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A hitherto unrecognized type of fermionic excitation in metals is described, which forms a chain of connected loops in momentum space (a nodal chain) along which conduction and valence bands touch. A new twist on fermions The elementary fermionic excitations—or quasiparticles—that characterize the behaviour of electrons in solids are proving a rich testing ground for exploring exotic physics, with possible practical ramifications. The excitations that give rise to topological insulators, for example, hold promise for the realization of a so-called topological quantum computer. But the full range of possible quasiparticle states remains to be discovered, as exemplified by the excitations described here. Tomáš Bzdušek and colleagues describe a new family of quasiparticle excitation in metals that forms a nodal chain—a chain of connected loops in momentum space—along which conduction and valence bands touch. The authors predict the materials in which this excitation might be found, and offer some initial thoughts on the physical properties that might result. The band theory of solids is arguably the most successful theory of condensed-matter physics, providing a description of the electronic energy levels in various materials. Electronic wavefunctions obtained from the band theory enable a topological characterization of metals for which the electronic spectrum may host robust, topologically protected, fermionic quasiparticles. Many of these quasiparticles are analogues of the elementary particles of the Standard Model 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , but others do not have a counterpart in relativistic high-energy theories 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 . A complete list of possible quasiparticles in solids is lacking, even in the non-interacting case. Here we describe the possible existence of a hitherto unrecognized type of fermionic excitation in metals. This excitation forms a nodal chain—a chain of connected loops in momentum space—along which conduction and valence bands touch. We prove that the nodal chain is topologically distinct from previously reported excitations. We discuss the symmetry requirements for the appearance of this excitation and predict that it is realized in an existing material, iridium tetrafluoride (IrF 4 ), as well as in other compounds of this class of materials. Using IrF 4 as an example, we provide a discussion of the topological surface states associated with the nodal chain. We argue that the presence of the nodal-chain fermions will result in anomalous magnetotransport properties, distinct from those of materials exhibiting previously known excitations.

Magnetically doped topological insulators enable the quantum anomalous Hall effect (QAHE), which provides quantized edge states for lossless charge-transport applications.sup.1-8. The edge states are hosted by a magnetic energy gap at the Dirac point.sup.2, but hitherto all attempts to observe this gap directly have been unsuccessful. Observing the gap is considered to be essential to overcoming the limitations of the QAHE, which so far occurs only at temperatures that are one to two orders of magnitude below the ferromagnetic Curie temperature, T.sub.C (ref. .sup.8). Here we use low-temperature photoelectron spectroscopy to unambiguously reveal the magnetic gap of Mn-doped Bi.sub.2Te.sub.3, which displays ferromagnetic out-of-plane spin texture and opens up only below T.sub.C. Surprisingly, our analysis reveals large gap sizes at 1 kelvin of up to 90 millielectronvolts, which is five times larger than theoretically predicted.sup.9. Using multiscale analysis we show that this enhancement is due to a remarkable structure modification induced by Mn doping: instead of a disordered impurity system, a self-organized alternating sequence of MnBi.sub.2Te.sub.4 septuple and Bi.sub.2Te.sub.3 quintuple layers is formed. This enhances the wavefunction overlap and size of the magnetic gap.sup.10. Mn-doped Bi.sub.2Se.sub.3 (ref. .sup.11) and Mn-doped Sb.sub.2Te.sub.3 form similar heterostructures, but for Bi.sub.2Se.sub.3 only a nonmagnetic gap is formed and the magnetization is in the surface plane. This is explained by the smaller spin-orbit interaction by comparison with Mn-doped Bi.sub.2Te.sub.3. Our findings provide insights that will be crucial in pushing lossless transport in topological insulators towards room-temperature applications.

Using a recently developed formalism called topological quantum chemistry, we perform a high-throughput search of ‘high-quality’ materials (for which the atomic positions and structure have been measured very accurately) in the Inorganic Crystal Structure Database in order to identify new topological phases. We develop codes to compute all characters of all symmetries of 26,938 stoichiometric materials, and find 3,307 topological insulators, 4,078 topological semimetals and no fragile phases. For these 7,385 materials we provide the electronic band structure, including some electronic properties (bandgap and number of electrons), symmetry indicators, and other topological information. Our results show that more than 27 per cent of all materials in nature are topological. We provide an open-source code that checks the topology of any material and allows other researchers to reproduce our results. Topological quantum chemistry and newly developed codes are used to analyse and compute the topological properties of materials in a large crystal database and to identify new topological phases, finding that more than 27 per cent of all materials in nature are topological.

A tunable optical lattice is used to engineer massless and massive Dirac fermions and realize the topological transition at which two Dirac points merge and annihilate each other. Tunable Dirac points The electronic structure of certain solids causes them to exhibit 'Dirac points', which lie at the heart of many fascinating phenomena in condensed-matter physics. In graphene, for example, they cause electrons to act as massless Dirac fermions, able to travel at the speed of light. Two very different methods for controlling the properties of Dirac fermions are presented in this issue of Nature . In conventional solids, the electronic structure of the material cannot be varied, so it is difficult to see how the properties of Dirac fermions could be controlled. To avoid this constraint, Tarruell et al . create a tunable system of ultracold quantum gases within an adjustable honeycomb optical lattice. This model simulates condensed-matter physics, with atoms in the role of electrons. The Dirac points can be moved and merged to explore the physics of exotic materials such as topological insulators and graphene. Gomes et al . describe a more direct approach, creating an artificial form of molecular graphene by arranging carbon monoxide molecules, with atomic precision, in a honeycomb pattern on top of a two-dimensional electron system. Lattice parameters are adjustable, allowing the study of the properties of Dirac electrons and even the production of 'pseudo' electric and magnetic fields. This work highlights an innovative technique for constructing artificial materials with molecular assembly, including designer Dirac materials harbouring new ground states. Dirac points are central to many phenomena in condensed-matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators 1 , 2 . At a Dirac point, two energy bands intersect linearly and the electrons behave as relativistic Dirac fermions. In solids, the rigid structure of the material determines the mass and velocity of the electrons, as well as their interactions. A different, highly flexible means of studying condensed-matter phenomena is to create model systems using ultracold atoms trapped in the periodic potential of interfering laser beams 3 , 4 . Here we report the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a minimum bandgap inside the Brillouin zone at the positions of the two Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to change the positions of the Dirac points inside the Brillouin zone. When the anisotropy exceeds a critical limit, the two Dirac points merge and annihilate each other—a situation that has recently attracted considerable theoretical interest 5 , 6 , 7 , 8 , 9 but that is extremely challenging to observe in solids 10 . We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials in which the topology of the band structure is crucial, but also provide an avenue to exploring many-body phases resulting from the interplay of complex lattice geometries with interactions 11 , 12 , 13 .

Topological electronic materials such as bismuth selenide, tantalum arsenide and sodium bismuthide show unconventional linear response in the bulk, as well as anomalous gapless states at their boundaries. They are of both fundamental and applied interest, with the potential for use in high-performance electronics and quantum computing. But their detection has so far been hindered by the difficulty of calculating topological invariant properties (or topological nodes), which requires both experience with materials and expertise with advanced theoretical tools. Here we introduce an effective, efficient and fully automated algorithm that diagnoses the nontrivial band topology in a large fraction of nonmagnetic materials. Our algorithm is based on recently developed exhaustive mappings between the symmetry representations of occupied bands and topological invariants. We sweep through a total of 39,519 materials available in a crystal database, and find that as many as 8,056 of them are topologically nontrivial. All results are available and searchable in a database with an interactive user interface. Topological materials are thought to be scarce, but an algorithm that diagnoses nontrivial topology in nonmagnetic materials finds the opposite: more than 30 per cent of the 26,688 materials studied are topological.

Silicon crystallized in the usual cubic (diamond) lattice structure has dominated the electronics industry for more than half a century. However, cubic silicon (Si), germanium (Ge) and SiGe alloys are all indirect-bandgap semiconductors that cannot emit light efficiently. The goal 1 of achieving efficient light emission from group-IV materials in silicon technology has been elusive for decades 2 – 6 . Here we demonstrate efficient light emission from direct-bandgap hexagonal Ge and SiGe alloys. We measure a sub-nanosecond, temperature-insensitive radiative recombination lifetime and observe an emission yield similar to that of direct-bandgap group-III–V semiconductors. Moreover, we demonstrate that, by controlling the composition of the hexagonal SiGe alloy, the emission wavelength can be continuously tuned over a broad range, while preserving the direct bandgap. Our experimental findings are in excellent quantitative agreement with ab initio theory. Hexagonal SiGe embodies an ideal material system in which to combine electronic and optoelectronic functionalities on a single chip, opening the way towards integrated device concepts and information-processing technologies. A hexagonal (rather than cubic) alloy of silicon and germanium that has a direct (rather than indirect) bandgap emits light efficiently across a range of wavelengths, enabling electronic and optoelectronic functionalities to be combined on a single chip.

Since the discovery of topological insulators and semimetals, there has been much research into predicting and experimentally discovering distinct classes of these materials, in which the topology of electronic states leads to robust surface states and electromagnetic responses. This apparent success, however, masks a fundamental shortcoming: topological insulators represent only a few hundred of the 200,000 stoichiometric compounds in material databases. However, it is unclear whether this low number is indicative of the esoteric nature of topological insulators or of a fundamental problem with the current approaches to finding them. Here we propose a complete electronic band theory, which builds on the conventional band theory of electrons, highlighting the link between the topology and local chemical bonding. This theory of topological quantum chemistry provides a description of the universal (across materials), global properties of all possible band structures and (weakly correlated) materials, consisting of a graph-theoretic description of momentum (reciprocal) space and a complementary group-theoretic description in real space. For all 230 crystal symmetry groups, we classify the possible band structures that arise from local atomic orbitals, and show which are topologically non-trivial. Our electronic band theory sheds new light on known topological insulators, and can be used to predict many more. A complete electronic band theory is presented that describes the global properties of all possible band structures and materials, and can be used to predict new topological insulators and semimetals. A quantum chemistry theory of electron bands Chemists and physicists have traditionally fostered very different perspectives on energy band theory. Barry Bradlyn et al . have developed a new and complete theory to calculate electronic band structure with the unique feature that it can be used to determine for any material whether it is topologically trivial or not. The theory consists of several parts, joining up the conventional band structure approach, which considers electron properties in non-local, momentum space, with a local viewpoint of chemical bonding and interactions. The authors classify the band structures for all 230 symmetry groups and show how this can be used to search for previously undiscovered materials with interesting topological properties.

In the quest to understand high-temperature superconductivity in copper oxides, debate has been focused on the pseudogap—a partial energy gap that opens over portions of the Fermi surface in the ‘normal’ state above the bulk critical temperature 1 . The pseudogap has been attributed to precursor superconductivity, to the existence of preformed pairs and to competing orders such as charge-density waves 1 – 4 . A direct determination of the charge of carriers as a function of temperature and bias could help resolve among these alternatives. Here we report measurements of the shot noise of tunnelling current in high-quality La 2− x Sr x CuO 4 /La 2 CuO 4 /La 2− x Sr x CuO 4 (LSCO/LCO/LSCO) heterostructures fabricated using atomic layer-by-layer molecular beam epitaxy at several doping levels. The data delineate three distinct regions in the bias voltage–temperature space. Well outside the superconducting gap region, the shot noise agrees quantitatively with independent tunnelling of individual charge carriers. Deep within the superconducting gap, shot noise is greatly enhanced, reminiscent of multiple Andreev reflections 5 – 7 . Above the critical temperature and extending to biases much larger than the superconducting gap, there is a broad region in which the noise substantially exceeds theoretical expectations for single-charge tunnelling, indicating pairing of charge carriers. These pairs are detectable deep into the pseudogap region of temperature and bias. The presence of these pairs constrains current models of the pseudogap and broken symmetry states, while phase fluctuations limit the domain of superconductivity. Shot-noise measurements in copper oxides reveal paired charge carriers existing in the pseudogap above the superconducting critical temperature, shedding light on the properties of high-temperature superconductivity in these materials.

This article provides a comprehensive review of wide and ultrawide bandgap power electronic semiconductor devices, comparing silicon (Si), silicon carbide (SiC), gallium nitride (GaN), and the emerging device diamond technology. Key parameters examined include bandgap, critical electric field, electron mobility, voltage/current ratings, switching frequency, and device packaging. The historical evolution of each material is traced from early research devices to current commercial offerings. Significant focus is given to SiC and GaN as they are now actively competing with Si devices in the market, enabled by their higher bandgaps. The paper details advancements in material growth, device architectures, reliability, and manufacturing that have allowed SiC and GaN adoption in electric vehicles, renewable energy, aerospace, and other applications requiring high power density, efficiency, and frequency operation. Performance enhancements over Si are quantified. However, the challenges associated with the advancements of these devices are also elaborately described: material availability, thermal management, gate drive design, electrical insulation, and electromagnetic interference. Alongside the cost reduction through improved manufacturing, material availability, thermal management, gate drive design, electrical insulation, and electromagnetic interference are critical hurdles of this technology. The review analyzes these issues and emerging solutions using advanced packaging, circuit integration, novel cooling techniques, and modeling. Overall, the manuscript provides a timely, rigorous examination of the state of the art in wide bandgap power semiconductors. It balances theoretical potential and practical limitations while assessing commercial readiness and mapping trajectories for further innovation. This article will benefit researchers and professionals advancing power electronic systems.

Black phosphorus (BP) and its two-dimensional derivative (2D-BP) have garnered significant attention as promising anode materials for electrochemical energy storage devices, including next-generation fast-charging batteries. However, the interactions between BP and light metal ions, as well as how these interactions influence BP’s electronic properties, remain poorly understood. Here, we employed density functional theory (DFT) to investigate the effects of monovalent (Li[sup.+] and Na[sup.+] ) and divalent (Mg[sup.2+] and Ca[sup.2+] ) ions on the valence electronic structure of 2D-BP. Molecular orbital analysis revealed that the adsorption of divalent cations can significantly reduce the band gap, suggesting an enhancement in charge transfer rates. In contrast, the adsorption of monovalent cations had minimal impact on the band gap, suggesting the preservation of 2D-BP’s intrinsic electrical properties. Energetic and charge analyses indicated that the extent of charge transfer primarily governs the ability of ions to modulate 2D-BP’s electronic structure, especially under high-pressure conditions where ions are in close proximity to the 2D-BP surface. Moreover, charge polarization calculations revealed that, compared with monovalent cations, divalent cations induced greater polarization, disrupting the symmetry of the pristine 2D-BP and further influencing its electronic characteristics. These findings provide a molecular-level understanding of how ion interactions influence 2D-BP’s electronic properties during ion-intercalation processes, where ions are in close proximity to the 2D-BP surface. Moreover, the calculated diffusion barrier results revealed the potential of 2D-BP as an effective anode material for lithium-ion, sodium-ion, and magnesium-ion batteries, though its performance may be limited for calcium-ion batteries. By extending our understanding of interactions between ions and 2D-BP, this work contributes to the design of efficient and reliable energy storage technologies, particularly for the next-generation fast-charging batteries.