Publisher Correction: A weak topological insulator state in quasi-one-dimensional bismuth iodide.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

A weak topological insulator state in quasi-one-dimensional bismuth iodide.

The major breakthroughs in understanding of topological materials over the past decade were all triggered by the discovery of the Z2-type topological insulator-a type of material that is insulating in its interior but allows electron flow on its surface. In three dimensions, a topological insulator is classified as either 'strong' or 'weak'1,2, and experimental confirmations of the strong topological insulator rapidly followed theoretical predictions3-5. By contrast, the weak topological insulator (WTI) has so far eluded experimental verification, because the topological surface states emerge only on particular side surfaces, which are typically undetectable in real three-dimensional crystals6-10. Here we provide experimental evidence for the WTI state in a bismuth iodide, ß-Bi4I4. Notably, the crystal has naturally cleavable top and side planes-stacked via van der Waals forces-which have long been desirable for the experimental realization of the WTI state11,12. As a definitive signature of this state, we find a quasi-one-dimensional Dirac topological surface state at the side surface (the (100) plane), while the top surface (the (001) plane) is topologically dark with an absence of topological surface states. We also find that a crystal transition from the ß-phase to the α-phase drives a topological phase transition from a nontrivial WTI to a normal insulator at roughly room temperature. The weak topological phase-viewed as quantum spin Hall insulators stacked three-dimensionally13,14-will lay a foundation for technology that benefits from highly directional, dense spin currents that are protected against backscattering.

The PERCIVAL detector: first user experiments.

The PERCIVAL detector is a CMOS imager designed for the soft X-ray regime at photon sources. Although still in its final development phase, it has recently seen its first user experiments: ptychography at a free-electron laser, holographic imaging at a storage ring and preliminary tests on X-ray photon correlation spectroscopy. The detector performed remarkably well in terms of spatial resolution achievable in the sample plane, owing to its small pixel size, large active area and very large dynamic range; but also in terms of its frame rate, which is significantly faster than traditional CCDs. In particular, it is the combination of these features which makes PERCIVAL an attractive option for soft X-ray science.

Maximal Rashba-like spin splitting via kinetic-energy-coupled inversion-symmetry breaking.

Engineering and enhancing the breaking of inversion symmetry in solids-that is, allowing electrons to differentiate between 'up' and 'down'-is a key goal in condensed-matter physics and materials science because it can be used to stabilize states that are of fundamental interest and also have potential practical applications. Examples include improved ferroelectrics for memory devices and materials that host Majorana zero modes for quantum computing. Although inversion symmetry is naturally broken in several crystalline environments, such as at surfaces and interfaces, maximizing the influence of this effect on the electronic states of interest remains a challenge. Here we present a mechanism for realizing a much larger coupling of inversion-symmetry breaking to itinerant surface electrons than is typically achieved. The key element is a pronounced asymmetry of surface hopping energies-that is, a kinetic-energy-coupled inversion-symmetry breaking, the energy scale of which is a substantial fraction of the bandwidth. Using spin- and angle-resolved photoemission spectroscopy, we demonstrate that such a strong inversion-symmetry breaking, when combined with spin-orbit interactions, can mediate Rashba-like spin splittings that are much larger than would typically be expected. The energy scale of the inversion-symmetry breaking that we achieve is so large that the spin splitting in the CoO2- and RhO2-derived surface states of delafossite oxides becomes controlled by the full atomic spin-orbit coupling of the 3d and 4d transition metals, resulting in some of the largest known Rashba-like spin splittings. The core structural building blocks that facilitate the bandwidth-scaled inversion-symmetry breaking are common to numerous materials. Our findings therefore provide opportunities for creating spin-textured states and suggest routes to interfacial control of inversion-symmetry breaking in designer heterostructures of oxides and other material classes.

Bulk and Surface Electronic Structure of the Dual-Topology Semimetal Pt_{2}HgSe_{3}.

We report high-resolution angle-resolved photoemission measurements on single crystals of Pt_{2}HgSe_{3} grown by high-pressure synthesis. Our data reveal a gapped Dirac nodal line whose (001) projection separates the surface Brillouin zone in topological and trivial areas. In the nontrivial k-space range, we find surface states with multiple saddle points in the dispersion, resulting in two van Hove singularities in the surface density of states. Based on density-functional theory calculations, we identify these surface states as signatures of a topological crystalline state, which coexists with a weak topological phase.

Ubiquitous formation of bulk Dirac cones and topological surface states from a single orbital manifold in transition-metal dichalcogenides.

Transition-metal dichalcogenides (TMDs) are renowned for their rich and varied bulk properties, while their single-layer variants have become one of the most prominent examples of two-dimensional materials beyond graphene. Their disparate ground states largely depend on transition metal d-electron-derived electronic states, on which the vast majority of attention has been concentrated to date. Here, we focus on the chalcogen-derived states. From density-functional theory calculations together with spin- and angle-resolved photoemission, we find that these generically host a co-existence of type-I and type-II three-dimensional bulk Dirac fermions as well as ladders of topological surface states and surface resonances. We demonstrate how these naturally arise within a single p-orbital manifold as a general consequence of a trigonal crystal field, and as such can be expected across a large number of compounds. Already, we demonstrate their existence in six separate TMDs, opening routes to tune, and ultimately exploit, their topological physics.

Experimental Determination of the Topological Phase Diagram in Cerium Monopnictides.

Experimental determinations of bulk band topology in the solid states have been so far restricted to only indirect investigation through the probing of surface states predicted by electronic structure calculations. We here present an alternative approach to determine the band topology by means of bulk-sensitive soft x-ray angle-resolved photoemission spectroscopy. We investigate the bulk electronic structures of the series materials, Ce monopnictides (CeP, CeAs, CeSb, and CeBi). By performing a paradigmatic study of the band structures as a function of their spin-orbit coupling, we draw the topological phase diagram and unambiguously reveal the topological phase transition from a trivial to a nontrivial regime in going from CeP to CeBi induced by the band inversion. The underlying mechanism of the phase transition is elucidated in terms of spin-orbit coupling in concert with their semimetallic band structures. Our comprehensive observations provide a new insight into the band topology hidden in the bulk states.

Fermiology and Superconductivity of Topological Surface States in PdTe_{2}.

We study the low-energy surface electronic structure of the transition-metal dichalcogenide superconductor PdTe_{2} by spin- and angle-resolved photoemission, scanning tunneling microscopy, and density-functional theory-based supercell calculations. Comparing PdTe_{2} with its sister compound PtSe_{2}, we demonstrate how enhanced interlayer hopping in the Te-based material drives a band inversion within the antibonding p-orbital manifold well above the Fermi level. We show how this mediates spin-polarized topological surface states which form rich multivalley Fermi surfaces with complex spin textures. Scanning tunneling spectroscopy reveals type-II superconductivity at the surface, and moreover shows no evidence for an unconventional component of its superconducting order parameter, despite the presence of topological surface states.

Tailoring the nature and strength of electron-phonon interactions in the SrTiO3(001) 2D electron liquid.

Surfaces and interfaces offer new possibilities for tailoring the many-body interactions that dominate the electrical and thermal properties of transition metal oxides. Here, we use the prototypical two-dimensional electron liquid (2DEL) at the SrTiO3(001) surface to reveal a remarkably complex evolution of electron-phonon coupling with the tunable carrier density of this system. At low density, where superconductivity is found in the analogous 2DEL at the LaAlO3/SrTiO3 interface, our angle-resolved photoemission data show replica bands separated by 100 meV from the main bands. This is a hallmark of a coherent polaronic liquid and implies long-range coupling to a single longitudinal optical phonon branch. In the overdoped regime the preferential coupling to this branch decreases and the 2DEL undergoes a crossover to a more conventional metallic state with weaker short-range electron-phonon interaction. These results place constraints on the theoretical description of superconductivity and allow a unified understanding of the transport properties in SrTiO3-based 2DELs.

Dimensional Crossover in a Charge Density Wave Material Probed by Angle-Resolved Photoemission Spectroscopy.

High-resolution angle-resolved photoemission spectroscopy data reveal evidence of a crossover from one-dimensional (1D) to three-dimensional (3D) behavior in the prototypical charge density wave (CDW) material NbSe_{3}. In the low-temperature 3D regime, gaps in the electronic structure are observed due to two incommensurate CDWs, in agreement with x-ray diffraction and electronic-structure calculations. At higher temperatures we observe a spectral weight depletion that approaches the power-law behavior expected in one dimension. From the warping of the quasi-1D Fermi surface at low temperatures, we extract the energy scale of the dimensional crossover. This is corroborated by a detailed analysis of the density of states, which reveals a change in dimensional behavior dependent on binding energy. Our results offer an important insight into the dimensionality of excitations in quasi-1D materials.

Multiband One-Dimensional Electronic Structure and Spectroscopic Signature of Tomonaga-Luttinger Liquid Behavior in K_{2}Cr_{3}As_{3}.

We present angle-resolved photoemission spectroscopy measurements of the quasi-one-dimensional superconductor K_{2}Cr_{3}As_{3}. We find that the Fermi surface contains two Fermi surface sheets, with linearly dispersing bands not displaying any significant band renormalizations. The one-dimensional band dispersions display a suppression of spectral intensity approaching the Fermi level according to a linear power law, over an energy range of ∼200 meV. This is interpreted as a signature of Tomonoga-Luttinger liquid physics, which provides a new perspective on the possibly unconventional superconductivity in this family of compounds.

Generation and Evolution of Spin-, Valley-, and Layer-Polarized Excited Carriers in Inversion-Symmetric WSe_{2}.

We report the spin-selective optical excitation of carriers in inversion-symmetric bulk samples of the transition metal dichalcogenide (TMDC) WSe_{2}. Employing time- and angle-resolved photoelectron spectroscopy (trARPES) and complementary time-dependent density functional theory (TDDFT), we observe spin-, valley-, and layer-polarized excited state populations upon excitation with circularly polarized pump pulses, followed by ultrafast (<100 fs) scattering of carriers towards the global minimum of the conduction band. TDDFT reveals the character of the conduction band, into which electrons are initially excited, to be two-dimensional and localized within individual layers, whereas at the minimum of the conduction band, states have a three-dimensional character, facilitating interlayer charge transfer. These results establish the optical control of coupled spin-, valley-, and layer-polarized states in centrosymmetric materials with locally broken symmetries and suggest the suitability of TMDC multilayer and heterostructure materials for valleytronic and spintronic device concepts.

A stable three-dimensional topological Dirac semimetal Cd3As2.

Three-dimensional (3D) topological Dirac semimetals (TDSs) are a recently proposed state of quantum matter that have attracted increasing attention in physics and materials science. A 3D TDS is not only a bulk analogue of graphene; it also exhibits non-trivial topology in its electronic structure that shares similarities with topological insulators. Moreover, a TDS can potentially be driven into other exotic phases (such as Weyl semimetals, axion insulators and topological superconductors), making it a unique parent compound for the study of these states and the phase transitions between them. Here, by performing angle-resolved photoemission spectroscopy, we directly observe a pair of 3D Dirac fermions in Cd3As2, proving that it is a model 3D TDS. Compared with other 3D TDSs, for example, ß-cristobalite BiO2 (ref. 3) and Na3Bi (refs 4, 5), Cd3As2 is stable and has much higher Fermi velocities. Furthermore, by in situ doping we have been able to tune its Fermi energy, making it a flexible platform for exploring exotic physical phenomena.

Collapse of the Mott Gap and Emergence of a Nodal Liquid in Lightly Doped Sr(2)IrO(4).

We report angle resolved photoemission experiments on the electron doped Heisenberg antiferromagnet (Sr(1-x)La(x))(2)IrO(4). For a doping level of x=0.05, we find an unusual metallic state with coherent nodal excitations and an antinodal pseudogap bearing strong similarities with underdoped cuprates. This state emerges from a rapid collapse of the Mott gap with doping resulting in a large underlying Fermi surface that is backfolded by a (π,π) reciprocal lattice vector which we attribute to the intrinsic structural distortion of Sr(2)IrO(4).

Signature of Strong Spin-Orbital Coupling in the Large Nonsaturating Magnetoresistance Material WTe2.

We report the detailed electronic structure of WTe2 by high resolution angle-resolved photoemission spectroscopy. We resolved a rather complicated Fermi surface of WTe2. Specifically, there are in total nine Fermi pockets, including one hole pocket at the Brillouin zone center Γ, and two hole pockets and two electron pockets on each side of Γ along the Γ-X direction. Remarkably, we have observed circular dichroism in our photoemission spectra, which suggests that the orbital angular momentum exhibits a rich texture at various sections of the Fermi surface. This is further confirmed by our density-functional-theory calculations, where the spin texture is qualitatively reproduced as the conjugate consequence of spin-orbital coupling. Since the spin texture would forbid backscatterings that are directly involved in the resistivity, our data suggest that the spin-orbit coupling and the related spin and orbital angular momentum textures may play an important role in the anomalously large magnetoresistance of WTe2. Furthermore, the large differences among spin textures calculated for magnetic fields along the in-plane and out-of-plane directions also provide a natural explanation of the large field-direction dependence on the magnetoresistance.

Suppression of thermal conductivity by rattling modes in thermoelectric sodium cobaltate.

The need for both high electrical conductivity and low thermal conductivity creates a design conflict for thermoelectric systems, leading to the consideration of materials with complicated crystal structures. Rattling of ions in cages results in low thermal conductivity, but understanding the mechanism through studies of the phonon dispersion using momentum-resolved spectroscopy is made difficult by the complexity of the unit cells. We have performed inelastic X-ray and neutron scattering experiments that are in remarkable agreement with our first-principles density-functional calculations of the phonon dispersion for thermoelectric Na(0.8)CoO2, which has a large-period superstructure. We have directly observed an Einstein-like rattling mode at low energy, involving large anharmonic displacements of the sodium ions inside multi-vacancy clusters. These rattling modes suppress the thermal conductivity by a factor of six compared with vacancy-free NaCoO2. Our results will guide the design of the next generation of materials for applications in solid-state refrigerators and power recovery.

Control of a two-dimensional electron gas on SrTiO3(111) by atomic oxygen.

We report on the formation of a two-dimensional electron gas (2DEG) at the bare surface of (111) oriented SrTiO3. Angle resolved photoemission experiments reveal highly itinerant carriers with a sixfold symmetric Fermi surface and strongly anisotropic effective masses. The electronic structure of the 2DEG is in good agreement with self-consistent tight-binding supercell calculations that incorporate a confinement potential due to surface band bending. We further demonstrate that alternate exposure of the surface to ultraviolet light and atomic oxygen allows tuning of the carrier density and the complete suppression of the 2DEG.

Coherent quasiparticles with a small fermi surface in lightly doped Sr(3)Ir(2)O(7).

We characterize the electron doping evolution of (Sr_{1-x}La_{x})_{3}Ir_{2}O_{7} by means of angle-resolved photoemission. Concomitant with the metal insulator transition around x≈0.05 we find the emergence of coherent quasiparticle states forming a closed small Fermi surface of volume 3x/2, where x is the independently measured La concentration. The quasiparticle weight Z remains large along the entire Fermi surface, consistent with the moderate renormalization of the low-energy dispersion, and no pseudogap is observed. This indicates a conventional, weakly correlated Fermi liquid state with a momentum independent residue Z≈0.5 in lightly doped Sr_{3}Ir_{2}O_{7}.

Circular dichroism in hard X-ray photoelectron diffraction observed by time-of-flight momentum microscopy.

X-ray photoelectron diffraction (XPD) is a powerful technique that yields detailed structural information of solids and thin films that complements electronic structure measurements. Among the strongholds of XPD we can identify dopant sites, track structural phase transitions, and perform holographic reconstruction. High-resolution imaging of kll-distributions (momentum microscopy) presents a new approach to core-level photoemission. It yields full-field kx-ky XPD patterns with unprecedented acquisition speed and richness in details. Here, we show that beyond the pure diffraction information, XPD patterns exhibit pronounced circular dichroism in the angular distribution (CDAD) with asymmetries up to 80%, alongside with rapid variations on a small kll-scale (0.1 Å-1). Measurements with circularly-polarized hard X-rays (hν = 6 keV) for a number of core levels, including Si, Ge, Mo and W, prove that core-level CDAD is a general phenomenon that is independent of atomic number. The fine structure in CDAD is more pronounced compared to the corresponding intensity patterns. Additionally, they obey the same symmetry rules as found for atomic and molecular species, and valence bands. The CD is antisymmetric with respect to the mirror planes of the crystal, whose signatures are sharp zero lines. Calculations using both the Bloch-wave approach and one-step photoemission reveal the origin of the fine structure that represents the signature of Kikuchi diffraction. To disentangle the roles of photoexcitation and diffraction, XPD has been implemented into the Munich SPRKKR package to unify the one-step model of photoemission and multiple scattering theory.

Understanding the complex phase diagram of uranium: the role of electron-phonon coupling.

We report an experimental determination of the dispersion of the soft phonon mode along [100] in uranium as a function of pressure. The energies of these phonons increase rapidly, with conventional behavior found by 20 GPa, as predicted by recent theory. New calculations demonstrate the strong pressure (and momentum) dependence of the electron-phonon coupling, whereas the Fermi-surface nesting is surprisingly independent of pressure. This allows a full understanding of the complex phase diagram of uranium and the interplay between the charge-density wave and superconductivity.