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.

Weyl spin-momentum locking in a chiral topological semimetal.

Spin-orbit coupling in noncentrosymmetric crystals leads to spin-momentum locking - a directional relationship between an electron's spin angular momentum and its linear momentum. Isotropic orthogonal Rashba spin-momentum locking has been studied for decades, while its counterpart, isotropic parallel Weyl spin-momentum locking has remained elusive in experiments. Theory predicts that Weyl spin-momentum locking can only be realized in structurally chiral cubic crystals in the vicinity of Kramers-Weyl or multifold fermions. Here, we use spin- and angle-resolved photoemission spectroscopy to evidence Weyl spin-momentum locking of multifold fermions in the chiral topological semimetal PtGa. We find that the electron spin of the Fermi arc surface states is orthogonal to their Fermi surface contour for momenta close to the projection of the bulk multifold fermion at the Γ point, which is consistent with Weyl spin-momentum locking of the latter. The direct measurement of the bulk spin texture of the multifold fermion at the R point also displays Weyl spin-momentum locking. The discovery of Weyl spin-momentum locking may lead to energy-efficient memory devices and Josephson diodes based on chiral topological semimetals.

Josephson diode effect from Cooper pair momentum in a topological semimetal.

Cooper pairs in non-centrosymmetric superconductors can acquire finite centre-of-mass momentum in the presence of an external magnetic field. Recent theory predicts that such finite-momentum pairing can lead to an asymmetric critical current, where a dissipationless supercurrent can flow along one direction but not in the opposite one. Here we report the discovery of a giant Josephson diode effect in Josephson junctions formed from a type-II Dirac semimetal, NiTe2. A distinguishing feature is that the asymmetry in the critical current depends sensitively on the magnitude and direction of an applied magnetic field and achieves its maximum value when the magnetic field is perpendicular to the current and is of the order of just 10 mT. Moreover, the asymmetry changes sign several times with an increasing field. These characteristic features are accounted for by a model based on finite-momentum Cooper pairing that largely originates from the Zeeman shift of spin-helical topological surface states. The finite pairing momentum is further established, and its value determined, from the evolution of the interference pattern under an in-plane magnetic field. The observed giant magnitude of the asymmetry in critical current and the clear exposition of its underlying mechanism paves the way to build novel superconducting computing devices using the Josephson diode effect.

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.

Observation and control of maximal Chern numbers in a chiral topological semimetal.

Topological semimetals feature protected nodal band degeneracies characterized by a topological invariant known as the Chern number (C). Nodal band crossings with linear dispersion are expected to have at most [Formula: see text], which sets an upper limit to the magnitude of many topological phenomena in these materials. Here, we show that the chiral crystal palladium gallium (PdGa) displays multifold band crossings, which are connected by exactly four surface Fermi arcs, thus proving that they carry the maximal Chern number magnitude of 4. By comparing two enantiomers, we observe a reversal of their Fermi-arc velocities, which demonstrates that the handedness of chiral crystals can be used to control the sign of their Chern numbers.

Handedness-dependent quasiparticle interference in the two enantiomers of the topological chiral semimetal PdGa.

It has recently been proposed that combining chirality with topological band theory results in a totally new class of fermions. Understanding how these unconventional quasiparticles propagate and interact remains largely unexplored so far. Here, we use scanning tunneling microscopy to visualize the electronic properties of the prototypical chiral topological semimetal PdGa. We reveal chiral quantum interference patterns of opposite spiraling directions for the two PdGa enantiomers, a direct manifestation of the change of sign of their Chern number. Additionally, we demonstrate that PdGa remains topologically non-trivial over a large energy range, experimentally detecting Fermi arcs in an energy window of more than 1.6 eV that is symmetrically centered around the Fermi level. These results are a consequence of the deep connection between chirality in real and reciprocal space in this class of materials, and, thereby, establish PdGa as an ideal topological chiral semimetal.

Weyl fermions, Fermi arcs, and minority-spin carriers in ferromagnetic CoS2.

Magnetic Weyl semimetals are a newly discovered class of topological materials that may serve as a platform for exotic phenomena, such as axion insulators or the quantum anomalous Hall effect. Here, we use angle-resolved photoelectron spectroscopy and ab initio calculations to discover Weyl cones in CoS2, a ferromagnet with pyrite structure that has been long studied as a candidate for half-metallicity, which makes it an attractive material for spintronic devices. We directly observe the topological Fermi arc surface states that link the Weyl nodes, which will influence the performance of CoS2 as a spin injector by modifying its spin polarization at interfaces. In addition, we directly observe a minority-spin bulk electron pocket in the corner of the Brillouin zone, which proves that CoS2 cannot be a true half-metal.

Signatures of Sixfold Degenerate Exotic Fermions in a Superconducting Metal PdSb2.

Multifold degenerate points in the electronic structure of metals lead to exotic behaviors. These range from twofold and fourfold degenerate Weyl and Dirac points, respectively, to sixfold and eightfold degenerate points that are predicted to give rise, under modest magnetic fields or strain, to topological semimetallic behaviors. The present study shows that the nonsymmorphic compound PdSb2 hosts six-component fermions or sextuplets. Using angle-resolved photoemission spectroscopy, crossing points formed by three twofold degenerate parabolic bands are directly observed at the corner of the Brillouin zone. The group theory analysis proves that under weak spin-orbit interaction, a band inversion occurs.

Electronic structures and unusually robust bandgap in an ultrahigh-mobility layered oxide semiconductor, Bi2O2Se.

Semiconductors are essential materials that affect our everyday life in the modern world. Two-dimensional semiconductors with high mobility and moderate bandgap are particularly attractive today because of their potential application in fast, low-power, and ultrasmall/thin electronic devices. We investigate the electronic structures of a new layered air-stable oxide semiconductor, Bi2O2Se, with ultrahigh mobility (~2.8 × 105 cm2/V⋅s at 2.0 K) and moderate bandgap (~0.8 eV). Combining angle-resolved photoemission spectroscopy and scanning tunneling microscopy, we mapped out the complete band structures of Bi2O2Se with key parameters (for example, effective mass, Fermi velocity, and bandgap). The unusual spatial uniformity of the bandgap without undesired in-gap states on the sample surface with up to ~50% defects makes Bi2O2Se an ideal semiconductor for future electronic applications. In addition, the structural compatibility between Bi2O2Se and interesting perovskite oxides (for example, cuprate high-transition temperature superconductors and commonly used substrate material SrTiO3) further makes heterostructures between Bi2O2Se and these oxides possible platforms for realizing novel physical phenomena, such as topological superconductivity, Josephson junction field-effect transistor, new superconducting optoelectronics, and novel lasers.

Substrate Doping Effect and Unusually Large Angle van Hove Singularity Evolution in Twisted Bi- and Multilayer Graphene.

Graphene has demonstrated great potential in new-generation electronic applications due to its unique electronic properties such as large carrier Fermi velocity, ultrahigh carrier mobility, and high material stability. Interestingly, the electronic structures can be further engineered in multilayer graphene by the introduction of a twist angle between different layers to create van Hove singularities (vHSs) at adjustable binding energy. In this work, using angle-resolved photoemission spectroscopy with sub-micrometer spatial resolution, the band structures and their evolution are systematically studied with twist angle in bilayer and trilayer graphene sheets. A doping effect is directly observed in graphene multilayer system as well as vHSs in bilayer graphene over a wide range of twist angles (from 5° to 31°) with wide tunable energy range over 2 eV. In addition, the formation of multiple vHSs (at different binding energies) is also observed in trilayer graphene. The large tuning range of vHS binding energy in twisted multilayer graphene provides a promising material base for optoelectrical applications with broadband wavelength selectivity from the infrared to the ultraviolet regime, as demonstrated by an example application of wavelength selective photodetector.