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.

Nematic Spin Correlations Pervading the Phase Diagram of FeSe_{1-x}S_{x}.

We use resonant inelastic x-ray scattering (RIXS) at the Fe-L_{3} edge to study the spin excitations of uniaxial-strained and unstrained FeSe_{1-x}S_{x} (0≤x≤0.21) samples. The measurements on unstrained samples reveal dispersive spin excitations in all doping levels, which show only minor doping dependence in energy dispersion, lifetime, and intensity, indicating that high-energy spin excitations are only marginally affected by sulfur doping. RIXS measurements on uniaxial-strained samples reveal that the high-energy spin-excitation anisotropy observed previously in FeSe is also present in the doping range 0200 K in x=0.18 and reaches a maximum around the nematic quantum critical doping (x_{c}≈0.17). Since the spin-excitation anisotropy directly reflects the existence of nematic spin correlations, our results indicate that high-energy nematic spin correlations pervade the regime of nematicity in the phase diagram and are enhanced by the nematic quantum criticality. These results emphasize the essential role of spin fluctuations in driving electronic nematicity and highlight the capability of uniaxial strain in tuning spin excitations in quantum materials hosting strong magnetoelastic coupling and electronic nematicity.

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.

Unraveling intrinsic correlation effects with angle-resolved photoemission spectroscopy.

Interaction effects can change materials properties in intriguing ways, and they have, in general, a huge impact on electronic spectra. In particular, satellites in photoemission spectra are pure many-body effects, and their study is of increasing interest in both experiment and theory. However, the intrinsic spectral function is only a part of a measured spectrum, and it is notoriously difficult to extract this information, even for simple metals. Our joint experimental and theoretical study of the prototypical simple metal aluminum demonstrates how intrinsic satellite spectra can be extracted from measured data using angular resolution in photoemission. A nondispersing satellite is detected and explained by electron-electron interactions and the thermal motion of the atoms. Additional nondispersing intensity comes from the inelastic scattering of the outgoing photoelectron. The ideal intrinsic spectral function, instead, has satellites that disperse both in energy and in shape. Theory and the information extracted from experiment describe these features with very good agreement.

Strain engineering of the charge and spin-orbital interactions in Sr2IrO4.

In the high spin-orbit-coupled Sr2IrO4, the high sensitivity of the ground state to the details of the local lattice structure shows a large potential for the manipulation of the functional properties by inducing local lattice distortions. We use epitaxial strain to modify the Ir-O bond geometry in Sr2IrO4 and perform momentum-dependent resonant inelastic X-ray scattering (RIXS) at the metal and at the ligand sites to unveil the response of the low-energy elementary excitations. We observe that the pseudospin-wave dispersion for tensile-strained Sr2IrO4 films displays large softening along the [h,0] direction, while along the [h,h] direction it shows hardening. This evolution reveals a renormalization of the magnetic interactions caused by a strain-driven cross-over from anisotropic to isotropic interactions between the magnetic moments. Moreover, we detect dispersive electron-hole pair excitations which shift to lower (higher) energies upon compressive (tensile) strain, manifesting a reduction (increase) in the size of the charge gap. This behavior shows an intimate coupling between charge excitations and lattice distortions in Sr2IrO4, originating from the modified hopping elements between the t2g orbitals. Our work highlights the central role played by the lattice degrees of freedom in determining both the pseudospin and charge excitations of Sr2IrO4 and provides valuable information toward the control of the ground state of complex oxides in the presence of high spin-orbit coupling.

hv2-concept breaks the photon-count limit of RIXS instrumentation.

Upon progressive refinement of energy resolution, the conventional resonant inelastic X-ray scattering (RIXS) instrumentation reaches the limit where the bandwidth of incident photons becomes insufficient to deliver an acceptable photon-count rate. Here it is shown that RIXS spectra as a function of energy loss are essentially invariant to their integration over incident energies within the core-hole lifetime. This fact permits RIXS instrumentation based on the hv2-concept to utilize incident synchrotron radiation over the whole core-hole lifetime window without any compromise on the much finer energy-loss resolution, thereby breaking the photon-count limit.

Electronic Structure of a Graphene-like Artificial Crystal of NdNiO3.

Artificial complex-oxide heterostructures containing ultrathin buried layers grown along the pseudocubic [111] direction have been predicted to host a plethora of exotic quantum states arising from the graphene-like lattice geometry and the interplay between strong electronic correlations and band topology. To date, however, electronic-structural investigations of such atomic layers remain an immense challenge due to the shortcomings of conventional surface-sensitive probes with typical information depths of a few angstroms. Here, we use a combination of bulk-sensitive soft X-ray angle-resolved photoelectron spectroscopy (SX-ARPES), hard X-ray photoelectron spectroscopy (HAXPES), and state-of-the-art first-principles calculations to demonstrate a direct and robust method for extracting momentum-resolved and angle-integrated valence-band electronic structure of an ultrathin buckled graphene-like layer of NdNiO3 confined between two 4-unit cell-thick layers of insulating LaAlO3. The momentum-resolved dispersion of the buried Ni d states near the Fermi level obtained via SX-ARPES is in excellent agreement with the first-principles calculations and establishes the realization of an antiferro-orbital order in this artificial lattice. The HAXPES measurements reveal the presence of a valence-band bandgap of 265 meV. Our findings open a promising avenue for designing and investigating quantum states of matter with exotic order and topology in a few buried layers.

Concept of a multichannel spin-resolving electron analyzer based on Mott scattering.

The concept of a multichannel electron spin detector based on optical imaging principles and Mott scattering (iMott) is presented. A multichannel electron image produced by a standard angle-resolving (photo) electron analyzer or microscope is re-imaged by an electrostatic lens at an accelerating voltage of 40 kV onto the Au target. Quasi-elastic electrons bearing spin asymmetry of the Mott scattering are imaged by magnetic lenses onto position-sensitive electron CCDs whose differential signals yield the multichannel spin asymmetry image. Fundamental advantages of this concept include acceptance of inherently divergent electron sources from the electron analyzer or microscope focal plane as well as small aberrations achieved by virtue of high accelerating voltages, as demonstrated by extensive ray-tracing analysis. The efficiency gain compared with the single-channel Mott detector can be a factor of more than 10(4) which opens new prospects of spin-resolved spectroscopies in application not only to standard bulk and surface systems (Rashba effect, topological insulators, etc.) but also to buried heterostructures. The simultaneous spin detection combined with fast CCD readout enables efficient use of the iMott detectors at X-ray free-electron laser facilities.

Tunable 2D Electron- and 2D Hole States Observed at Fe/SrTiO3 Interfaces.

Oxide electronics provide the key concepts and materials for enhancing silicon-based semiconductor technologies with novel functionalities. However, a basic but key property of semiconductor devices still needs to be unveiled in its oxidic counterparts: the ability to set or even switch between two types of carriers-either negatively (n) charged electrons or positively (p) charged holes. Here, direct evidence for individually emerging n- or p-type 2D band dispersions in STO-based heterostructures is provided using resonant photoelectron spectroscopy. The key to tuning the carrier character is the oxidation state of an adjacent Fe-based interface layer: For Fe and FeO, hole bands emerge in the empty bandgap region of STO due to hybridization of Ti- and Fe- derived states across the interface, while for Fe3O4 overlayers, an 2D electron system is formed. Unexpected oxygen vacancy characteristics arise for the hole-type interfaces, which as of yet had been exclusively assigned to the emergence of 2DESs. In general, this finding opens up the possibility to straightforwardly switch the type of conductivity at STO interfaces by the oxidation state of a redox overlayer. This will extend the spectrum of phenomena in oxide electronics, including the realization of combined n/p-type all-oxide transistors or logic gates.

Direct observation of altermagnetic band splitting in CrSb thin films.

Altermagnetism represents an emergent collinear magnetic phase with compensated order and an unconventional alternating even-parity wave spin order in the non-relativistic band structure. We investigate directly this unconventional band splitting near the Fermi energy through spin-integrated soft X-ray angular resolved photoemission spectroscopy. The experimentally obtained angle-dependent photoemission intensity, acquired from epitaxial thin films of the predicted altermagnet CrSb, demonstrates robust agreement with the corresponding band structure calculations. In particular, we observe the distinctive splitting of an electronic band on a low-symmetry path in the Brilliouin zone that connects two points featuring symmetry-induced degeneracy. The measured large magnitude of the spin splitting of approximately 0.6 eV and the position of the band just below the Fermi energy underscores the significance of altermagnets for spintronics based on robust broken time reversal symmetry responses arising from exchange energy scales, akin to ferromagnets, while remaining insensitive to external magnetic fields and possessing THz dynamics, akin to antiferromagnets.

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.

Optimization of the X-ray incidence angle in photoelectron spectrometers.

The interplay between the angle-dependent X-ray reflectivity, X-ray absorption and the photoelectron attenuation length in the photoelectron emission process determines the optimal X-ray incidence angle that maximizes the photoelectron signal. Calculations in the wide VUV to the hard X-ray energy range show that the optimal angle becomes more grazing with increasing energy, from a few tens of degrees at 50 eV to about one degree at 3.5 keV. This is accompanied by an intensity gain of a few tens of times, as long as the X-ray footprint on the sample stays within the analyzer field of view. This trend is fairly material-independent. The obtained results bear immediate implications for the design of (synchrotron-based) photoelectron spectrometers.

Determining the short-range spin correlations in the spin-chain Li2CuO2 and CuGeO3 compounds using resonant inelastic x-ray scattering.

We report a high-resolution resonant inelastic soft x-ray scattering study of the quantum magnetic spin-chain materials Li(2)CuO(2) and CuGeO(3). By tuning the incoming photon energy to the oxygen K edge, a strong excitation around 3.5 eV energy loss is clearly resolved for both materials. Comparing the experimental data to many-body calculations, we identify this excitation as a Zhang-Rice singlet exciton on neighboring CuO(4) plaquettes. We demonstrate that the strong temperature dependence of the inelastic scattering related to this high-energy exciton enables us to probe short-range spin correlations on the 1 meV scale with outstanding sensitivity.

Experimental Band Structure of Pb(Zr,Ti)O3 : Mechanism of Ferroelectric Stabilization.

Pb(Zr,Ti)O3 (PZT) is the most common ferroelectric (FE) material widely used in solid-state technology. Despite intense studies of PZT over decades, its intrinsic band structure, electron energy depending on 3D momentum k, is still unknown. Here, Pb(Zr0.2 Ti0.8 )O3 using soft-X-ray angle-resolved photoelectron spectroscopy (ARPES) is explored. The enhanced photoelectron escape depth in this photon energy range allows sharp intrinsic definition of the out-of-plane momentum k and thereby of the full 3D band structure. Furthermore, the problem of sample charging due to the inherently insulating nature of PZT is solved by using thin-film PZT samples, where a thickness-induced self-doping results in their heavy doping. For the first time, the soft-X-ray ARPES experiments deliver the intrinsic 3D band structure of PZT as well as the FE-polarization dependent electrostatic potential profile across the PZT film deposited on SrTiO3 and Lax SrMn1- x O3 substrates. The negative charges near the surface, required to stabilize the FE state pointing away from the sample (P+), are identified as oxygen vacancies creating localized in-gap states below the Fermi energy. For the opposite polarization state (P-), the positive charges near the surface are identified as cation vacancies resulting from non-ideal stoichiometry of the PZT film as deduced from quantitative XPS measurements.

Momentum-Space Imaging of Ultra-Thin Electron Liquids in δ-Doped Silicon.

Two-dimensional dopant layers (δ-layers) in semiconductors provide the high-mobility electron liquids (2DELs) needed for nanoscale quantum-electronic devices. Key parameters such as carrier densities, effective masses, and confinement thicknesses for 2DELs have traditionally been extracted from quantum magnetotransport. In principle, the parameters are immediately readable from the one-electron spectral function that can be measured by angle-resolved photoemission spectroscopy (ARPES). Here, buried 2DEL δ-layers in silicon are measured with soft X-ray (SX) ARPES to obtain detailed information about their filled conduction bands and extract device-relevant properties. This study takes advantage of the larger probing depth and photon energy range of SX-ARPES relative to vacuum ultraviolet (VUV) ARPES to accurately measure the δ-layer electronic confinement. The measurements are made on ambient-exposed samples and yield extremely thin (< 1 nm) and dense (≈1014  cm-2 ) 2DELs. Critically, this method is used to show that δ-layers of arsenic exhibit better electronic confinement than δ-layers of phosphorus fabricated under identical conditions.

First-Principles Assessment of CdTe as a Tunnel Barrier at the α-Sn/InSb Interface.

Majorana zero modes, with prospective applications in topological quantum computing, are expected to arise in superconductor/semiconductor interfaces, such as ß-Sn and InSb. However, proximity to the superconductor may also adversely affect the semiconductor's local properties. A tunnel barrier inserted at the interface could resolve this issue. We assess the wide band gap semiconductor, CdTe, as a candidate material to mediate the coupling at the lattice-matched interface between α-Sn and InSb. To this end, we use density functional theory (DFT) with Hubbard U corrections, whose values are machine-learned via Bayesian optimization (BO) [ npj Computational Materials 2020, 6, 180]. The results of DFT+U(BO) are validated against angle resolved photoemission spectroscopy (ARPES) experiments for α-Sn and CdTe. For CdTe, the z-unfolding method [ Advanced Quantum Technologies 2022, 5, 2100033] is used to resolve the contributions of different kz values to the ARPES. We then study the band offsets and the penetration depth of metal-induced gap states (MIGS) in bilayer interfaces of InSb/α-Sn, InSb/CdTe, and CdTe/α-Sn, as well as in trilayer interfaces of InSb/CdTe/α-Sn with increasing thickness of CdTe. We find that 16 atomic layers (3.5 nm) of CdTe can serve as a tunnel barrier, effectively shielding the InSb from MIGS from the α-Sn. This may guide the choice of dimensions of the CdTe barrier to mediate the coupling in semiconductor-superconductor devices in future Majorana zero modes experiments.

Charge fluctuations in the intermediate-valence ground state of SmCoIn5.

The microscopic mechanism of heavy band formation, relevant for unconventional superconductivity in CeCoIn5 and other Ce-based heavy fermion materials, depends strongly on the efficiency with which f electrons are delocalized from the rare earth sites and participate in a Kondo lattice. Replacing Ce3+ (4f1, J = 5/2) with Sm3+ (4f5, J = 5/2), we show that a combination of the crystal electric field and on-site Coulomb repulsion causes SmCoIn5 to exhibit a Γ7 ground state similar to CeCoIn5 with multiple f electrons. We show that with this single-ion ground state, SmCoIn5 exhibits a temperature-induced valence crossover consistent with a Kondo scenario, leading to increased delocalization of f holes below a temperature scale set by the crystal field, Tv ≈ 60 K. Our result provides evidence that in the case of many f electrons, the crystal field remains the dominant tuning knob in controlling the efficiency of delocalization near a heavy fermion quantum critical point, and additionally clarifies that charge fluctuations play a general role in the ground state of "115" materials.

Momentum-resolved spin-conserving two-triplon bound state and continuum in a cuprate ladder.

Studying multi-particle elementary excitations has provided unique access to understand collective many-body phenomena in correlated electronic materials, paving the way towards constructing microscopic models. In this work, we perform O K-edge resonant inelastic X-ray scattering (RIXS) on the quasi-one-dimensional cuprate Sr14Cu24O41 with weakly-doped spin ladders. The RIXS signal is dominated by a dispersing sharp mode ~ 270 meV on top of a damped incoherent component ~ 400-500 meV. Comparing with model calculations using the perturbative continuous unitary transformations method, the two components resemble the spin-conserving ΔS = 0 two-triplon bound state and continuum excitations in the spin ladders. Such multi-spin response with long-lived ΔS = 0 excitons is central to several exotic magnetic properties featuring Majorana fermions, yet remains unexplored given the generally weak cross-section with other experimental techniques. By investigating a simple spin-ladder model system, our study provides valuable insight into low-dimensional quantum magnetism.

Anomalous Hall Conductivity and Nernst Effect of the Ideal Weyl Semimetallic Ferromagnet EuCd2 As2.

Weyl semimetal is a unique topological phase with topologically protected band crossings in the bulk and robust surface states called Fermi arcs. Weyl nodes always appear in pairs with opposite chiralities, and they need to have either time-reversal or inversion symmetry broken. When the time-reversal symmetry is broken the minimum number of Weyl points (WPs) is two. If these WPs are located at the Fermi level, they form an ideal Weyl semimetal (WSM). In this study, intrinsic ferromagnetic (FM) EuCd2 As2 are grown, predicted to be an ideal WSM and studied its electronic structure by angle-resolved photoemission spectroscopy, and scanning tunneling microscopy which agrees closely with the first principles calculations. Moreover, anomalous Hall conductivity and Nernst effect are observed, resulting from the non-zero Berry curvature, and the topological Hall effect arising from changes in the band structure caused by spin canting produced by magnetic fields. These findings can help realize several exotic quantum phenomena in inorganic topological materials that are otherwise difficult to assess because of the presence of multiple pairs of Weyl nodes.

Visualization of Tunable Weyl Line in A-A Stacking Kagome Magnets.

Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena, in which the delicate interplay between frustrated crystal structure, magnetization, and spin-orbit coupling (SOC) can engender highly tunable topological states. Here, utilizing angle-resolved photoemission spectroscopy, the Weyl lines are directly visualized with strong out-of-plane dispersion in the A-A stacked kagome magnet GdMn6 Sn6 . Remarkably, the Weyl lines exhibit a strong magnetization-direction-tunable SOC gap and binding energy tunability after substituting Gd with Tb and Li, respectively. These results not only illustrate the magnetization direction and valence counting as efficient tuning knobs for realizing and controlling distinct 3D topological phases, but also demonstrate AMn6 Sn6 (A = rare earth, or Li, Mg, or Ca) as a versatile material family for exploring diverse emergent topological quantum responses.