Assessing Nontrivial Topology in Weyl Semimetals by Dichroic Photoemission.

The electronic structure of Weyl semimetals features Berry flux monopoles in the bulk and Fermi arcs at the surface. While angle-resolved photoelectron spectroscopy (ARPES) is successfully used to map the bulk and surface bands, it remains a challenge to explicitly resolve and pinpoint these topological features. Here we combine state-of-the-art photoemission theory and experiments over a wide range of excitation energies for the Weyl semimetals TaAs and TaP. Our results show that simple surface-band-counting schemes, proposed previously to identify nonzero Chern numbers, are ambiguous due to pronounced momentum-dependent spectral weight variations and the pronounced surface-bulk hybridization. Instead, our findings indicate that dichroic ARPES provides an improved approach to identify Fermi arcs but requires an accurate description of the photoelectron final state.

Momentum-space signatures of Berry flux monopoles in the Weyl semimetal TaAs.

Since the early days of Dirac flux quantization, magnetic monopoles have been sought after as a potential corollary of quantized electric charge. As opposed to magnetic monopoles embedded into the theory of electromagnetism, Weyl semimetals (WSM) exhibit Berry flux monopoles in reciprocal parameter space. As a function of crystal momentum, such monopoles locate at the crossing point of spin-polarized bands forming the Weyl cone. Here, we report momentum-resolved spectroscopic signatures of Berry flux monopoles in TaAs as a paradigmatic WSM. We carried out angle-resolved photoelectron spectroscopy at bulk-sensitive soft X-ray energies (SX-ARPES) combined with photoelectron spin detection and circular dichroism. The experiments reveal large spin- and orbital-angular-momentum (SAM and OAM) polarizations of the Weyl-fermion states, resulting from the broken crystalline inversion symmetry in TaAs. Supported by first-principles calculations, our measurements image signatures of a topologically non-trivial winding of the OAM at the Weyl nodes and unveil a chirality-dependent SAM of the Weyl bands. Our results provide directly bulk-sensitive spectroscopic support for the non-trivial band topology in the WSM TaAs, promising to have profound implications for the study of quantum-geometric effects in solids.

Orbital Complexity in Intrinsic Magnetic Topological Insulators MnBi_{4}Te_{7} and MnBi_{6}Te_{10}.

Using angle-resolved photoelectron spectroscopy (ARPES), we investigate the surface electronic structure of the magnetic van der Waals compounds MnBi_{4}Te_{7} and MnBi_{6}Te_{10}, the n=1 and 2 members of a modular (Bi_{2}Te_{3})_{n}(MnBi_{2}Te_{4}) series, which have attracted recent interest as intrinsic magnetic topological insulators. Combining circular dichroic, spin-resolved and photon-energy-dependent ARPES measurements with calculations based on density functional theory, we unveil complex momentum-dependent orbital and spin textures in the surface electronic structure and disentangle topological from trivial surface bands. We find that the Dirac-cone dispersion of the topologial surface state is strongly perturbed by hybridization with valence-band states for Bi_{2}Te_{3}-terminated surfaces but remains preserved for MnBi_{2}Te_{4}-terminated surfaces. Our results firmly establish the topologically nontrivial nature of these magnetic van der Waals materials and indicate that the possibility of realizing a quantized anomalous Hall conductivity depends on surface termination.

Robust Surface States and Coherence Phenomena in Magnetically Alloyed SmB_{6}.

Samarium hexaboride is a candidate for the topological Kondo insulator state, in which Kondo coherence is predicted to give rise to an insulating gap spanned by topological surface states. Here we investigate the surface and bulk electronic properties of magnetically alloyed Sm_{1-x}M_{x}B_{6} (M=Ce, Eu), using angle-resolved photoemission spectroscopy and complementary characterization techniques. Remarkably, topologically nontrivial bulk and surface band structures are found to persist in highly modified samples with up to 30% Sm substitution and with an antiferromagnetic ground state in the case of Eu doping. The results are interpreted in terms of a hierarchy of energy scales, in which surface state emergence is linked to the formation of a direct Kondo gap, while low-temperature transport trends depend on the indirect gap.

Prediction and observation of an antiferromagnetic topological insulator.

Magnetic topological insulators are narrow-gap semiconductor materials that combine non-trivial band topology and magnetic order1. Unlike their nonmagnetic counterparts, magnetic topological insulators may have some of the surfaces gapped, which enables a number of exotic phenomena that have potential applications in spintronics1, such as the quantum anomalous Hall effect2 and chiral Majorana fermions3. So far, magnetic topological insulators have only been created by means of doping nonmagnetic topological insulators with 3d transition-metal elements; however, such an approach leads to strongly inhomogeneous magnetic4 and electronic5 properties of these materials, restricting the observation of important effects to very low temperatures2,3. An intrinsic magnetic topological insulator-a stoichiometric well ordered magnetic compound-could be an ideal solution to these problems, but no such material has been observed so far. Here we predict by ab initio calculations and further confirm using various experimental techniques the realization of an antiferromagnetic topological insulator in the layered van der Waals compound MnBi2Te4. The antiferromagnetic ordering  that MnBi2Te4  shows makes it invariant with respect to the combination of the time-reversal and primitive-lattice translation symmetries, giving rise to a ℤ2 topological classification; ℤ2 = 1 for MnBi2Te4, confirming its topologically nontrivial nature. Our experiments indicate that the symmetry-breaking (0001) surface of MnBi2Te4 exhibits a large bandgap in the topological surface state. We expect this property to eventually enable the observation of a number of fundamental phenomena, among them quantized magnetoelectric coupling6-8 and axion electrodynamics9,10. Other exotic phenomena could become accessible at much higher temperatures than those reached so far, such as the quantum anomalous Hall effect2 and chiral Majorana fermions3.

Local electronic structure of the peptide bond probed by resonant inelastic soft X-ray scattering.

The local valence orbital structure of solid glycine, diglycine, and triglycine is studied using soft X-ray emission spectroscopy (XES), resonant inelastic soft X-ray scattering (RIXS) maps, and spectra calculations based on density-functional theory. Using a building block approach, the contributions of the different functional groups of the peptides are separated. Cuts through the RIXS maps furthermore allow monitoring selective excitations of the amino and peptide functional units, leading to a modification of the currently established assignment of spectral contributions. The results thus paint a new-and-improved picture of the peptide bond, enhance the understanding of larger molecules with peptide bonds, and simplify the investigation of such molecules in aqueous environment.

Site-specific electronic structure of imidazole and imidazolium in aqueous solutions.

The occupied and unoccupied electronic structure of imidazole (C3N2H4) and imidazolium (C3N2H5+) in aqueous solutions is studied by X-ray emission spectroscopy (XES) and resonant inelastic soft X-ray scattering (RIXS). Both systems show distinct RIXS fingerprints with strong resonant effects. A comparison with calculated X-ray emission spectra of isolated imidazole and imidazolium suggests only a small influence of hydrogen bonding in the aqueous solution on the electronic structure of imidazole and imidazolium, and allows the attribution of specific spectral features to the non-equivalent nitrogen and carbon atoms in the molecules. In the case of nitrogen, this can also be achieved by site-selective resonant excitation. Furthermore, we find spectator shifts and symmetry selectivity in the RIXS spectra, as well as indications for rapid proton dynamics on the femtosecond timescale of the RIXS process, and derive the HOMO-LUMO gaps for the two molecules in aqueous solution.

Matching DMFT calculations with photoemission spectra of heavy fermion insulators: universal properties of the near-gap spectra of SmB6.

Paramagnetic heavy fermion insulators consist of fully occupied quasiparticle bands inherent to Fermi liquid theory. The gap emergence below a characteristic temperature is the ultimate sign of coherence for a many-body system, which in addition can induce a non-trivial band topology. Here, we demonstrate a simple and efficient method to compare a model study and an experimental result for heavy fermion insulators. The temperature dependence of the gap formation in both local moment and mixed valence regimes is captured within the dynamical mean field (DMFT) approximation to the periodic Anderson model (PAM). Using the topological coherence temperature as the scaling factor and choosing the input parameter set within the mixed valence regime, we can unambiguously link the theoretical energy scales to the experimental ones. As a particularly important result, we find improved consistency between the scaled DMFT density of states and the photoemission near-gap spectra of samarium hexaboride (SmB6).

Strong Linear Dichroism in Spin-Polarized Photoemission from Spin-Orbit-Coupled Surface States.

A comprehensive understanding of spin-polarized photoemission is crucial for accessing the electronic structure of spin-orbit coupled materials. Yet, the impact of the final state in the photoemission process on the photoelectron spin has been difficult to assess in these systems. We present experiments for the spin-orbit split states in a Bi-Ag surface alloy showing that the alteration of the final state with energy may cause a complete reversal of the photoelectron spin polarization. We explain the effect on the basis of ab initio one-step photoemission theory and describe how it originates from linear dichroism in the angular distribution of photoelectrons. Our analysis shows that the modulated photoelectron spin polarization reflects the intrinsic spin density of the surface state being sampled differently depending on the final state, and it indicates linear dichroism as a natural probe of spin-orbit coupling at surfaces.

X-ray Emission Spectroscopy of Proteinogenic Amino Acids at All Relevant Absorption Edges.

Nonresonant N K, O K, C K, and S L2,3 X-ray emission spectra of the 20 most common proteinogenic amino acids in their solid zwitterionic form are reported. They represent a comprehensive database that can serve as a reliable basis for the X-ray absorption spectroscopy (XES) studies of peptides and proteins. At the most important N and O K edges, clear similarities and differences between the spectra of certain amino acids are observed and associated with the specific chemical structure of these molecules and their functional groups. Analysis of these spectra allows the generation of spectral fingerprints of the protonated amino group, the deprotonated carboxylic group, and, using a building block approach, the specific nitrogen- and oxygen-containing functional groups in the side chains of the amino acids. Some of these fingerprints are compared to the spectra of reference compounds with the respective functional groups; they exhibit reasonable similarity, underlining the validity of the spectral fingerprint approach. The C K and S L2,3 XES spectra are found to be specific for each amino acid, in accordance with the different local environments of the involved C and S atoms, respectively.

Direct 3D mapping of the Fermi surface and Fermi velocity.

We performed a full mapping of the bulk electronic structure including the Fermi surface and Fermi-velocity distribution vF(kF) of tungsten. The 4D spectral function ρ(EB; k) in the entire bulk Brillouin zone and 6 eV binding-energy (EB) interval was acquired in ∼3 h thanks to a new multidimensional photoemission data-recording technique (combining full-field k-microscopy with time-of-flight parallel energy recording) and the high brilliance of the soft X-rays used. A direct comparison of bulk and surface spectral functions (taken at low photon energies) reveals a time-reversal-invariant surface state in a local bandgap in the (110)-projected bulk band structure. The surface state connects hole and electron pockets that would otherwise be separated by an indirect local bandgap. We confirmed its Dirac-like spin texture by spin-filtered momentum imaging. The measured 4D data array enables extraction of the 3D dispersion of all bands, all energy isosurfaces, electron velocities, hole or electron conductivity, effective mass and inner potential by simple algorithms without approximations. The high-Z bcc metals with large spin-orbit-induced bandgaps are discussed as candidates for topologically non-trivial surface states.

Perpendicular Emission, Dichroism, and Energy Dependence in Angle-Resolved Photoemission: The Importance of The Final State.

Angle-resolved photoemission spectroscopy has been developed to a very high accuracy. However, effects that depend sensitively on the state of the emitted photoelectron were so far hard to compute for real molecules. We here show that the real-time propagation approach to time-dependent density functional theory allows us to obtain final-state effects consistently from first principles and with an accuracy that allows for the interpretation of experimental data. In a combined theoretical and experimental study we demonstrate that the approach captures three hallmark effects that are beyond the final-state plane-wave approximation: emission perpendicular to the light polarization, circular dichroism in the photoelectron angular distribution, and a pronounced energy dependence of the photoemission intensity.

Investigation of the Ionic Hydration in Aqueous Salt Solutions by Soft X-ray Emission Spectroscopy.

Understanding the molecular structure of the hydration shells and their impact on the hydrogen bond (HB) network of water in aqueous salt solutions is a fundamentally important and technically relevant question. In the present work, such hydration effects were studied for a series of representative salt solutions (NaCl, KCl, CaCl2, MgCl2, and KBr) by soft X-ray emission spectroscopy (XES) and resonant inelastic soft X-ray scattering (RIXS). The oxygen K-edge XES spectra could be described with three components, attributed to initial state HB configurations in pure water, water molecules that have undergone an ultrafast dissociation initiated by the X-ray excitation, and water molecules in contact with salt ions. The behavior of the individual components, as well as the spectral shape of the latter component, has been analyzed in detail. In view of the role of ions in such effects as protein denaturation (i.e., the Hofmeister series), we discuss the ion-specific nature of the hydration shells and find that the results point to a predominant role of anions as compared to cations. Furthermore, we observe a concentration-dependent suppression of ultrafast dissociation in all salt solutions, associated with a significant distortion of intact HB configurations of water molecules facilitating such a dissociation.

Electronic Structure of YbB_{6}: Is it a Topological Insulator or Not?

To finally resolve the controversial issue of whether or not the electronic structure of YbB_{6} is nontrivially topological, we have made a combined study using angle-resolved photoemission spectroscopy (ARPES) of the nonpolar (110) surface and density functional theory (DFT). The flat-band conditions of the (110) ARPES avoid the strong band bending effects of the polar (001) surface and definitively show that YbB_{6} has a topologically trivial B 2p-Yb 5d semiconductor band gap of ∼0.3 eV. Accurate determination of the low energy band topology in DFT requires the use of a modified Becke-Johnson exchange potential incorporating spin-orbit coupling and an on-site Yb 4f Coulomb interaction U as large as 7 eV. The DFT result, confirmed by a more precise GW band calculation, is similar to that of a small gap non-Kondo nontopological semiconductor. Additionally, the pressure-dependent electronic structure of YbB_{6} is investigated theoretically and found to transform into a p-d overlap semimetal with small Yb mixed valency.

Electron-Vibration Coupling in Molecular Materials: Assignment of Vibronic Modes from Photoelectron Momentum Mapping.

Electron-phonon coupling is one of the most fundamental effects in condensed matter physics. We here demonstrate that photoelectron momentum mapping can reveal and visualize the coupling between specific vibrational modes and electronic excitations. When imaging molecular orbitals with high energy resolution, the intensity patterns of photoelectrons of the vibronic sidebands of molecular states show characteristic changes due to the distortion of the molecular frame in the vibronically excited state. By comparison to simulations, an assignment of specific vibronic modes is possible, thus providing unique information on the coupling between electronic and vibronic excitation.

Isotope Effects in the Resonant Inelastic Soft X-ray Scattering Maps of Gas-Phase Methanol.

The electronic structure of gas-phase methanol molecules (H3COH, H3COD, and D3COD) at atmospheric pressure was investigated using resonant inelastic soft X-ray scattering (RIXS) at the O K and C K edges. We observe strong changes of the relative emission intensities of all valence orbitals as a function of excitation energy, which can be related to the symmetries of the involved orbitals causing an angularly anisotropic RIXS intensity. Furthermore, all observed emission lines are subject to strong spectator shifts of up to -0.9 eV at the O K edge and up to -0.3 eV at the C K edge. At the lowest O K resonance, we find clear evidence for dissociation of the methanol molecule on the time scale of the RIXS process, which is illustrated by comparing X-ray emission spectra of regular and deuterated methanol.

"Building block picture" of the electronic structure of aqueous cysteine derived from resonant inelastic soft X-ray scattering.

The electronic structure of the amino acid L-cysteine in an aqueous environment was studied using resonant inelastic soft X-ray scattering (RIXS) in a 2D map representation and analyzed in the framework of a "building block" approach. The element selectivity of RIXS allows a local investigation of the electronic structure of the three functional groups of cysteine, namely, the carboxyl, amino, and thiol groups, by measuring at the O K, N K, and S L2,3 edges, respectively. Variation of the pH value allows an investigation of molecules with protonated and deprotonated functional groups, which can then be compared with simple reference molecules that represent the isolated functional groups. We find that such building blocks can provide an excellent description of X-ray emission spectroscopy (XES) and RIXS spectra, but only if all nearest-neighbor atoms are included. This finding is analogous to the building block principle commonly used in X-ray absorption spectroscopy. The building blocks show a distinct spectral character (fingerprint) and allow a comprehensive interpretation of the cysteine spectra. This simple approach opens the path to investigate the electronic structure of more complex biological molecules in aqueous solutions using XES and RIXS.

Momentum-resolved hidden-order gap reveals symmetry breaking and origin of entropy loss in URu2Si2.

Spontaneous symmetry breaking in physical systems leads to salient phenomena at all scales, from the Higgs mechanism and the emergence of the mass of the elementary particles, to superconductivity and magnetism in solids. The hidden-order state arising below 17.5 K in URu2Si2 is a puzzling example of one of such phase transitions: its associated broken symmetry and gap structure have remained longstanding riddles. Here we directly image how, across the hidden-order transition, the electronic structure of URu2Si2 abruptly reconstructs. We observe an energy gap of 7 meV opening over 70% of a large diamond-like heavy-fermion Fermi surface, resulting in the formation of four small Fermi petals, and a change in the electronic periodicity from body-centred tetragonal to simple tetragonal. Our results explain the large entropy loss in the hidden-order phase, and the similarity between this phase and the high-pressure antiferromagnetic phase found in quantum-oscillation experiments.

Complete determination of molecular orbitals by measurement of phase symmetry and electron density.

Several experimental methods allow measuring the spatial probability density of electrons in atoms, molecules and solids, that is, the absolute square of the respective single-particle wave function. But it is an intrinsic problem of the measurement process that the information about the phase is generally lost during the experiment. The symmetry of this phase, however, is a crucial parameter for the knowledge of the full orbital information in real space. Here, we report on a key experiment that demonstrates that the phase symmetry can be derived from a strictly experimental approach from the circular dichroism in the angular distribution of photoelectrons. In combination with the electron density derived from the same experiment, the full quantum mechanical wave function can thus be determined experimentally.

Importance of charge fluctuations for the topological phase in SmB(6).

Typical Kondo insulators (KIs) can have a nontrivial Z_{2} topology because the energy gap opens at the Fermi energy (E_{F}) by a hybridization between odd- and even-parity bands. SmB_{6} deviates from such KI behavior, and it has been unclear how the insulating phase occurs. Here, we demonstrate that charge fluctuations are the origin of the topological insulating phase in SmB_{6}. Our angle-resolved photoemission spectroscopy results reveal that with decreasing temperature the bottom of the d-f hybridized band at the X[over ¯] point, which is predicted to have odd parity and is required for a topological phase, gradually shifts from below to above E_{F}. We conclude that SmB_{6} is a charge-fluctuating topological insulator.