Control of Andreev Bound States Using Superconducting Phase Texture.

Andreev bound states with opposite phase-inversion asymmetries are observed in local tunneling spectra at the two ends of a superconductor-semiconductor-superconductor planar Josephson junction in the presence of a perpendicular magnetic field, while the nonlocal spectra remain phase symmetric. Spectral signatures agree with a theoretical model, yielding a physical picture in which phase textures in superconducting leads localize and control the position of Andreev bound states in the junction, demonstrating a simple means of controlling the position and size of Andreev states within a planar junction.

Visualizing Higher-Fold Topology in Chiral Crystals.

Novel topological phases of matter are fruitful platforms for the discovery of unconventional electromagnetic phenomena. Higher-fold topology is one example, where the low-energy description goes beyond standard model analogs. Despite intensive experimental studies, conclusive evidence remains elusive for the multigap topological nature of higher-fold chiral fermions. In this Letter, we leverage a combination of fine-tuned chemical engineering and photoemission spectroscopy with photon energy contrast to discover the higher-fold topology of a chiral crystal. We identify all bulk branches of a higher-fold chiral fermion for the first time, critically important for allowing us to explore unique Fermi arc surface states in multiple interband gaps, which exhibit an emergent ladder structure. Through designer chemical gating of the samples in combination with our measurements, we uncover an unprecedented multigap bulk boundary correspondence. Our demonstration of multigap electronic topology will propel future research on unconventional topological responses.

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.

Unconventional Photocurrents from Surface Fermi Arcs in Topological Chiral Semimetals.

The nonlinear optical responses from topological semimetals are crucial in both understanding the fundamental properties of quantum materials and designing next-generation light sensors or solar cells. However, previous work focused on the optical effects from bulk states only, disregarding the responses from topological surface states. In this Letter, we propose a new surface-only photocurrent response from chiral Fermi arcs. Using the ideal topological chiral semimetal RhSi as a representative, we quantitatively compute the photogalvanic currents from Fermi arcs on different surfaces. By rigorous crystal symmetry analysis, we demonstrate that Fermi arc photogalvanic currents can be perpendicular to the bulk injection currents regardless of the choice of materials surface. We then generalize this finding to other cubic chiral space groups and predict material candidates. Our theory reveals a powerful notion where common crystalline symmetry can be used to completely disentangle bulk and surface optical responses in many conducting material families.

Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet.

Topological matter is known to exhibit unconventional surface states and anomalous transport owing to unusual bulk electronic topology. In this study, we use photoemission spectroscopy and quantum transport to elucidate the topology of the room temperature magnet Co2MnGa. We observe sharp bulk Weyl fermion line dispersions indicative of nontrivial topological invariants present in the magnetic phase. On the surface of the magnet, we observe electronic wave functions that take the form of drumheads, enabling us to directly visualize the crucial components of the bulk-boundary topological correspondence. By considering the Berry curvature field associated with the observed topological Weyl fermion lines, we quantitatively account for the giant anomalous Hall response observed in this magnet. Our experimental results suggest a rich interplay of strongly interacting electrons and topology in quantum matter.

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.

Topological quantum properties of chiral crystals.

Chiral crystals are materials with a lattice structure that has a well-defined handedness due to the lack of inversion, mirror or other roto-inversion symmetries. Although it has been shown that the presence of crystalline symmetries can protect topological band crossings, the topological electronic properties of chiral crystals remain largely uncharacterized. Here we show that Kramers-Weyl fermions are a universal topological electronic property of all non-magnetic chiral crystals with spin-orbit coupling and are guaranteed by structural chirality, lattice translation and time-reversal symmetry. Unlike conventional Weyl fermions, they appear at time-reversal-invariant momenta. We identify representative chiral materials in 33 of the 65 chiral space groups in which Kramers-Weyl fermions are relevant to the low-energy physics. We determine that all point-like nodal degeneracies in non-magnetic chiral crystals with relevant spin-orbit coupling carry non-trivial Chern numbers. Kramers-Weyl materials can exhibit a monopole-like electron spin texture and topologically non-trivial bulk Fermi surfaces over an unusually large energy window.

Unconventional Chiral Fermions and Large Topological Fermi Arcs in RhSi.

The theoretical proposal of chiral fermions in topological semimetals has led to a significant effort towards their experimental realization. In particular, the Fermi surfaces of chiral semimetals carry quantized Chern numbers, making them an attractive platform for the observation of exotic transport and optical phenomena. While the simplest example of a chiral fermion in condensed matter is a conventional |C|=1 Weyl fermion, recent theoretical works have proposed a number of unconventional chiral fermions beyond the standard model which are protected by unique combinations of topology and crystalline symmetries. However, materials candidates for experimentally probing the transport and response signatures of these unconventional fermions have thus far remained elusive. In this Letter, we propose the RhSi family in space group No. 198 as the ideal platform for the experimental examination of unconventional chiral fermions. We find that RhSi is a filling-enforced semimetal that features near its Fermi surface a chiral double sixfold-degenerate spin-1 Weyl node at R and a previously uncharacterized fourfold-degenerate chiral fermion at Γ. Each unconventional fermion displays Chern number ±4 at the Fermi level. We also show that RhSi displays the largest possible momentum separation of compensative chiral fermions, the largest proposed topologically nontrivial energy window, and the longest possible Fermi arcs on its surface. We conclude by proposing signatures of an exotic bulk photogalvanic response in RhSi.

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.

Signatures of a time-reversal symmetric Weyl semimetal with only four Weyl points.

Through intense research on Weyl semimetals during the past few years, we have come to appreciate that typical Weyl semimetals host many Weyl points. Nonetheless, the minimum nonzero number of Weyl points allowed in a time-reversal invariant Weyl semimetal is four. Realizing such a system is of fundamental interest and may simplify transport experiments. Recently, it was predicted that TaIrTe4 realizes a minimal Weyl semimetal. However, the Weyl points and Fermi arcs live entirely above the Fermi level, making them inaccessible to conventional angle-resolved photoemission spectroscopy (ARPES). Here, we use pump-probe ARPES to directly access the band structure above the Fermi level in TaIrTe4. We observe signatures of Weyl points and topological Fermi arcs. Combined with ab initio calculation, our results show that TaIrTe4 is a Weyl semimetal with the minimum number of four Weyl points. Our work provides a simpler platform for accessing exotic transport phenomena arising in Weyl semimetals.Weyl semimetals are interesting because they are characterized by topological invariants, but specific examples discovered to date tend to have complicated band structures with many Weyl points. Here, the authors show that TaIrTe4 has only four Weyl points, the minimal number required by time-reversal symmetry.

Type-II Symmetry-Protected Topological Dirac Semimetals.

The recent proposal of the type-II Weyl semimetal state has attracted significant interest. In this Letter, we propose the concept of the three-dimensional type-II Dirac fermion and theoretically identify this new symmetry-protected topological state in the large family of transition-metal icosagenides, MA_{3} (M=V, Nb, Ta; A=Al, Ga, In). We show that the VAl_{3} family features a pair of strongly Lorentz-violating type-II Dirac nodes and that each Dirac node can be split into four type-II Weyl nodes with chiral charge ±1 via symmetry breaking. Furthermore, we predict that the Landau level spectrum arising from the type-II Dirac fermions in VAl_{3} is distinct from that of known Dirac or Weyl semimetals. We also demonstrate a topological phase transition from a type-II Dirac semimetal to a quadratic Weyl semimetal or a topological crystalline insulator via crystalline distortions.

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.

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 a new type of topological Weyl fermion semimetal state in MoxW1-xTe2.

The recent discovery of a Weyl semimetal in TaAs offers the first Weyl fermion observed in nature and dramatically broadens the classification of topological phases. However, in TaAs it has proven challenging to study the rich transport phenomena arising from emergent Weyl fermions. The series MoxW1-xTe2 are inversion-breaking, layered, tunable semimetals already under study as a promising platform for new electronics and recently proposed to host Type II, or strongly Lorentz-violating, Weyl fermions. Here we report the discovery of a Weyl semimetal in MoxW1-xTe2 at x=25%. We use pump-probe angle-resolved photoemission spectroscopy (pump-probe ARPES) to directly observe a topological Fermi arc above the Fermi level, demonstrating a Weyl semimetal. The excellent agreement with calculation suggests that MoxW1-xTe2 is a Type II Weyl semimetal. We also find that certain Weyl points are at the Fermi level, making MoxW1-xTe2 a promising platform for transport and optics experiments on Weyl semimetals.

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.

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.

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.

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.

Signatures of the Adler-Bell-Jackiw chiral anomaly in a Weyl fermion semimetal.

Weyl semimetals provide the realization of Weyl fermions in solid-state physics. Among all the physical phenomena that are enabled by Weyl semimetals, the chiral anomaly is the most unusual one. Here, we report signatures of the chiral anomaly in the magneto-transport measurements on the first Weyl semimetal TaAs. We show negative magnetoresistance under parallel electric and magnetic fields, that is, unlike most metals whose resistivity increases under an external magnetic field, we observe that our high mobility TaAs samples become more conductive as a magnetic field is applied along the direction of the current for certain ranges of the field strength. We present systematically detailed data and careful analyses, which allow us to exclude other possible origins of the observed negative magnetoresistance. Our transport data, corroborated by photoemission measurements, first-principles calculations and theoretical analyses, collectively demonstrate signatures of the Weyl fermion chiral anomaly in the magneto-transport of TaAs.