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Carbon allotropes built from rings of two-coordinate atoms, known as cyclo[n]carbons, have fascinated chemists for many years, but until now they could not be isolated or structurally characterized because of their high reactivity. We generated cyclo[18]carbon (C18) using atom manipulation on bilayer NaCl on Cu(111) at 5 kelvin by eliminating carbon monoxide from a cyclocarbon oxide molecule, C24O₆. Characterization of cyclo[18]carbon by high-resolution atomic force microscopy revealed a polyynic structure with defined positions of alternating triple and single bonds. The high reactivity of cyclocarbon and cyclocarbon oxides allows covalent coupling between molecules to be induced by atom manipulation, opening an avenue for the synthesis of other carbon allotropes and carbon-rich materials from the coalescence of cyclocarbon molecules.

To access superconductivity via the electric field effect in a clean, two-dimensional device is a central goal of nanoelectronics. Recently, superconductivity has been realized in graphene moiré heterostructures 1 – 4 ; however, many of these structures are not mechanically stable, and experiments show signatures of strong disorder. Here we report the observation of superconductivity—manifesting as low or vanishing resistivity at sub-kelvin temperatures—in crystalline rhombohedral trilayer graphene 5 , 6 , a structurally metastable carbon allotrope. Superconductivity occurs in two distinct gate-tuned regions (SC1 and SC2), and is deep in the clean limit defined by the ratio of mean free path and superconducting coherence length. Mapping of the normal state Fermi surfaces by quantum oscillations reveals that both superconductors emerge from an annular Fermi sea, and are proximal to an isospin-symmetry-breaking transition where the Fermi surface degeneracy changes 7 . SC1 emerges from a paramagnetic normal state, whereas SC2 emerges from a spin-polarized, valley-unpolarized half-metal 1 7 and violates the Pauli limit for in-plane magnetic fields by at least one order of magnitude 8 , 9 . We discuss our results in view of several mechanisms, including conventional phonon-mediated pairing 10 , 11 , pairing due to fluctuations of the proximal isospin order 12 , and intrinsic instabilities of the annular Fermi liquid 13 , 14 . Our observation of superconductivity in a clean and structurally simple two-dimensional metal provides a model system to test competing theoretical models of superconductivity without the complication of modelling disorder, while enabling new classes of field-effect controlled electronic devices based on correlated electron phenomena and ballistic electron transport. Superconductivity is observed in rhombohedral trilayer graphene in the absence of a moiré superlattice, with two distinct superconducting states both occurring at a symmetry-breaking transition where the Fermi surface degeneracy changes.

The two natural allotropes of carbon, diamond and graphite, are extended networks of sp 3 -hybridized and sp 2 -hybridized atoms, respectively 1 . By mixing different hybridizations and geometries of carbon, one could conceptually construct countless synthetic allotropes. Here we introduce graphullerene, a two-dimensional crystalline polymer of C 60 that bridges the gulf between molecular and extended carbon materials. Its constituent fullerene subunits arrange hexagonally in a covalently interconnected molecular sheet. We report charge-neutral, purely carbon-based macroscopic crystals that are large enough to be mechanically exfoliated to produce molecularly thin flakes with clean interfaces—a critical requirement for the creation of heterostructures and optoelectronic devices 2 . The synthesis entails growing single crystals of layered polymeric (Mg 4 C 60 ) ∞ by chemical vapour transport and subsequently removing the magnesium with dilute acid. We explore the thermal conductivity of this material and find it to be much higher than that of molecular C 60 , which is a consequence of the in-plane covalent bonding. Furthermore, imaging few-layer graphullerene flakes using transmission electron microscopy and near-field nano-photoluminescence spectroscopy reveals the existence of moiré-like superlattices 3 . More broadly, the synthesis of extended carbon structures by polymerization of molecular precursors charts a clear path to the systematic design of materials for the construction of two-dimensional heterostructures with tunable optoelectronic properties. A two-dimensional crystalline polymer of C 60 , termed graphullerene, is synthesized by chemical vapour transport, and mechanically exfoliated to produce molecularly thin flakes with clean interfaces for potential optoelectronic applications.

The synthesis of 2D materials with no analogous bulk layered allotropes promises a substantial breadth of physical and chemical properties through the diverse structural options afforded by substrate-dependent epitaxy. However, despite the joint theoretical and experimental efforts to guide materials discovery, successful demonstrations of synthetic 2D materials have been rare. The recent synthesis of 2D boron polymorphs (that is, borophene) provides a notable example of such success. In this Perspective, we discuss recent progress and future opportunities for borophene research. Borophene combines unique mechanical properties with anisotropic metallicity, which complements the canon of conventional 2D materials. The multi-centre characteristics of boron–boron bonding lead to the formation of configurationally varied, vacancy-mediated structural motifs, providing unprecedented diversity in a mono-elemental 2D system with potential for electronic applications, chemical functionalization, materials synthesis and complex heterostructures. With its foundations in computationally guided synthesis, borophene can serve as a prototype for ongoing efforts to discover and exploit synthetic 2D materials.

Synthetic carbon allotropes such as graphene 1 , carbon nanotubes 2 and fullerenes 3 have revolutionized materials science and led to new technologies. Many hypothetical carbon allotropes have been discussed 4 , but few have been studied experimentally. Recently, unconventional synthetic strategies such as dynamic covalent chemistry 5 and on-surface synthesis 6 have been used to create new forms of carbon, including γ-graphyne 7 , fullerene polymers 8 , biphenylene networks 9 and cyclocarbons 10 , 11 . Cyclo[ N ]carbons are molecular rings consisting of N carbon atoms 12 , 13 ; the three that have been reported to date ( N  = 10, 14 and 18) 10 , 11 are doubly aromatic, which prompts the question: is it possible to prepare doubly anti-aromatic versions? Here we report the synthesis and characterization of an anti-aromatic carbon allotrope, cyclo[16]carbon, by using tip-induced on-surface chemistry 6 . In addition to structural information from atomic force microscopy, we probed its electronic structure by recording orbital density maps 14 with scanning tunnelling microscopy. The observation of bond-length alternation in cyclo[16]carbon confirms its double anti-aromaticity, in concordance with theory. The simple structure of C 16 renders it an interesting model system for studying the limits of aromaticity, and its high reactivity makes it a promising precursor to novel carbon allotropes 15 . The carbon allotrope cyclo[16]carbon has been synthesized using on-surface chemistry and characterized with scanning tunnelling microscopy and atomic force microscopy, revealing orbital densities and bond-length alternation, which show it to be doubly anti-aromatic.

A cyclo -N 5 − anion has been synthesized as a stable salt and characterized Polynitrogens have the potential for ultrahigh-performing explosives or propellants because singly or doubly bonded polynitrogens can decompose to triply bonded dinitrogen (N 2 ) with an extraordinarily large energy release. The large energy content and relatively low activation energy toward decomposition makes the synthesis of a stable polynitrogen allotrope an extraordinary challenge. Many elements exist in different forms (allotropes)—for example, carbon can exist as graphite, diamond, buckyballs, or graphene. However, no stable neutral allotropes are known for nitrogen, and only two stable homonuclear polynitrogen ions had been isolated until now—namely, the N 3 − anion ( 1 ) and the N 5 + cation ( 2 ). On page 374 of this issue, Zhang et al. ( 3 ) report the synthesis and characterization of the first stable salt of the cyclo -N 5 − anion, only the third stable homonuclear polynitrogen ion ever isolated.

All-carbon materials based on sp 2 -hybridized atoms, such as fullerenes 1 , carbon nanotubes 2 and graphene 3 , have been much explored due to their remarkable physicochemical properties and potential for applications. Another unusual all-carbon allotrope family are the cyclo[ n ]carbons (C n ) consisting of two-coordinated sp -hybridized atoms. They have been studied in the gas phase since the twentieth century 4 – 6 , but their high reactivity has meant that condensed-phase synthesis and real-space characterization have been challenging, leaving their exact molecular structure open to debate 7 – 11 . Only in 2019 was an isolated C 18 generated on a surface and its polyynic structure revealed by bond-resolved atomic force microscopy 12 , 13 , followed by a recent report 14 on C 16 . The C 18 work trigged theoretical studies clarifying the structure of cyclo[ n ]carbons up to C 100 (refs. 15 – 20 ), although the synthesis and characterization of smaller C n allotropes remains difficult. Here we modify the earlier on-surface synthesis approach to produce cyclo[10]carbon (C 10 ) and cyclo[14]carbon (C 14 ) via tip-induced dehalogenation and retro-Bergman ring opening of fully chlorinated naphthalene (C 10 Cl 8 ) and anthracene (C 14 Cl 10 ) molecules, respectively. We use atomic force microscopy imaging and theoretical calculations to show that, in contrast to C 18 and C 16 , C 10 and C 14 have a cumulenic and cumulene-like structure, respectively. Our results demonstrate an alternative strategy to generate cyclocarbons on the surface, providing an avenue for characterizing annular carbon allotropes for structure and stability. We provide a modified strategy for the on-surface synthesis of cyclocarbons with 10 or 14 carbon atoms that provides a route for characterizing annular carbon allotropes.

Allotropes of carbon, such as diamond and graphene, are among the best conductors of heat. We monitored the evolution of thermal conductivity in thin graphite as a function of temperature and thickness and found an intimate link between high conductivity, thickness, and phonon hydrodynamics. The room-temperature in-plane thermal conductivity of 8.5-micrometer-thick graphite was 4300 watts per meter-kelvin—a value well above that for diamond and slightly larger than in isotopically purified graphene. Warming enhances thermal diffusivity across a wide temperature range, supporting partially hydrodynamic phonon flow. The enhancement of thermal conductivity that we observed with decreasing thickness points to a correlation between the out-of-plane momentum of phonons and the fraction of momentum-relaxing collisions. We argue that this is due to the extreme phonon dispersion anisotropy in graphite.

Elemental phosphorus is attracting growing interest across fundamental and applied fields of research. However, atomistic simulations of phosphorus have remained an outstanding challenge. Here, we show that a universally applicable force field for phosphorus can be created by machine learning (ML) from a suitably chosen ensemble of quantum-mechanical results. Our model is fitted to density-functional theory plus many-body dispersion (DFT + MBD) data; its accuracy is demonstrated for the exfoliation of black and violet phosphorus (yielding monolayers of “phosphorene” and “hittorfene”); its transferability is shown for the transition between the molecular and network liquid phases. An application to a phosphorene nanoribbon on an experimentally relevant length scale exemplifies the power of accurate and flexible ML-driven force fields for next-generation materials modelling. The methodology promises new insights into phosphorus as well as other structurally complex, e.g., layered solids that are relevant in diverse areas of chemistry, physics, and materials science. Atomistic simulations of phosphorus represent a challenge due to the element’s highly diverse allotropic structures. Here the authors propose a general-purpose machine-learning force field for elemental phosphorus, which can describe a broad range of relevant bulk and nanostructured allotropes.

Unalloyed titanium boasts an impressive combination of ductility, biocompatibility and corrosion resistance. However, its strength properties are moderate, which constrains its use in demanding structural applications. Traditional alloying methods used to strengthen titanium often compromise ductility and tend to be costly and energy intensive. Here we present a lean alloy design approach to create a strong and ductile dual-phase titanium–oxygen alloy. By embedding a coherent nanoscale allotropic face-centred cubic titanium phase into the hexagonal close-packed titanium matrix, we significantly enhance strength while preserving substantial ductility. This hexagonal-close-packed/face-centred-cubic dual-phase titanium–oxygen alloy is created by leveraging the tailored oxide-layer thickness of the powders and the rapid cooling inherent in laser-based powder bed fusion. The as-printed Ti–0.67 wt% O alloy exhibits an ultimate tensile strength of 1,119.3 ± 29.2 MPa and a ductility of 23.3 ± 1.9%. Our strategy of incorporating a coherent nanoscale allotropic phase offers a promising pathway to developing high-performance, cost-effective and sustainable lean alloys. A hexagonal-close-packed/face-centred-cubic dual-phase titanium–oxygen alloy is lean designed and fabricated by laser-based powder bed fusion using titanium powders with customized oxide-layer thickness. The as-printed alloy achieves an excellent combination of high strength and ductility.