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Layered or chain materials have received significant research attention owing to their interesting physical properties, which can dramatically change when the material is thinned from bulk (three-dimensional) to thin two-dimensional sheet or one-dimensional (1D) chain form. Materials with the stoichiometry AX2 with A = Si or Ge and X = S or Se form an especially intriguing semiconducting class. For example, bulk silicon dichalcogenides (SiX2) consist of 1D chains held together by van der Waals forces. Although this structural configuration has the potential to reveal interesting physical phenomena within the 1D limit, obtaining SiX2 single chains has been challenging. We here examine experimentally and theoretically SiX2 materials in the low chain number limit. Carbon nanotubes serve as growth templates and stabilize and protect the structures, and atomic-resolution scanning transmission electron microscopy directly identifies the atomic structure. Two distinct chain structures are observed for SiX2. SixGe1-xS2(1-y)Se2y quaternary alloy chains are also synthesized and characterized, demonstrating tunable semiconducting properties at the atomic-chain level. Density functional theory calculations reveal that the band gap of these alloy chains can be widely tuned through composition engineering. This work offers the possibilities for synthesizing and controlling semiconductor compositions at the single-chain limit to tailor material properties.

High-pressure studies on elements play an essential role in superconductivity research, with implications for both fundamental science and applications. Here we report the experimental discovery of surprisingly low pressure driving a novel germanium allotrope into a superconducting state in comparison to that for α-Ge. Raman measurements revealed structural phase transitions and possible electronic topological transitions under pressure up to 58 GPa. Based on pressure-dependent resistivity measurements, superconductivity was induced above 2 GPa and the maximum Tc of 6.8 K was observed under 4.6 GPa. Interestingly, a superconductivity enhancement was discovered during decompression, indicating the possibility of maintaining pressure-induced superconductivity at ambient pressure with better superconducting performance. Density functional theory analysis further suggested that the electronic structure of Ge (oP32) is sensitive to its detailed geometry and revealed that disorder in the β-tin structure leads to a higher Tc in comparison to the perfect β-tin Ge.

Elucidating the phase diagram of solid hydrogen is a key objective in condensed matter physics. Several decades ago, it was proposed that at low temperatures and high pressures, solid hydrogen would be a metal with a high superconducting transition temperature. This transition to a metallic state can happen through the closing of the energy gap in the molecular solid or through a transition to an atomic solid. Recent experiments have managed to reach pressures in the range of 400-500 GPa, providing valuable insights. There is strong evidence suggesting that metallization via either of these mechanisms occurs within this pressure range. Computational and experimental studies have identified multiple promising crystal phases, but the limited accuracy of calculations and the limited capabilities of experiments prevent us from determining unequivocally the observed phase or phases. Therefore, it is crucial to investigate the superconducting properties of all the candidate phases. Recently, we reported the superconducting properties of theC2/c-24,Cmca-12,Cmca-4 andI41/amd-2 phases, including anharmonic effects. Here, we report the effects of anisotropy on superconducting properties using Eliashberg theory. Then, we investigate the superconducting properties of deuterium and estimate the size of the isotope effect for each phase. We find that the isotope effect on superconductivity is diminished by anharmonicity in theC2/c-24 andCmca-12 phases and enlarged in theCmca-4 andI41/amd-2 phases. Our anharmonic calculations of theC2/c-24 phase of deuterium agree closely with the most recent experiment by Loubeyreet al(2022Phys. Rev. Lett.29035501), indicating that theC2/c-24 phase remains the leading candidate in this pressure range, and has a strong anharmonic character. These characteristics can serve to distinguish among crystal phases in experiment. Furthermore, expanding our understanding of superconductivity in pure hydrogen holds significance in the study of high-Tchydrides.

Magnetic materials in reduced dimensions are not only excellent platforms for fundamental studies of magnetism, but they play crucial roles in technological advances. The discovery of intrinsic magnetism in monolayer 2D van der Waals systems has sparked enormous interest, but the single-chain limit of 1D magnetic van der Waals materials has been largely unexplored. This paper reports on a family of 1D magnetic van der Waals materials with composition MX3 (M = Cr, V, and X = Cl, Br, I), prepared in fully-isolated fashion within the protective cores of carbon nanotubes. Atomic-resolution scanning transmission electron microscopy identifies unique structures that differ from the well-known 2D honeycomb lattice MX3 structure. Density functional theory calculations reveal charge-driven reversible magnetic phase transitions.

The packing and connectivity of tetrahedral units are central themes in the structural and electronic properties of a host of solids. Here, we report one-dimensional (1D) chains of GeX2 (X = S or Se) with modification of the tetrahedral connectivity at the single-chain limit. Precise tuning of the edge- and corner-sharing modes between GeX2 blocks is achieved by diameter-dependent 1D confinement inside a carbon nanotube. Atomic-resolution scanning transmission electron microscopy directly confirms the existence of two distinct types of GeX2 chains. Density functional theory calculations corroborate the diameter-dependent stability of the system and reveal an intriguing electronic structure that sensitively depends on tetrahedral connectivity and composition. GeS2(1-x)Se2x compound chains are also realized, which demonstrate the tunability of the system's semiconducting properties through composition engineering.

Nanotube encapsulation is a powerful technique for coaxing solids into unconventional configurations. By synthesizing materials within the interior confines of hollow nanotubes, lower dimensional morphologies, such as one-dimensional chains or nanoribbons, are favored. We have used carbon nanotube encapsulation to realize ultranarrow, atomically precise HfTe2 nanoribbons. A local, electron-beam-stimulated transition from the metallic 1T phase to the previously unreported semiconducting 1H phase is observed. We study computationally how charging can drive the phase transition and the stability of the different atomic configurations.

Although doping with alkali atoms is a powerful technique for introducing charge carriers into physical systems, the resulting charge-transfer systems are generally not air stable. Here we describe computationally a strategy towards increasing the stability of alkali-doped materials that employs stoichiometrically unbalanced salt crystals with excess cations (which could be deposited during, e.g., in situ gating) to achieve doping levels similar to those attained by pure alkali metal doping. The crystalline interior of the salt crystal acts as a template to stabilize the excess dopant atoms against oxidation and deintercalation, which otherwise would be highly favorable. We characterize this doping method for graphene, NbSe_{2}, and Bi_{2}Se_{3} and its effect on direct-to-indirect band gap transitions, 2D superconductivity, and thermoelectric performance. Salt intercalation should be generally applicable to systems which can accommodate this "ionic crystal" doping (and particularly favorable when geometrical packing constraints favor nonstoichiometry).

We investigate the electromigration forces for weakly bonded adsorbates on graphene by using density-functional based calculations. We find that the nature of electromigration forces on an adsorbate critically depends on the energy level alignment between the adsorbate state and the Fermi level of the graphene. For a resonant adsorbate, whose frontier orbitals lie close to the Fermi level, the electromigration force is dominated by the electron wind force that is strongly enhanced along the electron flow direction, irrespective of the sign of the adsorbate charge. For a nonresonant adsorbate, the electromigration force is essentially the direct force that depends on the adsorbate charge. We also show that the magnitude of electromigration forces can be continuously tunable through electrostatic gating for resonant adsorbates. Our results provide new insight for understanding and controlling how nanoscale objects behave in or on host materials.

As the simplest element in nature, unraveling the phase diagram of hydrogen is a primary task for condensed matter physics. As conjectured many decades ago, in the low-temperature and high-pressure part of the phase diagram, solid hydrogen is expected to become metallic with a high superconducting transition temperature. The metallization may occur via band gap closure in the molecular solid or via a transition to the atomic solid. Recently, a few experimental studies pushed the achievable pressures into the 400-500 GPa range. There are strong indications that at some pressure in this range metallization via either of these mechanisms occurs, although there are disagreements between experimental reports. Furthermore, there are multiple good candidate crystal phases that have emerged from recent computational and experimental studies which may be realized in upcoming experiments. Therefore, it is crucial to determine the superconducting properties of these candidate phases. In a recent study, we reported the superconducting properties of theC2/c-24 phase, which we believe to be a strong candidate for metallization via band gap closure (Doganet al2022Phys. Rev. B105L020509). Here, we report the superconducting properties of theCmca-12,Cmca-4 andI41/amd-2 phases including the anharmonic effects using a Wannier function-based densek-point andq-point sampling. We find that theCmca-12 phase has a superconducting transition temperature that rises from 86 K at 400 GPa to 212 K at 500 GPa, whereas theCmca-4 andI41/amd-2 phases show a less pressure-dependent behavior with theirTcin the 74-94 K and 307-343 K ranges, respectively. These properties can be used to distinguish between crystal phases in future experiments. Understanding superconductivity in pure hydrogen is also important in the study of high-Tchydrides.

Fine control over material synthesis on the nanoscale can facilitate the stabilization of competing crystalline structures. Here, we demonstrate how carbon nanotube reaction vessels can be used to selectively create one-dimensional TaTe3 chains or two-dimensional TaTe2 nanoribbons with exquisite control of the chain number or nanoribbon thickness and width. Transmission electron microscopy and scanning transmission electron microscopy reveal the detailed atomic structure of the encapsulated materials. Complex superstructures such as multichain spiraling and apparent multilayer moirés are observed. The rare 2H phase of TaTe2 (1H in monolayer) is found to be abundant as an encapsulated nanoribbon inside carbon nanotubes. The experimental results are complemented by density functional theory calculations for the atomic and electronic structure, which uncovers the prevalence of 2H-TaTe2 due to nanotube-to-nanoribbon charge transfer and size confinement. Calculations also reveal new 1T' type charge density wave phases in TaTe2 that could be observed in experimental studies.

Recent experimental developments in hydrogen-rich materials at high pressures have put this class of materials above others in the race toward room-temperature superconductivity. As it is the basis of all the materials in this class, the efforts to determine the properties of pure solid hydrogen at high pressures remain intense. Most notably, a recent experimental study of the metallization of hydrogen identified the crystal phase of the solid as the C2/c-24 molecular phase up to ∼425 GPa [Loubeyre et al., Nature (London) 577, 631 (2020)10.1038/s41586-019-1927-3]. It is possible that the observed metallization is caused by band structure effects and not a structural phase transition, and the material remains in this crystal phase up to higher pressures [Dogan et al., J. Phys.: Condens. Matter 33, 03LT01 (2020)10.1088/1361-648X/abba8a]. Therefore, it is of crucial importance to determine the superconducting properties of the C2/c-24 phase. Here, we employ a Wannier function-based dense k-point and q-point sampling to compute the electron-phonon coupling and superconducting properties of molecular hydrogen in the C2/c-24 phase. We find that the material has a high superconducting transition temperature of 242 K at 500 GPa. We also find that the transition temperature rapidly increases with pressure in the 400-500-GPa range.

Imposing additional confinement in two-dimensional (2D) materials yields further control over their electronic, optical, and topological properties. However, synthesis of ultranarrow nanoribbons (NRs) remains challenging, particularly for transition metal dichalcogenides (TMDs), and synthesizing TMD NRs narrower than 50 nm has remained elusive. Here, we report the vapor-phase synthesis of ultranarrow TaS2 NRs. The NRs are grown within carbon nanotubes, limiting their width and layer number, while stabilizing them against the environment. The NRs reach monolayer thickness and exhibit widths down to 2.5 nm. Atomic-resolution scanning transmission electron microscopy reveals the detailed atomic structure of the ultranarrow NRs and we observe a hitherto unseen atomic structure supermodulation of ordered defect arrays within the NRs. Density functional theory calculations show the presence of flat bands and boundary-localized states, and help identify the atomic configuration of the supermodulation. Nanotube-templated synthesis represents a unique, transferable, and broadly deployable route toward ultranarrow TMD NR growth.

A new experimental study by Snider et al. [2020 Nature 586 373–7] reported behavior in a high-pressure carbon-sulfur-hydrogen system that has been interpreted by the authors as superconductivity at room temperature. The sudden change of electrical resistance at a critical temperature and the change of the R vs. T behavior with an applied magnetic field point to superconductivity. This is a very exciting study in one of the most important areas of science, hence, it is crucial for the community to investigate these findings and hopefully reproduce these results. In this paper, we present calculations that expand upon the arguments put forth by Hirsch and Marsiglio [arXiv:2010.10307], and offer some speculations about physical mechanisms that might explain the observed data. We show that there are errors in the analysis presented in the experimental paper, and with the correct analysis, the reported R vs. T data significantly deviate from the expected behavior. In particular, the extremely sharp change in resistance at the superconducting transition is not consistent with a strongly type II superconductor.

The structure of MX3 transition metal trichalcogenides (TMTs, with M a transition metal and X a chalcogen) is typified by one-dimensional (1D) chains weakly bound together via van der Waals interactions. This structural motif is common across a range of M and X atoms (e.g., NbSe3, HfTe3,TaS3), but not all M and X combinations are stable. We report here that three new members of the MX3 family which are not stable in bulk, specifically NbTe3, VTe3, and TiTe3, can be synthesized in the few- (2-4) to single-chain limit via nanoconfined growth within the stabilizing cavity of multiwalled carbon nanotubes. Transmission electron microscopy (TEM) and atomic-resolution scanning transmission electron microscopy (STEM) reveal the chain-like nature and the detailed atomic structure. The synthesized materials exhibit behavior unique to few-chain quasi-1D structures, such as few-chain spiraling and a trigonal antiprismatic rocking distortion in the single-chain limit. Density functional theory (DFT) calculations provide insight into the crystal structure and stability of the materials, as well as their electronic structure.

A recent experimental study of the metallization of hydrogen tracked the direct band gap and vibron frequency via infrared measurements up to ∼425 GPa (Loubeyreet al(2020Nature577631). Above this pressure, the direct gap has a discontinuous drop to below the minimum experimentally accessible energy (∼0.1 eV). The authors suggested that this observation is caused by a structural phase transition between theC2/c-24 molecular phase to another molecular phase such asCmca-12. Here, throughab initiocalculations of pressure dependent vibron frequency and direct band gap, we find that the experimental data is consistent with theC2/c-24 phase up to 425 GPa, and suggest that this consistency extends beyond that pressure. Specifically, we find that qualitative changes in the band structure of theC2/c-24 phase lead to a discontinuous drop of the direct band gap, which can explain the observed drop without a structural transition. This alternative scenario, which naturally explains the absence of hysteresis in the measurements, will hopefully motivate further experimental studies to ascertain the structure of the phase above the high pressure 'phase transition'.

In order to plan and implement lessons that will be effective for a wide variety of learners, teachers must assess what students know and how they know it. They must also know students' academic strengths, challenges, and preferences. Careful observation of what students do and say as they work provides a rich source of data about both their knowledge and ways of learning. We highlight three strategies we use to help teachers refine their understanding of individual students: (a) building teachers' skills in observing without making judgements; (b) teaching teachers to use a shared, neurodevelopmental framework through which to view student learning and behavior; and (c) facilitating collaboration among general education and special education teachers in using these tools to assess student learning and plan lessons. The combination of careful observations, a neurodevelopmental lens through which to see and interpret the observations, and the different perspectives of general and special education teachers, builds a foundation for planning appropriately leveled and rigorous lessons that leverage students' strengths while supporting them in their weaker areas.

Carbon has numerous one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) allotropic structures. The study of carbon materials has long been a major focus of material sciences and condensed matter physics. Recently, a number of topological semi-metallic carbon allotropes with vastly different topological phases have been predicted from first-principles, showing exceptionally clean and robust topological properties near the Fermi surfaces. In this review, we provide a brief summary of the development of carbon allotropes from 1D to 3D. Then, we discuss topological properties of pure carbon materials, despite their exceedingly small spin–orbit coupling. Instead, the nearest-neighbor p z orbit interaction has been identified as the origin for the non-trivial topological properties, which vary due to different p z connectivity:​ zigzag, armchair, or pentagonal, as well as the interactions among further neighboring atoms. Next, we consider possible expansions of the topological properties of carbon materials to other light-element materials such as boron. Finally, we discuss future prospects in light of experimental feasibility and the recent surge in pursue of exotic carbon physics due to twisted graphene, which may also be viewed as a subset of the topological physics involving sp 2 /p z carbon.

We present the G0W0 band structure, core levels, and deformation potential of monolayer FeSe in the paramagnetic phase based on a starting mean field of the Kohn-Sham density functional theory (DFT) with the Perdew, Burke, and Ernzerhof functional. We find the GW correction increases the bandwidth of the states forming the M pocket near the Fermi energy, while leaving the Γ pocket roughly unchanged. We then compare the G0W0 quasiparticle band energies with the band structure from a simple empirical +A approach, which was recently proposed to capture the renormalization of the electron-phonon interaction going beyond DFT in FeSe, when used as a starting point in density functional perturbation theory. We show that this empirical correction succeeds in approximating the GW nonlocal and dynamical self-energy in monolayer FeSe and reproduces the GW band structure near the Fermi surface, the core energy levels, and the deformation potential (electron-phonon coupling).

The synthesis of new materials with novel or useful properties is one of the most important drivers in the fields of condensed matter physics and materials science. Discoveries of this kind are especially significant when they point to promising future basic research and applications. van der Waals bonded materials comprised of lower-dimensional building blocks have been shown to exhibit emergent properties when isolated in an atomically thin form [1-8]. Here, we report the discovery of a transition metal chalcogenide in a heretofore unknown segmented linear chain form, where basic building blocks each consisting of two hafnium atoms and nine tellurium atoms (Hf_{2}Te_{9}) are van der Waals bonded end to end. First-principle calculations based on density functional theory reveal striking crystal-symmetry-related features in the electronic structure of the segmented chain, including giant spin splitting and nontrivial topological phases of selected energy band states. Atomic-resolution scanning transmission electron microscopy reveals single segmented Hf_{2}Te_{9} chains isolated within the hollow cores of carbon nanotubes, with a structure consistent with theoretical predictions. van der Waals bonded segmented linear chain transition metal chalcogenide materials could open up new opportunities in low-dimensional, gate-tunable, magnetic, and topological crystalline systems.

We examine physical properties of heavily boron-doped sp3-hybridized carbon allotropes: cubic diamond, hexagonal diamond, and body centered tetragonal C4. The structural similarity between cubic diamond and hexagonal diamond leads to similar responses to substitutional boron doping. On the other hand, body centered tetragonal C4 exhibits distinct structural and electronic properties because of its characteristic structure. Our study also shows that the superconducting transition temperatures up to 60 K are possible in heavily doped carbon materials despite their various atomistic structures.

Frustrated interactions can lead to short-range ordering arising from incompatible interactions of fundamental physical quantities with the underlying lattice. The simplest example is the triangular lattice of spins with antiferromagnetic interactions, where the nearest-neighbor spin-spin interactions cannot simultaneously be energy minimized. Here we show that engineering frustrated interactions is a possible route for controlling structural and electronic phenomena in semiconductor alloys. Using aberration-corrected scanning transmission electron microscopy in conjunction with density functional theory calculations, we demonstrate atomic ordering in a two-dimensional semiconductor alloy as a result of the competition between geometrical constraints and nearest-neighbor interactions. Statistical analyses uncover the presence of short-range ordering in the lattice. In addition, we show how the induced ordering can be used as another degree of freedom to considerably modify the band gap of monolayer semiconductor alloys.

We study strong electron-phonon interacting systems where the geometry of the crystalline lattice frustrates the formation of charge order. Our results show that under such condition, high-Tc superconductivity can occur in a wide range of electron-phonon coupling strengths. This result is obtained by studying the Holstein model on triangular lattice using sign-problem-free quantum Monte Carlo method.

We study the effect of atomic coordination (orbital hybridization) on superconducting properties of boron-doped amorphous carbon. The ratio of threefold coordinated (sp2-hybridized) and fourfold coordinated (sp3-hybridized) atoms in the system is found to have an impact on their electronic, vibrational, and superconducting properties. Our findings show that a high proportion of fourfold coordination in both carbon and boron atoms is important for realizing a high superconducting transition temperature.

We investigate the atomic and electronic structures of cyclooctatetraene (COT) molecules on graphene and analyze their dependence on external gate voltage using first-principles calculations. The external gate voltage is simulated by adding or removing electrons using density functional theory calculations. This allows us to investigate how changes in carrier density modify the molecular shape, orientation, adsorption site, diffusion barrier, and diffusion path. For increased hole doping, COT molecules gradually change their shape to a more flattened conformation and the distance between the molecules and graphene increases while the diffusion barrier drastically decreases. For increased electron doping, an abrupt transition to a planar conformation at a carrier density of -8 × 1013 e/cm2 is observed. These calculations imply that the shape and mobility of adsorbed COT molecules can be controlled by externally gating graphene devices.

We propose insulating titanium oxynitrides TinN2O2n-3 as promising water-splitting photocatalytic materials in the visible light range. Using first-principles many-body perturbation theory based on the GW approximation, we show that corundum-type Ti2N2O (an example TinN2O2n-3 compound with n=2) has a smaller band gap of about 2.5 eV, which is more suitable to absorb visible light, compared to other Ti-based oxides such as TiO2 and SrTiO3 with a band gap of more than 3 eV. Band-gap reduction in Ti2N2O is caused by an upward shift of the valence band (negative shift to the oxidation potential of H2O to O2) due to the presence of nitrogen 2p states. The conduction band is dominated by Ti 3d states and the conduction-band minimum is nearly unchanged. As a result, the band-edge potentials of Ti2N2O are better aligned to the water reduction and oxidation levels. Our theoretical predictions provide useful insights for the discovery of efficient visible-light-driven photocatalysts for water splitting.

We report investigation of the geometry and electronic structure of iridium atoms adsorbed onto graphene through a combined experimental and theoretical study. Ir atoms were deposited onto a flake of graphene on a Pt(111) surface and found to form clusters even at low temperatures. The areal density of the observed clusters on the graphene flake suggests the clusters are most likely pairs of Ir atoms. Theoretical ab initio density functional (DFT) calculations indicate that these Ir dimers are oriented horizontally, near neighboring "bridge" sites of the graphene lattice, as this configuration has the strongest adsorption energy of all high-symmetry configurations for the Ir dimer. A large peak in the local density of states (LDOS) at the Dirac point energy was measured via scanning tunneling spectroscopy, and this result is reproduced by a DFT calculation of the LDOS. The peak at the Dirac point energy is found to be from the Ir s and p states. The LDOS in the monomer case was also calculated, and is found to significantly differ from the experimentally determined data, further supporting the hypothesis of low-temperature clustering.