Observation of Termination-Dependent Topological Connectivity in a Magnetic Weyl Kagome Lattice.

Engineering surfaces and interfaces of materials promises great potential in the field of heterostructures and quantum matter designers, with the opportunity to drive new many-body phases that are absent in the bulk compounds. Here, we focus on the magnetic Weyl kagome system Co3Sn2S2 and show how for the terminations of different samples the Weyl points connect differently, still preserving the bulk-boundary correspondence. Scanning tunneling microscopy has suggested such a scenario indirectly, and here, we probe the Fermiology of Co3Sn2S2 directly, by linking it to its real space surface distribution. By combining micro-ARPES and first-principles calculations, we measure the energy-momentum spectra and the Fermi surfaces of Co3Sn2S2 for different surface terminations and show the existence of topological features depending on the top-layer electronic environment. Our work helps to define a route for controlling bulk-derived topological properties by means of surface electrostatic potentials, offering a methodology for using Weyl kagome metals in responsive magnetic spintronics.

Deep Learning the Functional Renormalization Group.

We perform a data-driven dimensionality reduction of the scale-dependent four-point vertex function characterizing the functional renormalization group (FRG) flow for the widely studied two-dimensional t-t^{'} Hubbard model on the square lattice. We demonstrate that a deep learning architecture based on a neural ordinary differential equation solver in a low-dimensional latent space efficiently learns the FRG dynamics that delineates the various magnetic and d-wave superconducting regimes of the Hubbard model. We further present a dynamic mode decomposition analysis that confirms that a small number of modes are indeed sufficient to capture the FRG dynamics. Our Letter demonstrates the possibility of using artificial intelligence to extract compact representations of the four-point vertex functions for correlated electrons, a goal of utmost importance for the success of cutting-edge quantum field theoretical methods for tackling the many-electron problem.

Observation of room temperature excitons in an atomically thin topological insulator.

Optical spectroscopy of ultimately thin materials has significantly enhanced our understanding of collective excitations in low-dimensional semiconductors. This is particularly reflected by the rich physics of excitons in atomically thin crystals which uniquely arises from the interplay of strong Coulomb correlation, spin-orbit coupling (SOC), and lattice geometry. Here we extend the field by reporting the observation of room temperature excitons in a material of non-trivial global topology. We study the fundamental optical excitation spectrum of a single layer of bismuth atoms epitaxially grown on a SiC substrate (hereafter bismuthene or Bi/SiC) which has been established as a large-gap, two-dimensional (2D) quantum spin Hall (QSH) insulator. Strongly developed optical resonances are observed to emerge around the direct gap at the K and K' points of the Brillouin zone, indicating the formation of bound excitons with considerable oscillator strength. These experimental findings are corroborated, concerning both the character of the excitonic resonances as well as their energy scale, by ab-initio GW and Bethe-Salpeter equation calculations, confirming strong Coulomb interaction effects in these optical excitations. Our observations provide evidence of excitons in a 2D QSH insulator at room temperature, with excitonic and topological physics deriving from the very same electronic structure.

Triplet Superconductivity from Nonlocal Coulomb Repulsion in an Atomic Sn Layer Deposited onto a Si(111) Substrate.

Atomic layers deposited on semiconductor substrates introduce a platform for the realization of the extended electronic Hubbard model, where the consideration of electronic repulsion beyond the on-site term is paramount. Recently, the onset of superconductivity at 4.7 K has been reported in the hole-doped triangular lattice of tin atoms on a silicon substrate. Through renormalization group methods designed for weak and intermediate coupling, we investigate the nature of the superconducting instability in hole-doped Sn/Si(111). We find that the extended Hubbard nature of interactions is crucial to yield triplet pairing, which is f-wave (p-wave) for moderate (higher) hole doping. In light of persisting challenges to tailor triplet pairing in an electronic material, our finding promises to pave unprecedented ways for engineering unconventional triplet superconductivity.

Nature of Unconventional Pairing in the Kagome Superconductors AV_{3}Sb_{5} (A=K,Rb,Cs).

The recent discovery of AV_{3}Sb_{5} (A=K,Rb,Cs) has uncovered an intriguing arena for exotic Fermi surface instabilities in a kagome metal. Among them, superconductivity is found in the vicinity of multiple van Hove singularities, exhibiting indications of unconventional pairing. We show that the sublattice interference mechanism is central to understanding the formation of superconductivity in a kagome metal. Starting from an appropriately chosen minimal tight-binding model with multiple van Hove singularities close to the Fermi level for AV_{3}Sb_{5}, we provide a random phase approximation analysis of superconducting instabilities. Nonlocal Coulomb repulsion, the sublattice profile of the van Hove bands, and the interaction strength turn out to be the crucial parameters to determine the preferred pairing symmetry. Implications for potentially topological surface states are discussed, along with a proposal for additional measurements to pin down the nature of superconductivity in AV_{3}Sb_{5}.

Design and realization of topological Dirac fermions on a triangular lattice.

Large-gap quantum spin Hall insulators are promising materials for room-temperature applications based on Dirac fermions. Key to engineer the topologically non-trivial band ordering and sizable band gaps is strong spin-orbit interaction. Following Kane and Mele's original suggestion, one approach is to synthesize monolayers of heavy atoms with honeycomb coordination accommodated on templates with hexagonal symmetry. Yet, in the majority of cases, this recipe leads to triangular lattices, typically hosting metals or trivial insulators. Here, we conceive and realize "indenene", a triangular monolayer of indium on SiC exhibiting non-trivial valley physics driven by local spin-orbit coupling, which prevails over inversion-symmetry breaking terms. By means of tunneling microscopy of the 2D bulk we identify the quantum spin Hall phase of this triangular lattice and unveil how a hidden honeycomb connectivity emerges from interference patterns in Bloch px ± ipy-derived wave functions.

Turbulent hydrodynamics in strongly correlated Kagome metals.

A current challenge in condensed matter physics is the realization of strongly correlated, viscous electron fluids. These fluids can be described by holography, that is, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canonical system considered for realizations has been graphene. In this work, we show that Kagome systems with electron fillings adjusted to the Dirac nodes provide a much more compelling platform for realizations of viscous electron fluids, including non-linear effects such as turbulence. In particular, we find that in Scandium Herbertsmithite, the fine-structure constant, which measures the effective Coulomb interaction, is enhanced by a factor of about 3.2 as compared to graphene. We employ holography to estimate the ratio of the shear viscosity over the entropy density in Sc-Herbertsmithite, and find it about three times smaller than in graphene. These findings put the turbulent flow regime described by holography within the reach of experiments.

Orbital-Driven Rashba Effect in a Binary Honeycomb Monolayer AgTe.

The Rashba effect is fundamental to the physics of two-dimensional electron systems and underlies a variety of spintronic phenomena. It has been proposed that the formation of Rashba-type spin splittings originates microscopically from the existence of orbital angular momentum (OAM) in the Bloch wave functions. Here, we present detailed experimental evidence for this OAM-based origin of the Rashba effect by angle-resolved photoemission (ARPES) and two-photon photoemission experiments for a monolayer AgTe on Ag(111). Using quantitative low-energy electron diffraction analysis, we determine the structural parameters and the stacking of the honeycomb overlayer with picometer precision. Based on an orbital-symmetry analysis in ARPES and supported by first-principles calculations, we unequivocally relate the presence and absence of Rashba-type spin splittings in different bands of AgTe to the existence of OAM.

Orbital Fingerprint of Topological Fermi Arcs in the Weyl Semimetal TaP.

The monopnictides TaAs and TaP are well-established Weyl semimetals. Yet, a precise assignment of Fermi arcs, accommodating the predicted chiral charge of the bulk Weyl points, has been difficult in these systems, and the topological character of different surface features in the Fermi surface is not fully understood. Here, employing a joint analysis from linear dichroism in angle-resolved photoemission and first-principles calculations, we unveil the orbital texture on the full Fermi surface of TaP(001). We observe pronounced switches in the orbital texture at the projected Weyl nodes, and show how they facilitate a topological classification of the surface band structure. Our findings establish a critical role of the orbital degrees of freedom in mediating the surface-bulk connectivity in Weyl semimetals.

Tunable metal-insulator transition, Rashba effect and Weyl Fermions in a relativistic charge-ordered ferroelectric oxide.

Controllable metal-insulator transitions (MIT), Rashba-Dresselhaus (RD) spin splitting, and Weyl semimetals are promising schemes for realizing processing devices. Complex oxides are a desirable materials platform for such devices, as they host delicate and tunable charge, spin, orbital, and lattice degrees of freedoms. Here, using first-principles calculations and symmetry analysis, we identify an electric-field tunable MIT, RD effect, and Weyl semimetal in a known, charge-ordered, and polar relativistic oxide Ag2BiO3 at room temperature. Remarkably, a centrosymmetric BiO6 octahedral-breathing distortion induces a sizable spontaneous ferroelectric polarization through Bi3+/Bi5+ charge disproportionation, which stabilizes simultaneously the insulating phase. The continuous attenuation of the Bi3+/Bi5+ disproportionation obtained by applying an external electric field reduces the band gap and RD spin splitting and drives the phase transition from a ferroelectric RD insulator to a paraelectric Dirac semimetal, through a topological Weyl semimetal intermediate state. These findings suggest that Ag2BiO3 is a promising material for spin-orbitonic applications.

Ferroelectric Control of the Spin Texture in GeTe.

The electric and nonvolatile control of the spin texture in semiconductors would represent a fundamental step toward novel electronic devices combining memory and computing functionalities. Recently, GeTe has been theoretically proposed as the father compound of a new class of materials, namely ferroelectric Rashba semiconductors. They display bulk bands with giant Rashba-like splitting due to the inversion symmetry breaking arising from the ferroelectric polarization, thus allowing for the ferroelectric control of the spin. Here, we provide the experimental demonstration of the correlation between ferroelectricity and spin texture. A surface-engineering strategy is used to set two opposite predefined uniform ferroelectric polarizations, inward and outward, as monitored by piezoresponse force microscopy. Spin and angular resolved photoemission experiments show that these GeTe(111) surfaces display opposite sense of circulation of spin in bulk Rashba bands. Furthermore, we demonstrate the crafting of nonvolatile ferroelectric patterns in GeTe films at the nanoscale by using the conductive tip of an atomic force microscope. Based on the intimate link between ferroelectric polarization and spin in GeTe, ferroelectric patterning paves the way to the investigation of devices with engineered spin configurations.

Three-Dimensional Electronic Structure of the Type-II Weyl Semimetal WTe_{2}.

By combining bulk sensitive soft-x-ray angular-resolved photoemission spectroscopy and first-principles calculations we explored the bulk electron states of WTe_{2}, a candidate type-II Weyl semimetal featuring a large nonsaturating magnetoresistance. Despite the layered geometry suggesting a two-dimensional electronic structure, we directly observe a three-dimensional electronic dispersion. We report a band dispersion in the reciprocal direction perpendicular to the layers, implying that electrons can also travel coherently when crossing from one layer to the other. The measured Fermi surface is characterized by two well-separated electron and hole pockets at either side of the Γ point, differently from previous more surface sensitive angle-resolved photoemission spectroscopy experiments that additionally found a pronounced quasiparticle weight at the zone center. Moreover, we observe a significant sensitivity of the bulk electronic structure of WTe_{2} around the Fermi level to electronic correlations and renormalizations due to self-energy effects, previously neglected in first-principles descriptions.

Disorder-Driven Metal-Insulator Transitions in Deformable Lattices.

We show that, in the presence of a deformable lattice potential, the nature of the disorder-driven metal-insulator transition is fundamentally changed with respect to the noninteracting (Anderson) scenario. For strong disorder, even a modest electron-phonon interaction is found to dramatically renormalize the random potential, opening a mobility gap at the Fermi energy. This process, which reflects disorder-enhanced polaron formation, is here given a microscopic basis by treating the lattice deformations and Anderson localization effects on the same footing. We identify an intermediate "bad insulator" transport regime which displays resistivity values exceeding the Mott-Ioffe-Regel limit and with a negative temperature coefficient, as often observed in strongly disordered metals. Our calculations reveal that this behavior originates from significant temperature-induced rearrangements of electronic states due to enhanced interaction effects close to the disorder-driven metal-insulator transition.

Giant Rashba Splitting in Pb1-x Snx Te (111) Topological Crystalline Insulator Films Controlled by Bi Doping in the Bulk.

The topological properties of lead-tin chalcogenide topological crystalline insulators can be widely tuned by temperature and composition. It is shown that bulk Bi doping of epitaxial Pb1-x Snx Te (111) films induces a giant Rashba splitting at the surface that can be tuned by the doping level. Tight binding calculations identify their origin as Fermi level pinning by trap states at the surface.

Robust spin-polarized midgap states at step edges of topological crystalline insulators.

Topological crystalline insulators are materials in which the crystalline symmetry leads to topologically protected surface states with a chiral spin texture, rendering them potential candidates for spintronics applications. Using scanning tunneling spectroscopy, we uncover the existence of one-dimensional (1D) midgap states at odd-atomic surface step edges of the three-dimensional topological crystalline insulator (Pb,Sn)Se. A minimal toy model and realistic tight-binding calculations identify them as spin-polarized flat bands connecting two Dirac points. This nontrivial origin provides the 1D midgap states with inherent stability and protects them from backscattering. We experimentally show that this stability results in a striking robustness to defects, strong magnetic fields, and elevated temperature.

Lone-Pair-Electron-Driven Ionic Displacements in a Ferroelectric Metal-Organic Hybrid.

A displacive-type mechanism, which accounts for the occurrence of ferroelectricity in most inorganic ferroelectrics, is rarely found in molecule-based ferroelectrics. Its role is often covered by the predominant order-disorder one. Herein, we report a lone-pair-electron-driven displacive-type ferroelectric organic-inorganic hybrid compound, [H2dmdap][SbCl5] (1; dmdap = N,N-dimethyl-1,3-diaminopropane). The structure of 1 features a typical zigzag chain of [SbCl5]∞ containing cis-connected anionic octahedra. The compound undergoes a second-order paraelectric-ferroelectric phase transition at 143 K (P21/c ↔ Pc) with a saturation polarization of 1.36 µC·cm-2 and a coercive field of 3.5 kV·cm-1 at 119 K. Theoretical study discloses the ferroelectricity mainly originating from the relative displacements of the Sb and Cl ions in the crystal lattice, which are driven by the 5s2 lone-pair electrons of the SbIII center. Furthermore, on the basis of analysis, possible routes are suggested to enhance ferroelectric polarization in this class of compounds.

Intertwined Rashba, Dirac, and Weyl Fermions in Hexagonal Hyperferroelectrics.

By means of density functional theory based calculations, we study the role of spin-orbit coupling in the new family of ABC hyperferroelectrics [Garrity, Rabe, and Vanderbilt Phys. Rev. Lett. 112, 127601 (2014)]. We unveil an extremely rich physics strongly linked to ferroelectric properties, ranging from the electric control of bulk Rashba effect to the existence of a three-dimensional topological insulator phase, with concomitant topological surface states even in the ultrathin film limit. Moreover, we predict that the topological transition, as induced by alloying, is followed by a Weyl semimetal phase of finite concentration extension, which is robust against disorder, putting forward hyperferroelectrics as promising candidates for spin-orbitronic applications.

Experimental and theoretical studies of structural phase transition in a novel polar perovskite-like [C2H5NH3][Na0.5Fe0.5(HCOO)3] formate.

We report the synthesis, single crystal X-ray diffraction, and thermal, dielectric, Raman and infrared studies of a novel heterometallic formate [C2H5NH3][Na0.5Fe0.5(HCOO)3] (EtANaFe). The thermal studies show that EtANaFe undergoes a second-order phase transition at about 360 K. X-ray diffraction data revealed that the high-temperature structure is monoclinic, space group P2(1)/n, with dynamically disordered ethylammonium (EtA(+)) cations. EtANaFe possesses a polar low-temperature structure with the space group Pn and, in principle, is ferroelectric below 360 K. Dielectric data show that the reciprocal of the real part of dielectric permittivity above and below the phase transition temperature follows the Curie-Weiss, as expected for a ferroelectric phase transition. Based on theoretical calculations, we estimated the polarization as (0.2, 0, 0.8) µC cm(-2), i.e., lying within the ac plane. The obtained data also indicate that the driving force of the phase transition is ordering of EtA(+) cations. However, this ordering is accompanied by significant distortion of the metal formate framework.

Giant Rashba-Type Spin Splitting in Ferroelectric GeTe(111).

Photoelectron spectroscopy in combination with piezoforce microscopy reveals that the helicity of Rashba bands is coupled to the nonvolatile ferroelectric polarization of GeTe(111). A novel surface Rashba band is found and fingerprints of a bulk Rashba band are identified by comparison with density functional theory calculations.

Strain tuning of ferroelectric polarization in hybrid organic inorganic perovskite compounds.

Metal-organic frameworks (MOFs) are hybrid crystalline compounds comprised of an extended ordered network made up of organic molecules, organic linkers and metal cations. In particular, MOFs with the same topology as inorganic perovskites have been shown to possess interesting properties, e.g., coexistence of ferroelectric and magnetic ordering. Using first-principles density functional theory, we have investigated the effect of strain on the compounds C(NH2)3Cr(HCOO)3 and (CH3CH2NH3)Mn(HCOO)3. Here, we show that compressive strain can substantially increase the ferroelectric polarization by more than 300%, and we discuss the mechanism involved in the strain enhancement of polarization. Our study highlights the complex interplay between strain and organic cations' dipoles and put forward the possibility of tuning of ferroelectric polarization through appropriate thin film growing.