Observation of a linked-loop quantum state in a topological magnet.

Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state1-13. Over the past decades, these invariants have come to play a central role in describing matter, providing the foundation for understanding superfluids5, magnets6,7, the quantum Hall effect3,8, topological insulators9,10, Weyl semimetals11-13 and other phenomena. Here we report an unusual linking-number (knot theory) invariant associated with loops of electronic band crossings in a mirror-symmetric ferromagnet14-20. Using state-of-the-art spectroscopic methods, we directly observe three intertwined degeneracy loops in the material's three-torus, T3, bulk Brillouin zone. We find that each loop links each other loop twice. Through systematic spectroscopic investigation of this linked-loop quantum state, we explicitly draw its link diagram and conclude, in analogy with knot theory, that it exhibits the linking number (2, 2, 2), providing a direct determination of the invariant structure from the experimental data. We further predict and observe, on the surface of our samples, Seifert boundary states protected by the bulk linked loops, suggestive of a remarkable Seifert bulk-boundary correspondence. Our observation of a quantum loop link motivates the application of knot theory to the exploration of magnetic and superconducting quantum matter.

Charge Transfer and Orbital Reconstruction at an Organic-Oxide Interface.

The two-dimensional electron system (2DES) located at the surface of strontium titanate (STO) and at several other STO-based interfaces has been an established platform for the study of novel physical phenomena since its discovery. Here we report how the interfacing of STO and tetracyanoquinodimethane (TCNQ) results in a charge transfer that depletes the number of free carriers at the STO surface, with a strong impact on its electronic structure. Our study paves the way for efficient tuning of the electronic properties, which promises novel applications in the framework of oxide/organic-based electronics.

Visualizing Higher-Fold Topology in Chiral Crystals.

Novel topological phases of matter are fruitful platforms for the discovery of unconventional electromagnetic phenomena. Higher-fold topology is one example, where the low-energy description goes beyond standard model analogs. Despite intensive experimental studies, conclusive evidence remains elusive for the multigap topological nature of higher-fold chiral fermions. In this Letter, we leverage a combination of fine-tuned chemical engineering and photoemission spectroscopy with photon energy contrast to discover the higher-fold topology of a chiral crystal. We identify all bulk branches of a higher-fold chiral fermion for the first time, critically important for allowing us to explore unique Fermi arc surface states in multiple interband gaps, which exhibit an emergent ladder structure. Through designer chemical gating of the samples in combination with our measurements, we uncover an unprecedented multigap bulk boundary correspondence. Our demonstration of multigap electronic topology will propel future research on unconventional topological responses.

Spin Orientation of Two-Dimensional Electrons Driven by Temperature-Tunable Competition of Spin-Orbit and Exchange-Magnetic Interactions.

Finding ways to create and control the spin-dependent properties of two-dimensional electron states (2DESs) is a major challenge for the elaboration of novel spin-based devices. Spin-orbit and exchange-magnetic interactions (SOI and EMI) are two fundamental mechanisms that enable access to the tunability of spin-dependent properties of carriers. The silicon surface of HoRh2Si2 appears to be a unique model system, where concurrent SOI and EMI can be visualized and controlled by varying the temperature. The beauty and simplicity of this system lie in the 4f moments, which act as a multiple tuning instrument on the 2DESs, as the 4f projections parallel and perpendicular to the surface order at essentially different temperatures. Here we show that the SOI locks the spins of the 2DESs exclusively in the surface plane when the 4f moments are disordered: the Rashba-Bychkov effect. When the temperature is gradually lowered and the system experiences magnetic order, the rising EMI progressively competes with the SOI leading to a fundamental change in the spin-dependent properties of the 2DESs. The spins rotate and reorient toward the out-of-plane Ho 4f moments. Our findings show that the direction of the spins and the spin-splitting of the two-dimensional electrons at the surface can be manipulated in a controlled way by using only one parameter: the temperature.

Observation of single-spin Dirac fermions at the graphene/ferromagnet interface.

With the discovery and first characterization of graphene, its potential for spintronic applications was recognized immediately. Since then, an active field of research has developed trying to overcome the practical hurdles. One of the most severe challenges is to find appropriate interfaces between graphene and ferromagnetic layers, which are granting efficient injection of spin-polarized electrons. Here, we show that graphene grown under appropriate conditions on Co(0001) demonstrates perfect structural properties and simultaneously exhibits highly spin-polarized charge carriers. The latter was conclusively proven by observation of a single-spin Dirac cone near the Fermi level. This was accomplished experimentally using spin- and angle-resolved photoelectron spectroscopy, and theoretically with density functional calculations. Our results demonstrate that the graphene/Co(0001) system represents an interesting candidate for applications in devices using the spin degree of freedom.

Direct Spectroscopic Evidence of Magnetic Proximity Effect in MoS2 Monolayer on Graphene/Co.

A magnetic field modifies optical properties and provides valley splitting in a molybdenum disulfide (MoS2) monolayer. Here we demonstrate a scalable approach to the epitaxial synthesis of MoS2 monolayer on a magnetic graphene/Co system. Using spin- and angle-resolved photoemission spectroscopy we observe a magnetic proximity effect that causes a 20 meV spin-splitting at the Γ̅ point and canting of spins at the K̅ point in the valence band toward the in-plane direction of cobalt magnetization. Our density functional theory calculations reveal that the in-plane spin component at K̅ is localized on Co atoms in the valence band, while in the conduction band it is localized on the MoS2 layer. The calculations also predict a 16 meV spin-splitting at the Γ̅ point and 8 meV K̅-K'¯ valley asymmetry for an out-of-plane magnetization. These findings suggest control over optical transitions in MoS2 via Co magnetization. Our estimations show that the magnetic proximity effect is equivalent to the action of the magnetic field as large as 100 T.

Band Structure Extraction at Hybrid Narrow-Gap Semiconductor-Metal Interfaces.

The design of epitaxial semiconductor-superconductor and semiconductor-metal quantum devices requires a detailed understanding of the interfacial electronic band structure. However, the band alignment of buried interfaces is difficult to predict theoretically and to measure experimentally. This work presents a procedure that allows to reliably determine critical parameters for engineering quantum devices; band offset, band bending profile, and number of occupied quantum well subbands of interfacial accumulation layers at semiconductor-metal interfaces. Soft X-ray angle-resolved photoemission is used to directly measure the quantum well states as well as valence bands and core levels for the InAs(100)/Al interface, an important platform for Majorana-zero-mode based topological qubits, and demonstrate that the fabrication process strongly influences the band offset, which in turn controls the topological phase diagrams. Since the method is transferable to other narrow gap semiconductors, it can be used more generally for engineering semiconductor-metal and semiconductor-superconductor interfaces in gate-tunable superconducting devices.

Proximity Effects on the Charge Density Wave Order and Superconductivity in Single-Layer NbSe2.

Collective electronic states such as the charge density wave (CDW) order and superconductivity (SC) respond sensitively to external perturbations. Such sensitivity is dramatically enhanced in two dimensions (2D), where 2D materials hosting such electronic states are largely exposed to the environment. In this regard, the ineludible presence of supporting substrates triggers various proximity effects on 2D materials that may ultimately compromise the stability and properties of the electronic ground state. In this work, we investigate the impact of proximity effects on the CDW and superconducting states in single-layer (SL) NbSe2 on four substrates of diverse nature, namely, bilayer graphene (BLG), SL-boron nitride (h-BN), Au(111), and bulk WSe2. By combining low-temperature (340 mK) scanning tunneling microscopy/spectroscopy and angle-resolved photoemission spectroscopy, we compare the electronic structure of this prototypical 2D superconductor on each substrate. We find that, even when the electronic band structure of SL-NbSe2 remains largely unaffected by the substrate except when placed on Au(111), where a charge transfer occurs, both the CDW and SC show disparate behaviors. On the insulating h-BN/Ir(111) substrate and the metallic BLG/SiC(0001) substrate, both the 3 × 3 CDW and superconducting phases persist in SL-NbSe2 with very similar properties, which reveals the negligible impact of graphene on these electronic phases. In contrast, these collective electronic phases are severely weakened and even absent on the bulk insulating WSe2 substrate and the metallic single-crystal Au(111) substrate. Our results provide valuable insights into the fragile stability of such electronic ground states in 2D materials.

Band-Order Anomaly at the γ-Al2O3/SrTiO3 Interface Drives the Electron-Mobility Boost.

The rich functionalities of transition-metal oxides and their interfaces bear an enormous technological potential. Its realization in practical devices requires, however, a significant improvement of yet relatively low electron mobility in oxide materials. Recently, a mobility boost of about 2 orders of magnitude has been demonstrated at the spinel-perovskite γ-Al2O3/SrTiO3 interface compared to the paradigm perovskite-perovskite LaAlO3/SrTiO3 interface. We explore the fundamental physics behind this phenomenon from direct measurements of the momentum-resolved electronic structure of this interface using resonant soft-X-ray angle-resolved photoemission. We find an anomaly in orbital ordering of the mobile electrons in γ-Al2O3/SrTiO3 which depopulates electron states in the top SrTiO3 layer. This rearrangement of the mobile electron system pushes the electron density away from the interface, which reduces its overlap with the interfacial defects and weakens the electron-phonon interaction, both effects contributing to the mobility boost. A crystal-field analysis shows that the band order alters owing to the symmetry breaking between the spinel γ-Al2O3 and perovskite SrTiO3. Band-order engineering, exploiting the fundamental symmetry properties, emerges as another route to boost the performance of oxide devices.

Emergence of Nontrivial Low-Energy Dirac Fermions in Antiferromagnetic EuCd2 As2.

Parity-time symmetry plays an essential role for the formation of Dirac states in Dirac semimetals. So far, all of the experimentally identified topologically nontrivial Dirac semimetals (DSMs) possess both parity and time reversal symmetry. The realization of magnetic topological DSMs remains a major issue in topological material research. Here, combining angle-resolved photoemission spectroscopy with density functional theory calculations, it is ascertained that band inversion induces a topologically nontrivial ground state in EuCd2 As2 . As a result, ideal magnetic Dirac fermions with simplest double cone structure near the Fermi level emerge in the antiferromagnetic (AFM) phase. The magnetic order breaks time reversal symmetry, but preserves inversion symmetry. The double degeneracy of the Dirac bands is protected by a combination of inversion, time-reversal, and an additional translation operation. Moreover, the calculations show that a deviation of the magnetic moments from the c-axis leads to the breaking of C3 rotation symmetry, and thus, a small bandgap opens at the Dirac point in the bulk. In this case, the system hosts a novel state containing three different types of topological insulator: axion insulator, AFM topological crystalline insulator (TCI), and higher order topological insulator. The results provide an enlarged platform for the quest of topological Dirac fermions in a magnetic system.

Orbital Ordering of the Mobile and Localized Electrons at Oxygen-Deficient LaAlO3/SrTiO3 Interfaces.

Interfacing different transition-metal oxides opens a route to functionalizing their rich interplay of electron, spin, orbital, and lattice degrees of freedom for electronic and spintronic devices. Electronic and magnetic properties of SrTiO3-based interfaces hosting a mobile two-dimensional electron system (2DES) are strongly influenced by oxygen vacancies, which form an electronic dichotomy, where strongly correlated localized electrons in the in-gap states (IGSs) coexist with noncorrelated delocalized 2DES. Here, we use resonant soft-X-ray photoelectron spectroscopy to prove the eg character of the IGSs, as opposed to the t2g character of the 2DES in the paradigmatic LaAlO3/SrTiO3 interface. We furthermore separate the d xy and d xz/d xz orbital contributions based on deeper consideration of the resonant photoexcitation process in terms of orbital and momentum selectivity. Supported by a self-consistent combination of density functional theory and dynamical mean field theory calculations, this experiment identifies local orbital reconstruction that goes beyond the conventional eg- vs-t2g band ordering. A hallmark of oxygen-deficient LaAlO3/SrTiO3 is a significant hybridization of the eg and t2g orbitals. Our findings provide routes for tuning the electronic and magnetic properties of oxide interfaces through "defect engineering" with oxygen vacancies.