We report the experimental discovery of orbital vortex lines in the three-dimensional (3D) band structure of a topological semimetal. Combining linear and circular dichroism in soft x-ray angle-resolved photoemission (SX-ARPES) with first-principles theory, we image the winding of atomic orbital angular momentum, thereby revealing-and determining the location of-lines of vorticity in full 3D momentum space. We determine the core of the orbital angular momentum vortex to host an almost movable, twofold, spin-degenerate Weyl nodal line, a topological feature predicted to occur in certain nonsymmorphic crystals. These results establish bimodal dichroism in SX-ARPES as a robust approach to trace 3D orbital textures. Our findings constitute the first imaging of nontrivial quantum-phase winding at line nodes and may pave the way to new orbitronic phenomena in quantum materials.

Atomic monolayers on semiconductor surfaces represent an emerging class of functional quantum materials in the two-dimensional limit — ranging from superconductors and Mott insulators to ferroelectrics and quantum spin Hall insulators. Indenene, a triangular monolayer of indium with a gap of ~ 120 meV is a quantum spin Hall insulator whose micron-scale epitaxial growth on SiC(0001) makes it technologically relevant. However, its suitability for room-temperature spintronics is challenged by the instability of its topological character in air. It is imperative to develop a strategy to protect the topological nature of indenene during ex situ processing and device fabrication. Here we show that intercalation of indenene into epitaxial graphene provides effective protection from the oxidising environment, while preserving an intact topological character. Our approach opens a rich realm of ex situ experimental opportunities, priming monolayer quantum spin Hall insulators for realistic device fabrication and access to topologically protected edge channels.

We report the experimental discovery of orbital vortex lines in the three-dimensional (3D) band structure of a topological semimetal. Combining linear and circular dichroism in soft x-ray angle-resolved photoemission (SX-ARPES) with first-principles theory, we image the winding of atomic orbital angular momentum, thereby revealing - and determining the location of - lines of vorticity in full 3D momentum space. Our observation of momentum-space vortex lines with quantized winding number establishes an analogue to real-space quantum vortices, for instance, in type-II superconductors and certain non-collinear magnets. These results establish multimodal dichroism in SX-ARPES as an approach to trace 3D orbital textures. Our present findings particularly constitute the first imaging of non-trivial quantum-phase winding at line nodes and may pave the way to new orbitronic phenomena in quantum materials

The demonstration of a topological band inversion constitutes the most elementary proof of a quantum spin Hall insulator (QSHI). On a fundamental level, such an inverted band gap is intrinsically related to the bulk Berry curvature, a gauge-invariant fingerprint of the wave function's quantum geometric properties in Hilbert space. Intimately tied to orbital angular momentum (OAM), the Berry curvature can be, in principle, extracted from circular dichroism in angle-resolved photoemission spectroscopy (CD-ARPES), were it not for interfering final state photoelectron emission channels that obscure the initial state OAM signature. Here, we outline a full-experimental strategy to avoid such interference artifacts and isolate the clean OAM from the CD-ARPES response. Bench-marking this strategy for the recently discovered atomic monolayer system indenene, we demonstrate its distinct QSHI character and establish CD-ARPES as a scalable bulk probe to experimentally classify the topology of two-dimensional quantum materials with time reversal symmetry.

Berry phase and the related concept of Berry curvature can give rise to many unconventional phenomena in solids. In this work, we discover colossal orbital Zeeman effect of topological origin in a newly synthesized bilayer kagome metal TbV6Sn6. We use spectroscopic-imaging scanning tunneling microscopy to study the magnetic field induced renormalization of the electronic band structure. The nonmagnetic vanadium d-orbitals form Dirac crossings at the K point with a small mass gap and strong Berry curvature induced by the spin-orbit coupling. We reveal that the magnetic field leads to the splitting of gapped Dirac dispersion into two branches with giant momentum-dependent g factors, resulting in the substantial renormalization of the Dirac band. These measurements provide a direct observation of the magnetic field controlled orbital Zeeman coupling to the enormous orbital magnetic moments of up to 200 Bohr magnetons near the gapped Dirac points. Interestingly, the effect is increasingly non-linear, and becomes gradually suppressed at higher magnetic fields. Theoretical modeling further confirms the existence of orbital magnetic moments in TbV6Sn6 produced by the non-trivial spin-Berry curvature of the Bloch wave functions. Our work provides the first direct insight into the momentum-dependent nature of topological orbital moments and their tunability by magnetic field concomitant with the evolution of the spin-Berry curvature. Significantly large orbital magnetic moments driven by the Berry curvature can also be generated by other quantum numbers beyond spin, such as the valley in certain graphene-based structures, which may be unveiled using the same tools highlighted in our work.

Atomic monolayers on semiconductor surfaces represent a new class of functional quantum materials at the ultimate two-dimensional limit, ranging from superconductors [1, 2] to Mott insulators [3, 4] and ferroelectrics [5] to quantum spin Hall insulators (QSHI) [6, 7]. A case in point is the recently discovered QSHI indenene [7, 8], a triangular monolayer of indium epitaxially grown on SiC(0001), exhibiting a ∼120meV gap and substrate-matched monodomain growth on the technologically relevant μm scale [9]. Its suitability for room-temperature spintronics is countered, however, by the instability of pristine indenene in air, which destroys the system along with its topological character, nullifying hopes of ex-situ processing and device fabrication. Here we show how indenene intercalation into epitaxial graphene offers effective protection from the oxidizing environment, while it leaves the topological character fully intact. This opens an unprecedented realm of ex-situ experimental opportunities, bringing this monolayer QSHI within realistic reach of actual device fabrication and edge channel transport.

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.

We present a recipe for an electronic 2D higher order topological insulator (HOTI) on the triangular lattice that can be realized in a large family of materials. The essential ingredient is mirror symmetry breaking, which allows for a finite quadrupole moment and trivial $\mathbb{Z}_2$ index. The competition between spin-orbit coupling and the symmetry breaking terms gives rise to four topologically distinct phases; the HOTI phase appears when symmetry breaking dominates, including in the absence of spin-orbit coupling. We identify triangular monolayer adsorbate systems on the (111) surface of zincblende/diamond type substrates as ideal material platforms and predict the HOTI phase for $X=$(Al,B,Ga) on SiC.

Structural moiré superstructures arising from two competing lattices may lead to unexpected electronic behavior. Sb is predicted to show thickness-dependent topological properties, providing potential applications for low-energy-consuming electronic devices. Here we successfully synthesize ultrathin Sb films on semi-insulating InSb(111)A. Despite the covalent nature of the substrate, which has dangling bonds on the surface, we prove by scanning transmission electron microscopy that the first layer of Sb atoms grows in an unstrained manner. Rather than compensating for the lattice mismatch of -6.4% by structural modifications, the Sb films form a pronounced moiré pattern as we evidence by scanning tunneling microscopy. Our model calculations assign the moiré pattern to a periodic surface corrugation. In agreement with theoretical predictions, irrespective of the moiré modulation, the topological surface state known on a thick Sb film is experimentally confirmed to persist down to small film thicknesses, and the Dirac point shifts toward lower binding energies with a decrease in Sb thickness.

We study the interplay of lattice, spin and orbital degrees of freedom in a two-dimensional model system: a flat square lattice of Te atoms on a Au(100) surface. The atomic structure of the Te monolayer is determined by scanning tunneling microscopy (STM) and quantitative low-energy electron diffraction (LEED-IV). Using spin- and angle-resolved photoelectron spectroscopy (ARPES) and density functional theory (DFT), we observe a Te-Au interface state with highly anisotropic Rashba-type spin-orbit splitting at the X point of the Brillouin zone. Based on a profound symmetry and tight-binding analysis, we show how in-plane square lattice symmetry and broken inversion symmetry at the Te-Au interface together enforce a remarkably anisotropic orbital Rashba effect which strongly modulates the spin splitting.

The direct observation of spin Berry curvature, an important aspect of non-trivial band topology, has not been achieved in quantum materials. Now it is observed in a bilayer Kagome metal. Kagome materials have emerged as a setting for emergent electronic phenomena that encompass different aspects of symmetry and topology. It is debated whether the XV6Sn6 kagome family (where X is a rare-earth element), a recently discovered family of bilayer kagome metals, hosts a topologically non-trivial ground state resulting from the opening of spin-orbit coupling gaps. These states would carry a finite spin Berry curvature, and topological surface states. Here we investigate the spin and electronic structure of the XV6Sn6 kagome family. We obtain evidence for a finite spin Berry curvature contribution at the centre of the Brillouin zone, where the nearly flat band detaches from the dispersing Dirac band because of spin-orbit coupling. In addition, the spin Berry curvature is further investigated in the charge density wave regime of ScV6Sn6 and it is found to be robust against the onset of the temperature-driven ordered phase. Utilizing the sensitivity of angle-resolved photoemission spectroscopy to the spin and orbital angular momentum, our work unveils the spin Berry curvature of topological kagome metals and helps to define its spectroscopic fingerprint.

The recently introduced classification of two-dimensional insulators in terms of topological crystalline in-variants has been applied so far to "obstructed" atomic insulators characterized by a mismatch between the centers of the electronic Wannier functions and the ionic positions. We extend this notion to quantum spin Hall insulators in which the ground state cannot be described in terms of time-reversal symmetric localized Wannier functions. A system equivalent to graphene in all its relevant electronic and topological properties except for a real-space obstruction is identified and studied via symmetry analysis as well as with density functional theory. The low-energy model comprises a local spin-orbit coupling and a nonlocal symmetry breaking potential, which turn out to be the essential ingredients for an obstructed quantum spin Hall insulator. An experimental fingerprint of the obstruction is then measured in a large-gap triangular quantum spin Hall material.

Indenene-the triangular single layer phase of indium-is a novel large gap (similar to 120 meV) quantum spin Hall (QSH) insulator that stabilizes on SiC(0001) substrates. Thanks to excellent lattice matching, indenene nucleates in monodomains that are promising for devices if synthesized in the micrometer range. Here, we establish a simple, but robust and scalable indenene fabrication protocol based on an initial Stranski-Krastanov growth stage followed by a short anneal whose temperature selects between a three, two, or one monolayer In coverage. Their specific structural and electronic properties produce distinct fingerprints in experimental surface characterization by electron microscopy, diffraction, and spectroscopy, thus providing an efficient metric for the synthesis of large scale high-quality indenene on SiC.

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.

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 p x ± i p y -derived wave functions.

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.

In search for a new generation of spintronics hardware, material candidates for room temperature quantum spin Hall effect (QSHE) have become a contemporary focus of investigation. Inspired by the original proposal for QSHE in graphene, several heterostructures have been synthesized, aiming at a hexagonal monolayer of heavier group IV elements in order to promote the QSHE bulk gap via increased spin-orbit coupling. So far, however, the monolayer/substrate coupling, which can manifest itself in strain, deformation, and hybridization, has proven to be detrimental to the aspired QSHE conditions for the monolayer. Specifically focusing on stanene, the Sn analogue of graphene, we investigate how an interposing buffer layer mediates between monolayer and substrate in order to optimize the QSHE setting. From a detailed density functional theory study, we highlight the principal mechanisms induced by such a buffer layer to accomplish quasi-free standing stanene in its QSHE phase. We complement our theoretical predictions by presenting the first real attempts to grow a buffer layer on SiC(0001) on which stanene can be deposited.

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.

Experimentelle Physik VII, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany National High Magnetic Field Laboratory, Tallahassee, FL 32310, USA Theoretische Physik I, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Department of Chemical and Biomedical Engineering, FAMU-FSU College of Engineering Tallahassee, FL 32310, USA