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.

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.

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.

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.

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 Mo_xW_1−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 Mo_xW_1−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 Mo_xW_1−xTe₂ is a Type II Weyl semimetal. We also find that certain Weyl points are at the Fermi level, making Mo_xW_1−xTe₂ a promising platform for transport and optics experiments on Weyl semimetals.

A Type II Weyl fermion semimetal has been predicted in Mo_xW_1−xTe₂, but it awaits experimental evidence. Here, Belopolski et al. observe a topological Fermi arc in Mo_xW_1−xTe₂, showing it originates from a Type II Weyl fermion and offering a new platform to study novel transport phenomena in Weyl semimetals.

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.

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.

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.

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.

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.

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.

Topological nodal-line fermions in spin-orbit metal PbTaSe2

Topological semimetals can support one-dimensional Fermi lines or zero-dimensional Weyl points in momentum space, where the valence and conduction bands touch. While the degeneracy points in Weyl semimetals are robust against any perturbation that preserves translational symmetry, nodal lines require protection by additional crystalline symmetries such as mirror reflection. Here we report, based on a systematic theoretical study and a detailed experimental characterization, the existence of topological nodal-line states in the non-centrosymmetric compound PbTaSe₂ with strong spin-orbit coupling. Remarkably, the spin-orbit nodal lines in PbTaSe₂ are not only protected by the reflection symmetry but also characterized by an integer topological invariant. Our detailed angle-resolved photoemission measurements, first-principles simulations and theoretical topological analysis illustrate the physical mechanism underlying the formation of the topological nodal-line states and associated surface states for the first time, thus paving the way towards exploring the exotic properties of the topological nodal-line fermions in condensed matter systems.

Nodal-line shaped bands appearing near the Fermi level host unique properties in topological matter, which has yet to be confirmed in real materials. Here, the authors report the existence of topological nodal-line states in the non-centrosymmetric single-crystalline spin-orbit semimetal PbTaSe₂.

Atomic-Scale Visualization of Quantum Interference on a Weyl Semimetal Surface by Scanning Tunneling Microscopy

Weyl semimetals may open a new era in condensed matter physics, materials science, and nanotechnology after graphene and topological insulators. We report the first atomic scale view of the surface states of a Weyl semimetal (NbP) using scanning tunneling microscopy/spectroscopy. We observe coherent quantum interference patterns that arise from the scattering of quasiparticles near point defects on the surface. The measurements reveal the surface electronic structure both below and above the chemical potential in both real and reciprocal spaces. Moreover, the interference maps uncover the scattering processes of NbP's exotic surface states. Through comparison between experimental data and theoretical calculations, we further discover that the orbital and/or spin texture of the surface bands may suppress certain scattering channels on NbP. These results provide a comprehensive understanding of electronic properties on Weyl semimetal surfaces.

Experimental discovery of a topological Weyl semimetal state in TaP

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 tantalum arsenide, tantalum phosphide (TaP), niobium arsenide, and niobium phosphide, was predicted as a Weyl semimetal candidates. 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 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.

DNA kinks and bubbles: temperature dependence of the elastic energy of sharply bent 10-nm-size DNA molecules

A 10-nm-long DNA molecule can bend through large angles reversibly. Past the linear regime, its equilibrium nonlinear bending elasticity is governed by a critical bending torque τ(c)≈30pN×nm at which the molecule develops a kink. This nonlinearity has long been attributed to the nucleation of a bubble or melted region in the molecule. Here we measure the temperature dependence of the critical bending torque for nicked DNA, and determine that the entropy associated with the kink in the nonlinear regime is negligible. Thus in the case of nicked DNA the kink is not a bubble, but a compact region deformed beyond a yield strain. We further argue that, with our boundary conditions, the same is likely true for intact DNA. The present measurements confirm that the critical bending torque τ(c) is a materials parameter of DNA mechanics analogous to the bending modulus B≈200pN×nm.