Causal structure of interacting Weyl fermions in condensed matter systems.

The spacetime light cone is central to the definition of causality in the theory of relativity. Recently, links between relativistic and condensed matter physics have been uncovered, where relativistic particles can emerge as quasiparticles in the energy-momentum space of matter. Here, we unveil an energy-momentum analogue of the spacetime light cone by mapping time to energy, space to momentum, and the light cone to the Weyl cone. We show that two Weyl quasiparticles can only interact to open a global energy gap if they lie in each other's energy-momentum dispersion cones-analogous to two events that can only have a causal connection if they lie in each other's light cones. Moreover, we demonstrate that the causality of surface chiral modes in quantum matter is entangled with the causality of bulk Weyl fermions. Furthermore, we identify a unique quantum horizon region and an associated 'thick horizon' in the emergent causal structure.

Uniaxial Strain Dependence on Angle-Resolved Optical Second Harmonic Generation from a Few Layers of Indium Selenide.

Indium selenide (InSe) is an emerging van der Waals material, which exhibits the potential to serve in excellent electronic and optoelectronic devices. One of the advantages of layered materials is their application to flexible devices. How strain alters the electronic and optical properties is, thus, an important issue. In this work, we experimentally measured the strain dependence on the angle-resolved second harmonic generation (SHG) pattern of a few layers of InSe. We used the exfoliation method to fabricate InSe flakes and measured the SHG images of the flakes with different azimuthal angles. We found the SHG intensity of InSe decreased, while the compressive strain increased. Through first-principles electronic structure calculations, we investigated the strain dependence on SHG susceptibilities and the corresponding angle-resolved SHG pattern. The experimental data could be fitted well by the calculated results using only a fitting parameter. The demonstrated method based on first-principles in this work can be used to quantitatively model the strain-induced angle-resolved SHG patterns in 2D materials. Our obtained results are very useful for the exploration of the physical properties of flexible devices based on 2D materials.

Bandgap Shrinkage and Charge Transfer in 2D Layered SnS2 Doped with V for Photocatalytic Efficiency Improvement.

Effects of electronic and atomic structures of V-doped 2D layered SnS2 are studied using X-ray spectroscopy for the development of photocatalytic/photovoltaic applications. Extended X-ray absorption fine structure measurements at V K-edge reveal the presence of VO and VS bonds which form the intercalation of tetrahedral OVS sites in the van der Waals (vdW) gap of SnS2 layers. X-ray absorption near-edge structure (XANES) reveals not only valence state of V dopant in SnS2 is ≈4+ but also the charge transfer (CT) from V to ligands, supported by V Lα,ß resonant inelastic X-ray scattering. These results suggest V doping produces extra interlayer covalent interactions and additional conducting channels, which increase the electronic conductivity and CT. This gives rapid transport of photo-excited electrons and effective carrier separation in layered SnS2 . Additionally, valence-band photoemission spectra and S K-edge XANES indicate that the density of states near/at valence-band maximum is shifted to lower binding energy in V-doped SnS2 compare to pristine SnS2 and exhibits band gap shrinkage. These findings support first-principles density functional theory calculations of the interstitially tetrahedral OVS site intercalated in the vdW gap, highlighting the CT from V to ligands in V-doped SnS2 .

Partitioning interatomic force constants for first-principles phonon calculations: applications to NaCl, PbTiO3, monolayer CrI3, and twisted bilayer graphene.

First-principles phonon calculations have been widely performed for studying vibrational properties of condensed matter, where the dynamical matrix is commonly constructed via supercell force-constant calculations or the linear response approach. With different manners, a supercell can be introduced in both methods. Unless the supercell is large enough, the interpolated phonon property highly depends on the shape and size of the supercell and the imposed periodicity could give unphysical results that can be easily overlooked. Along this line, we discuss how a traditional method can be used to partition the force constants at the supercell boundary and then propose a more flexible method based on the translational symmetry and interatomic distances. The partition method is also compatible with the mixed-space approach for describing LO-TO splitting. We have applied the proposed partition method to NaCl, PbTiO3, monolayer CrI3, and twisted bilayer graphene, where we show how the method can deliver reasonable results. The proper partition is especially important for studying moderate-size systems with low symmetry, such as two-dimensional materials on substrates, and useful for the implementation of phonon calculations in first-principles packages using atomic basis functions, where symmetry operations are usually not applied owing to the suitability for large-scale calculations.

Formation of BN-covered silicene on ZrB2/Si(111) by adsorption of NO and thermal processes.

We have investigated the adsorption and thermal reaction processes of NO with silicene spontaneously formed on the ZrB2/Si(111) substrate using synchrotron radiation x-ray photoelectron spectroscopy (XPS) and density-functional theory calculations. NO is dissociatively adsorbed on the silicene surface at 300 K. An atomic nitrogen is bonded to three Si atoms most probably by a substitutional adsorption with a Si atom of silicene (N≡Si3). An atomic oxygen is inserted between two Si atoms of the silicene (Si-O-Si). With increasing NO exposure, the two-dimensional honeycomb silicene structure gets destroyed, judging from the decay of typical Si 2p spectra for silicene. After a large amount of NO exposure, the oxidation state of Si becomes Si4+ predominantly, and the intensity of the XPS peaks of the ZrB2 substrate decreases, indicating that complicated silicon oxinitride species have developed three-dimensionally. By heating above 900 K, the oxide species start to desorb from the surface, but nitrogen-bonded species still exist. After flashing at 1053 K, no oxygen species is observed on the surface; SiN species are temporally formed as a metastable species and BN species also start to develop. In addition, the silicene structure is restored on the ZrB2/Si(111) substrate. After prolonged heating at 1053 K, most of nitrogen atoms are bonded to B atoms to form a BN layer at the topmost surface. Thus, BN-covered silicene is formed on the ZrB2/Si(111) substrate by the adsorption of NO at 300 K and prolonged heating at 1053 K.

Scanning tunneling microscopy on cleaved Mn3Sn(0001) surface.

We have studied in-situ cleaved (0001) surfaces of the magnetic Weyl semimetal Mn3Sn by low-temperature scanning tunneling microscopy and spectroscopy (STM/S). It was found that freshly cleaved Mn3Sn surfaces are covered with unknown clusters, and the application of voltage pulses in the tunneling condition was needed to achieve atomically flat surfaces. STM topographs taken on the flat terrace show a bulk-terminated 1 × 1 honeycomb lattice with the Sn site brightest. First-principles calculations reveal that the brightest contrast at the Sn site originates from the surrounding surface Mn d orbitals. Tunneling spectroscopy performed on the as-cleaved and voltage-pulsed surfaces show a prominent semimetal valley near the Fermi energy.

Non-saturating quantum magnetization in Weyl semimetal TaAs.

Detecting the spectroscopic signatures of relativistic quasiparticles in emergent topological materials is crucial for searching their potential applications. Magnetometry is a powerful tool for fathoming electrons in solids, by which a clear method for discerning relativistic quasiparticles has not yet been established. Adopting the probes of magnetic torque and parallel magnetization for the archetype Weyl semimetal TaAs in strong magnetic field, we observed a quasi-linear field dependent effective transverse magnetization and a non-saturating parallel magnetization when the system enters the quantum limit. Distinct from the saturating magnetic responses for non-relativistic quasiparticles, the non-saturating signals of TaAs in strong field is consistent with our newly developed magnetization calculation for a Weyl fermion system in an arbitrary angle. Our results establish a high-field thermodynamic method for detecting the magnetic response of relativistic quasiparticles in topological materials.

Realization of intrinsically broken Dirac cones in graphene via the momentum-resolved electronic band structure.

A way to represent the band structure that distinguishes between energy-momentum and energy-crystal momentum relationships is proposed upon the band-unfolding concept. This momentum-resolved band structure offers better understanding of the physical processes requiring the information of wave functions in momentum space and provides a direct connection to angle-resolved photoelectron spectroscopy (ARPES) spectra. Following this approach, we demonstrate that Dirac cones in graphene are intrinsically broken in momentum space and can be described by a conceptual unit cell smaller than the primitive unit cell. This hidden degree of freedom can be measured by ARPES experiments as missing weight that is retrievable by investigating the effect of different polarized light. Having the energy-momentum relationship, we provide alternative understanding of the retrieved momentum intensity beyond the periodic-zone scheme, that is, the retrieved momentum intensity is assisted with the properties of final states, not from the Dirac cones directly. The revealed broken Dirac cones and momenta supplied by the lattice give interesting ingredients for designing advanced nanodevices.

Atomic-scale visualization of surface-assisted orbital order.

Orbital-related physics attracts growing interest in condensed matter research, but direct real-space access of the orbital degree of freedom is challenging. We report a first, real-space, imaging of a surface-assisted orbital ordered structure on a cobalt-terminated surface of the well-studied heavy fermion compound CeCoIn5. Within small tip-sample distances, the cobalt atoms on a cleaved (001) surface take on dumbbell shapes alternatingly aligned in the [100] and [010] directions in scanning tunneling microscopy topographies. First-principles calculations reveal that this structure is a consequence of the staggered d xz -d yz orbital order triggered by enhanced on-site Coulomb interaction at the surface. This so far overlooked surface-assisted orbital ordering may prevail in transition metal oxides, heavy fermion superconductors, and other materials.

Absolute Binding Energies of Core Levels in Solids from First Principles.

A general method is presented to calculate absolute binding energies of core levels in metals and insulators, based on a penalty functional and an exact Coulomb cutoff method in the framework of density functional theory. The spurious interaction of core holes between supercells is avoided by the exact Coulomb cutoff method, while the variational penalty functional enables us to treat multiple splittings due to chemical shift, spin-orbit coupling, and exchange interaction on equal footing, both of which are not accessible by previous methods. It is demonstrated that the absolute binding energies of core levels for both metals and insulators are calculated by the proposed method in a mean absolute (relative) error of 0.4 eV (0.16%) for eight cases compared to experimental values measured with x-ray photoemission spectroscopy within a generalized gradient approximation to the exchange-correlation functional.

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.

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.

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.

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.

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.

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.

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.

Two-dimensional Topological Crystalline Insulator Phase in Sb/Bi Planar Honeycomb with Tunable Dirac Gap.

We predict planar Sb/Bi honeycomb to harbor a two-dimensional (2D) topological crystalline insulator (TCI) phase based on first-principles computations. Although buckled Sb and Bi honeycombs support 2D topological insulator (TI) phases, their structure becomes planar under tensile strain. The planar Sb/Bi honeycomb structure restores the mirror symmetry, and is shown to exhibit non-zero mirror Chern numbers, indicating that the system can host topologically protected edge states. Our computations show that the electronic spectrum of a planar Sb/Bi nanoribbon with armchair or zigzag edges contains two Dirac cones within the band gap and an even number of edge bands crossing the Fermi level. Lattice constant of the planar Sb honeycomb is found to nearly match that of hexagonal-BN. The Sb nanoribbon on hexagonal-BN exhibits gapped edge states, which we show to be tunable by an out-of-the-plane electric field, providing controllable gating of edge state important for device applications.