than the predicted value in WTe2. Moreover, all Weyl nodes in Ta3S2 are of type II. Therefore, Ta3S2 is a type II Weyl semimetal. Furthermore, we predict that increasing the lattice by <4% can annihilate all Weyl nodes, driving a novel topological metal-to-insulator transition from a Weyl semimetal state to a topological insulator state. The robust type II Weyl semimetal state and the topological metal-to-insulator transition in Ta3S2 are potentially useful in device applications. Our methodology can be generally applied to search for new Weyl semimetals.

Electronic structure and relaxation dynamics in a superconducting topological material.

Topological superconductors host new states of quantum matter which show a pairing gap in the bulk and gapless surface states providing a platform to realize Majorana fermions. Recently, alkaline-earth metal Sr intercalated Bi2Se3 has been reported to show superconductivity with a Tc ~ 3 K and a large shielding fraction. Here we report systematic normal state electronic structure studies of Sr0.06Bi2Se3 (Tc ~ 2.5 K) by performing photoemission spectroscopy. Using angle-resolved photoemission spectroscopy (ARPES), we observe a quantum well confined two-dimensional (2D) state coexisting with a topological surface state in Sr0.06Bi2Se3. Furthermore, our time-resolved ARPES reveals the relaxation dynamics showing different decay mechanism between the excited topological surface states and the two-dimensional states. Our experimental observation is understood by considering the intra-band scattering for topological surface states and an additional electron phonon scattering for the 2D states, which is responsible for the superconductivity. Our first-principles calculations agree with the more effective scattering and a shorter lifetime of the 2D states. Our results will be helpful in understanding low temperature superconducting states of these topological materials.

Room-temperature magnetic topological Weyl fermion and nodal line semimetal states in half-metallic Heusler Co2TiX (X=Si, Ge, or Sn).

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 states in the ferromagnetic half-metal compounds Co2TiX (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, Co2TiX 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 temperature, but also suggest potential applications such as unusual anomalous Hall effect in engineered monolayers of the Co2TiX compounds at high temperature.

Prediction of an arc-tunable Weyl Fermion metallic state in Mo(x)W(1-x)Te2.

A Weyl semimetal is a new state of matter that hosts Weyl fermions as emergent quasiparticles. The Weyl fermions correspond to isolated points of bulk band degeneracy, Weyl nodes, which are connected only through the crystal's boundary by exotic Fermi arcs. The length of the Fermi arc gives a measure of the topological strength, because the only way to destroy the Weyl nodes is to annihilate them in pairs in the reciprocal space. To date, Weyl semimetals are only realized in the TaAs class. Here, we propose a tunable Weyl state in Mo(x)W(1-x)Te2 where Weyl nodes are formed by touching points between metallic pockets. We show that the Fermi arc length can be changed as a function of Mo concentration, thus tuning the topological strength. Our results provide an experimentally feasible route to realizing Weyl physics in the layered compound Mo(x)W(1-x)Te2, where non-saturating magneto-resistance and pressure-driven superconductivity have been observed.

Observation of the spin-polarized surface state in a noncentrosymmetric superconductor BiPd.

Recently, noncentrosymmetric superconductor BiPd has attracted considerable research interest due to the possibility of hosting topological superconductivity. Here we report a systematic high-resolution angle-resolved photoemission spectroscopy (ARPES) and spin-resolved ARPES study of the normal state electronic and spin properties of BiPd. Our experimental results show the presence of a surface state at higher-binding energy with the location of Dirac point at around 700 meV below the Fermi level. The detailed photon energy, temperature-dependent and spin-resolved ARPES measurements complemented by our first-principles calculations demonstrate the existence of the spin-polarized surface states at high-binding energy. The absence of such spin-polarized surface states near the Fermi level negates the possibility of a topological superconducting behaviour on the surface. Our direct experimental observation of spin-polarized surface states in BiPd provides critical information that will guide the future search for topological superconductivity in noncentrosymmetric materials.