Axial Higgs mode detected by quantum pathway interference in RTe3.

The observation of the Higgs boson solidified the standard model of particle physics. However, explanations of anomalies (for example, dark matter) rely on further symmetry breaking, calling for an undiscovered axial Higgs mode1. The Higgs mode was also seen in magnetic, superconducting and charge density wave (CDW) systems2,3. Uncovering the vector properties of a low-energy mode is challenging, and requires going beyond typical spectroscopic or scattering techniques. Here we discover an axial Higgs mode in the CDW system RTe3 using the interference of quantum pathways. In RTe3 (R = La, Gd), the electronic ordering couples bands of equal or different angular momenta4-6. As such, the Raman scattering tensor associated with the Higgs mode contains both symmetric and antisymmetric components, which are excited via two distinct but degenerate pathways. This leads to constructive or destructive interference of these pathways, depending on the choice of the incident and Raman-scattered light polarization. The qualitative behaviour of the Raman spectra is well captured by an appropriate tight-binding model, including an axial Higgs mode. Elucidation of the antisymmetric component is direct evidence that the Higgs mode contains an axial vector representation (that is, a pseudo-angular momentum) and hints that the CDW is unconventional. Thus, we provide a means for measuring quantum properties of collective modes without resorting to extreme experimental conditions.

Catalogue of flat-band stoichiometric materials.

Topological electronic flattened bands near or at the Fermi level are a promising route towards unconventional superconductivity and correlated insulating states. However, the related experiments are mostly limited to engineered materials, such as moiré systems1-3. Here we present a catalogue of the naturally occuring three-dimensional stoichiometric materials with flat bands around the Fermi level. We consider 55,206 materials from the Inorganic Crystal Structure Database catalogued using the Topological Quantum Chemistry website4,5, which provides their structural parameters, space group, band structure, density of states and topological characterization. We combine several direct signatures and properties of band flatness with a high-throughput analysis of all crystal structures. In particular, we identify materials hosting line-graph or bipartite sublattices-in either two or three dimensions-that probably lead to flat bands. From this trove of information, we create the Materials Flatband Database website, a powerful search engine for future theoretical and experimental studies. We use the database to extract a curated list of 2,379 high-quality flat-band materials, from which we identify 345 promising candidates that potentially host flat bands with charge centres that are not strongly localized on the atomic sites. We showcase five representative materials and provide a theoretical explanation for the origin of their flat bands close to the Fermi energy using the S-matrix method introduced in a parallel work6.

One-dimensional Luttinger liquids in a two-dimensional moiré lattice.

The Luttinger liquid (LL) model of one-dimensional (1D) electronic systems provides a powerful tool for understanding strongly correlated physics, including phenomena such as spin-charge separation1. Substantial theoretical efforts have attempted to extend the LL phenomenology to two dimensions, especially in models of closely packed arrays of 1D quantum wires2-13, each being described as a LL. Such coupled-wire models have been successfully used to construct two-dimensional (2D) anisotropic non-Fermi liquids2-6, quantum Hall states7-9, topological phases10,11 and quantum spin liquids12,13. However, an experimental demonstration of high-quality arrays of 1D LLs suitable for realizing these models remains absent. Here we report the experimental realization of 2D arrays of 1D LLs with crystalline quality in a moiré superlattice made of twisted bilayer tungsten ditelluride (tWTe2). Originating from the anisotropic lattice of the monolayer, the moiré pattern of tWTe2 hosts identical, parallel 1D electronic channels, separated by a fixed nanoscale distance, which is tuneable by the interlayer twist angle. At a twist angle of approximately 5 degrees, we find that hole-doped tWTe2 exhibits exceptionally large transport anisotropy with a resistance ratio of around 1,000 between two orthogonal in-plane directions. The across-wire conductance exhibits power-law scaling behaviours, consistent with the formation of a 2D anisotropic phase that resembles an array of LLs. Our results open the door for realizing a variety of correlated and topological quantum phases based on coupled-wire models and LL physics.

Landau quantization and highly mobile fermions in an insulator.

In strongly correlated materials, quasiparticle excitations can carry fractional quantum numbers. An intriguing possibility is the formation of fractionalized, charge-neutral fermions-for example, spinons1 and fermionic excitons2,3-that result in neutral Fermi surfaces and Landau quantization4,5 in an insulator. Although previous experiments in quantum spin liquids1, topological Kondo insulators6-8 and quantum Hall systems3,9 have hinted at charge-neutral Fermi surfaces, evidence for their existence remains inconclusive. Here we report experimental observation of Landau quantization in a two-dimensional insulator, monolayer tungsten ditelluride (WTe2), a large-gap topological insulator10-13. Using a detection scheme that avoids edge contributions, we find large quantum oscillations in the material's magnetoresistance, with an onset field as small as about 0.5 tesla. Despite the huge resistance, the oscillation profile, which exhibits many periods, mimics the Shubnikov-de Haas oscillations in metals. At ultralow temperatures, the observed oscillations evolve into discrete peaks near 1.6 tesla, above which the Landau quantized regime is fully developed. Such a low onset field of quantization is comparable to the behaviour of high-mobility conventional two-dimensional electron gases. Our experiments call for further investigation of the unusual ground state of the WTe2 monolayer, including the influence of device components and the possible existence of mobile fermions and charge-neutral Fermi surfaces inside its insulating gap.

Friends not Foes: Exfoliation of Non-van der Waals Materials.

ConspectusTwo-dimensional materials have been a focus of study for decades, resulting in the development of a library of nanosheets made by a variety of methods. However, many of these atomically thin materials are exfoliated from van der Waals (vdW) compounds, which inherently have weaker bonding between layers in the bulk crystal. Even though there are diverse properties and structures within this class of compounds, it would behoove the community to look beyond these compounds toward the exfoliation of non-vdW compounds as well. A particular class of non-vdW compounds that may be amenable to exfoliation are the ionically bonded layered materials, which are structurally similar to vdW compounds but have alkali ions intercalated between the layers. Although initially they may have been more difficult to exfoliate due to a lack of methodology beyond mechanical exfoliation, many synthesis techniques have been developed that have been used successfully in exfoliating non-vdW materials. In fact, as we will show, in some cases it has even proven to be advantageous to start the exfoliation from a non-vdW compound.The method we will highlight here is chemical exfoliation, which has developed significantly and is better understood mechanistically compared to when it was first conceived. Encompassing many methods, such as acid/base reactions, solvent reactions, and oxidative extractions, chemical exfoliation can be tailored to the delamination of non-vdW materials, which opens up many more possibilities of compounds to study. In addition, beginning with intercalated analogues of vdW materials can even lead to more consistent and higher quality results, overcoming some challenges associated with chemical exfoliation in general. To exemplify this, we will discuss our group's work on the synthesis of a 1T'-WS2 monolayer ink. By starting with K0.5WS2, the exfoliated 1T'-WS2 nanosheets obtained were larger and more uniform in thickness than those from previous syntheses beginning with vdW materials. The crystallinity of the nanosheets was high enough that films made from this ink were superconducting. We will also show how soft chemical methods can be used to make new phases from existing compounds, such as HxCrS2 from NaCrS2. This material was found to have alternating amorphous and crystalline layers. Its biphasic structure improved the material's performance as a battery electrode, enabling reversible Cr redox and faster Na-ion diffusion. From these and other examples, we will see how chemical exfoliation of non-vdW materials compares to other methods, as well as how this technique can be further extended to known compounds that can be deintercalated electrochemically and to quasi-one-dimensional crystals.

Phase tuning of multiple Andreev reflections of Dirac fermions and the Josephson supercurrent in Al-MoTe2-Al junctions.

When an electron is incident on a superconductor from a metal, it is reflected as a hole in a process called Andreev reflection. If the metal N is sandwiched between two superconductors S in an SNS junction, multiple Andreev reflections (MARs) occur. We have found that, in SNS junctions with high transparency ([Formula: see text]) based on the Dirac semimetal MoTe2, the MAR features are observed with exceptional resolution. By tuning the phase difference [Formula: see text] between the bracketing Al superconductors, we establish that the MARs coexist with a Josephson supercurrent [Formula: see text]. As we vary the junction voltage V, the supercurrent amplitude [Formula: see text] varies in step with the MAR order n, revealing a direct relation between them. Two successive Andreev reflections serve to shuttle a Cooper pair across the junction. If the pair is shuttled coherently, it contributes to [Formula: see text]. The experiment measures the fraction of pairs shuttled coherently vs. V. Surprisingly, superconductivity in MoTe2 does not affect the MAR features.

Diradicals as Topological Charge Carriers in Metal-Organic Toy Model Pt3(HIB)2.

We explore the eclipsed stacking of a metal-organic Kagome lattice containing heavy-metal nodes. Our model is Pt3(HIB)2, a hypothetical but viable member of a well-known family of hexaaminobenzene based metal-organic frameworks (MOFs). Applying space group theory, it is shown how molecular diradicals, brought into play by a noninnocent ligand, become topologically nontrivial bands when moving in a periodic potential. Three factors are required to enable this: (1) eclipsed stacking, which shifts the Fermi level near a symmetry-protected band crossing (2) the emergence of an electride-like band that renders the topological Z2 invariant equal to 1, thus nontrivial, and (3) Pt-induced spin-orbit coupling, to turn the crossing into a bulk band gap. The electride band, with its unforeseen role, bears kinship to the interlayer band in hexagonal superconductors. It places its charge density in the voids of the crystal, rather than around the atomic nuclei, and we name it a "pore band". While the synthesis of truly conductive MOFs has proven challenging, the analysis shows that intrinsically nonlocal physics may emerge from tunable molecular building blocks. With the richness of redox-active MOF chemistry, this offers a pathway to tailored topological electronics.

Chemical Bonding Induces One-Dimensional Physics in Bulk Crystal BiIr4Se8.

One-dimensional (1D) systems persist as some of the most interesting because of the rich physics that emerges from constrained degrees of freedom. A desirable route to harness the properties therein is to grow bulk single crystals of a physically three-dimensional (3D) but electronically 1D compound. Most bulk compounds which approach the electronic 1D limit still field interactions across the other two crystallographic directions and, consequently, deviate from the 1D models. In this paper, we lay out chemical concepts to realize the physics of 1D models in 3D crystals. These are based on both structural and electronic arguments. We present BiIr4Se8, a bulk crystal consisting of linear Bi2+ chains within a scaffolding of IrSe6 octahedra, as a prime example. Through crystal structure analysis, density functional theory calculations, X-ray diffraction, and physical property measurements, we demonstrate the unique 1D electronic configuration in BiIr4Se8. This configuration at ambient temperature is a gapped Su-Schriefer-Heeger system, generated by way of a canonical Peierls distortion involving Bi dimerization that relieves instabilities in a 1D metallic state. At 190 K, an additional 1D charge density wave distortion emerges, which affects the Peierls distortion. The experimental evidence validates our design principles and distinguishes BiIr4Se8 among other quasi-1D bulk compounds. We thus show that it is possible to realize unique electronically 1D materials applying chemical concepts.

Atomic Resolution Imaging of Highly Air-Sensitive Monolayer and Twisted-Bilayer WTe2.

Bulk Td-WTe2 is a semimetal, while its monolayer counterpart is a two-dimensional (2D) topological insulator. Recently, electronic transport resembling a Luttinger liquid state was found in twisted-bilayer WTe2 (tWTe2) with a twist angle of ∼5°. Despite the strong interest in 2D WTe2 systems, little experimental information is available about their intrinsic microstructure, leaving obstacles in modeling their physical properties. The monolayer, and consequently tWTe2, are highly air-sensitive, and therefore, probing their atomic structures is difficult. In this study, we develop a robust method for atomic-resolution visualization of monolayers and tWTe2 obtained through mechanical exfoliation and fabrication. We confirm the high crystalline quality of mechanically exfoliated WTe2 samples and observe that tWTe2 with twist angles of ∼5 and ∼2° retains its pristine moiré structure without substantial deformations or reconstructions. The results provide a structural foundation for future electronic modeling of monolayer and tWTe2 moiré lattices.

Atomically Sharp Internal Interface in a Chiral Weyl Semimetal Nanowire.

Internal interfaces in Weyl semimetals (WSMs) are predicted to host distinct topological features that are different from the commonly studied external interfaces (crystal-to-vacuum boundaries). However, the lack of atomically sharp and crystallographically oriented internal interfaces in WSMs makes it difficult to experimentally investigate topological states buried inside the material. Here, we study a unique internal interface known as merohedral twin boundary in chemically synthesized single-crystal nanowires (NWs) of CoSi, a chiral WSM of space group P213 (No. 198). Scanning transmission electron microscopy reveals that this internal interface is a (001) twin plane which connects two enantiomeric counterparts at an atomically sharp interface with inversion twinning. Ab initio calculations show localized internal Fermi arcs at the (001) twin plane that can be clearly distinguished from both external Fermi arcs and bulk states. These merohedrally twinned CoSi NWs provide an ideal platform to explore topological properties associated with internal interfaces in WSMs.

Simple Chemical Rules for Predicting Band Structures of Kagome Materials.

Compounds featuring a kagome lattice are studied for a wide range of properties, from localized magnetism to massless and massive Dirac Fermions. These properties come from the symmetry of the kagome lattice, which gives rise to Dirac cones and flat bands. However, not all compounds with a kagome sublattice show properties related to it. We derive chemical rules predicting if the low-energy physics of a material is determined by the kagome sublattice and bands arising from it. After sorting out all known crystals with the kagome lattice into four groups, we use chemical heuristics and local symmetry to explain additional conditions that need to be met to have kagome bands near the Fermi level.

A Class of Magnetic Topological Material Candidates with Hypervalent Bi Chains.

The link between crystal and electronic structure is crucial for understanding structure-property relations in solid-state chemistry. In particular, it has been instrumental in understanding topological materials, where electrons behave differently than they would in conventional solids. Herein, we identify 1D Bi chains as a structural motif of interest for topological materials. We focus on Sm3ZrBi5, a new quasi-one-dimensional (1D) compound in the Ln3MPn5 (Ln = lanthanide; M = metal; Pn = pnictide) family that crystallizes in the P63/mcm space group. Density functional theory calculations indicate a complex, topologically nontrivial electronic structure that changes significantly in the presence of spin-orbit coupling. Magnetic measurements show a quasi-1D antiferromagnetic structure with two magnetic transitions at 11.7 and 10.7 K that are invariant to applied field up to 9 T, indicating magnetically frustrated spins. Heat capacity, electrical, and thermoelectric measurements support this claim and suggest complex scattering behavior in Sm3ZrBi5. This work highlights 1D chains as an unexplored structural motif for identifying topological materials, as well as the potential for rich physical phenomena in the Ln3MPn5 family.

The Role of Delocalized Chemical Bonding in Square-Net-Based Topological Semimetals.

Principles that predict reactions or properties of materials define the discipline of chemistry. In this work, we derive chemical rules, based on atomic distances and chemical bond character, which predict topological materials in compounds that feature the structural motif of a square-net. Using these rules, we identify over 300 potential new topological materials. We show that simple chemical heuristics can be a powerful tool to characterize topological matter. In contrast to previous database-driven materials' categorization, our approach allows us to identify candidates that are alloys, solid-solutions, or compounds with statistical vacancies. While previous material searches relied on density functional theory, our approach is not limited by this method and could also be used to discover magnetic and statistically disordered topological semimetals.

Change in Magnetic Properties upon Chemical Exfoliation of FeOCl.

The development of novel, intrinsic two-dimensional (2D) antiferromagnets presents the opportunity to vastly improve the efficiency of spintronic devices and sensors. The strong intrinsic antiferromagnetism and van der Waals layered structure exhibited by the bulk transition-metal oxychlorides provide a convenient system for the synthesis of such materials. In this work, we report the exfoliation of bulk FeOCl into and subsequent characterization of intrinsically antiferromagnetic thin-layer FeOCl nanosheets. The magnetic properties of bulk FeOCl, its lithium intercalate, and its nanosheet pellet are measured to determine the evolution of magnetic properties from the three-dimensional to the quasi-two-dimensional system. This work establishes FeOCl and isostructural compounds as a source for the development of two-dimensional intrinsic antiferromagnets.

Large, non-saturating magnetoresistance in WTe2.

Magnetoresistance is the change in a material's electrical resistance in response to an applied magnetic field. Materials with large magnetoresistance have found use as magnetic sensors, in magnetic memory, and in hard drives at room temperature, and their rarity has motivated many fundamental studies in materials physics at low temperatures. Here we report the observation of an extremely large positive magnetoresistance at low temperatures in the non-magnetic layered transition-metal dichalcogenide WTe2: 452,700 per cent at 4.5 kelvins in a magnetic field of 14.7 teslas, and 13 million per cent at 0.53 kelvins in a magnetic field of 60 teslas. In contrast with other materials, there is no saturation of the magnetoresistance value even at very high applied fields. Determination of the origin and consequences of this effect, and the fabrication of thin films, nanostructures and devices based on the extremely large positive magnetoresistance of WTe2, will represent a significant new direction in the study of magnetoresistivity.

Soft Chemical Synthesis of HxCrS2: An Antiferromagnetic Material with Alternating Amorphous and Crystalline Layers.

We report a new HxCrS2-based crystalline/amorphous layered material synthesized by soft chemical methods. We study the structural nature and composition of this material with atomic resolution scanning transmission electron microscopy (STEM), revealing a complex structure consisting of alternating layers of amorphous and crystalline lamellae. Furthermore, the magnetic properties show evidence for increased magnetic frustration compared to the parent compound NaCrS2. Finally, we show that this material can be exfoliated, thus providing a facile synthesis method for chromium-sulfide-based ultrathin layers. The material reported herein can not only be a source of new thin TMD-related sheets for potential application in catalysis but also be of interest for realizing new 2D magnetic materials.

A New Three-Dimensional Subsulfide Ir2In8S with Dirac Semimetal Behavior.

Dirac and Weyl semimetals host exotic quasiparticles with unconventional transport properties, such as high magnetoresistance and carrier mobility. Recent years have witnessed a huge number of newly predicted topological semimetals from existing databases; however, experimental verification often lags behind such predictions. Common reasons are synthetic difficulties or the stability of predicted phases. Here, we report the synthesis of the type-II Dirac semimetal Ir2In8S, an air-stable compound with a new structure type. This material has two Dirac crossings in its electronic structure along the Γ-Z direction of the Brillouin zone. We further show that Ir2In8S has a high electron carrier mobility of ∼10 000 cm2/(V s) at 1.8 K and a large, nonsaturating transverse magnetoresistance of ∼6000% at 3.34 K in a 14 T applied field. Shubnikov de-Haas oscillations reveal several small Fermi pockets and the possibility of a nontrivial Berry phase. With its facile crystal growth, novel structure type, and striking electronic structure, Ir2In8S introduces a new material system to study topological semimetals and enable advances in the field of topological materials.

Electrical Transport Signature of the Magnetic Fluctuation-Structure Relation in α-RuCl3 Nanoflakes.

The small gap semiconductor α-RuCl3 has emerged as a promising candidate for quantum spin liquid materials. Thus far, Raman spectroscopy, neutron scattering, and magnetization measurements have provided valuable hints for collective spin behavior in α-RuCl3 bulk crystals. However, the goal of implementing α-RuCl3 into spintronic devices would strongly benefit from the possibility of electrically probing these phenomena. To address this, we first investigated nanoflakes of α-RuCl3 by Raman spectroscopy and observed similar behavior as in the case of the bulk material, including the signatures of possible fractionalized excitations. In complementary experiments, we investigated the electrical charge transport properties of individual α-RuCl3 nanoflakes in the temperature range between 120 and 290 K. The observed temperature-dependent electrical resistivity is consistent with variable range hopping behavior and exhibits a transition at about 180 K, close to the onset temperature observed in our Raman measurements. In conjunction with the established relation between structure and magnetism in the bulk, we interpret this transition to coincide with the emergence of fractionalized excitations due to the Kitaev interactions in the nanoflakes. Compared to the bulk samples, the transition temperature of the underlying structural change is larger in the nanoflakes. This difference is tentatively attributed to the dimensionality of the nanoflakes as well as the formation of stacking faults during mechanical exfoliation. The demonstrated devices open up novel perspectives toward manipulating the Kitaev-phase in α-RuCl3 via electrical means.