Anisotropy and isotope effect in superconducting solid hydrogen

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.

1D Magnetic MX3 Single-Chains (M = Cr, V and X = Cl, Br, I)

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.

Tuning the Sharing Modes and Composition in a Tetrahedral GeX2 (X = S, Se) System via One-Dimensional Confinement

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. GeS_2(1-x)Se_2x compound chains are also realized, which demonstrate the tunability of the system's semiconducting properties through composition engineering.

Nonstoichiometric Salt Intercalation as a Means to Stabilize Alkali Doping of 2D Materials

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).

Resonantly Enhanced Electromigration Forces for Adsorbates on Graphene

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.

Magnetism and interlayer bonding in pores of Bernal-stacked hexagonal boron nitride

When single-layer h-BN is subjected to a high-energy electron beam, triangular pores with nitrogen edges are formed. Because of the broken sp² bonds, these pores are known to possess magnetic states. We report on the magnetism and electronic structure of triangular pores as a function of their size. Moreover, in the Bernal-stacked h-BN (AB-h-BN), multilayer pores with parallel edges can be created, which is not possible in the commonly fabricated multilayer AA'-h-BN. Given that these pores can be manufactured in a well-controlled fashion using an electron beam, it is important to understand the interactions of pores in neighboring layers. We find that in certain configurations, the edges of the neighboring pores remain open and retain their magnetism, and in others, they form interlayer bonds. We present a comprehensive report on these configurations for small nanopores. We find that at low temperatures, these pores have near degenerate magnetic configurations, and may be utilized in magnetoresistance and spintronics applications. In the process of forming larger multilayer nanopores, interlayer bonds can form, reducing the magnetization. Yet, unbonded parallel multilayer edges remain available at all sizes. Understanding these pores is also helpful in a multitude of applications such as DNA sequencing and quantum emission.

Targeting One- and Two-Dimensional Ta-Te Structures via Nanotube Encapsulation

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.

High temperature superconductivity in the candidate phases of solid hydrogen

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 theirT_cin 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-T_chydrides.

Experimental and Theoretical Study of Possible Collective Electronic States in Exfoliable Re-Doped NbS2

Metallic transition-metal dichalcogenides (TMDs) are rich material systems in which the interplay between strong electron-electron and electron-phonon interactions often results in a variety of collective electronic states, such as charge density waves (CDWs) and superconductivity. While most metallic group V TMDs exhibit coexisting superconducting and CDW phases, 2H-NbS₂ stands out with no charge ordering. Further, due to strong interlayer interaction, the preparation of ultrathin samples of 2H-NbS₂ has been challenging, limiting the exploration of presumably rich quantum phenomena in reduced dimensionality. Here, we demonstrate experimentally and theoretically that light substitutional doping of NbS₂ with heavy atoms is an effective approach to modify both interlayer interaction and collective electronic states in NbS₂. Very low concentrations of Re dopants (<1%) make NbS₂ exfoliable (down to monolayer) while maintaining its 2H crystal structure and superconducting behavior. In addition, first-principles calculations suggest that Re dopants can stabilize some native CDW patterns that are not stable in pristine NbS₂.

Ultranarrow TaS2 Nanoribbons

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.

Stabilization of NbTe3, VTe3, and TiTe3 via Nanotube Encapsulation

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, HfTe_3,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.

Observed metallization of hydrogen interpreted as a band structure effect

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'.

High-Performance Atomically-Thin Room-Temperature NO2 Sensor

The development of room-temperature sensing devices for detecting small concentrations of molecular species is imperative for a wide range of low-power sensor applications. We demonstrate a room-temperature, highly sensitive, selective, stable, and reversible chemical sensor based on a monolayer of the transition-metal dichalcogenide Re_0.5Nb_0.5S₂. The sensing device exhibits a thickness-dependent carrier type, and upon exposure to NO₂ molecules, its electrical resistance considerably increases or decreases depending on the layer number. The sensor is selective to NO₂ with only minimal response to other gases such as NH₃, CH₂O, and CO₂. In the presence of humidity, not only are the sensing properties not deteriorated but also the monolayer sensor shows complete reversibility with fast recovery at room temperature. We present a theoretical analysis of the sensing platform and identify the atomically sensitive transduction mechanism.

Emergence of Topologically Nontrivial Spin-Polarized States in a Segmented Linear Chain

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.

Frustration and Atomic Ordering in a Monolayer Semiconductor Alloy

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.

Simulating the Nanomechanical Response of Cyclooctatetraene Molecules on a Graphene Device

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.

Electrostatically Driven Nanoballoon Actuator

We demonstrate an inflatable nanoballoon actuator based on geometrical transitions between the inflated (cylindrical) and collapsed (flattened) forms of a carbon nanotube. In situ transmission electron microscopy experiments employing a nanoelectromechanical manipulator show that a collapsed carbon nanotube can be reinflated by electrically charging the nanotube, thus realizing an electrostatically driven nanoballoon actuator. We find that the tube actuator can be reliably cycled with only modest control voltages (few volts) with no apparent wear or fatigue. A complementary theoretical analysis identifies critical parameters for nanotube nanoballoon actuation.

Inhibiting Klein Tunneling in a Graphene p-n Junction without an External Magnetic Field

We study by first-principles calculations a densely packed island of organic molecules (F_{4}TCNQ) adsorbed on graphene. We find that with electron doping the island naturally forms a p-n junction in the graphene sheet. For example, a doping level of ∼3×10^{13}  electrons per cm^{2} results in a p-n junction with an 800 meV electrostatic potential barrier. Unlike in a conventional p-n junction in graphene, in the case of the junction formed by an adsorbed organic molecular island we expect that the Klein tunneling is inhibited, even without an applied external magnetic field. Here Klein tunneling is inhibited by the ferromagnetic order that spontaneously occurs in the molecular island upon doping. We estimate that the magnetic barrier in the graphene sheet is around 10 mT.

Towards three-dimensional Weyl-surface semimetals in graphene networks

Graphene as a two-dimensional topological semimetal has attracted much attention for its outstanding properties. In contrast, three-dimensional (3D) topological semimetals of carbon are still rare. Searching for such materials with salient physics has become a new direction in carbon research. Here, using first-principles calculations and tight-binding modeling, we propose a new class of Weyl semimetals based on three types of 3D graphene networks. In the band structures of these materials, two flat Weyl surfaces appear in the Brillouin zone, which straddle the Fermi level and are robust against external strain. Their unique atomic and electronic structures enable applications in correlated electronics, as well as in energy storage, molecular sieves, and catalysis. When the networks are cut, the resulting slabs and nanowires remain semimetallic with Weyl lines and points at the Fermi surfaces, respectively. Between the Weyl lines, flat surface bands emerge with possible strong magnetism. The robustness of these structures can be traced back to a bulk topological invariant, ensured by the sublattice symmetry, and to the one-dimensional Weyl semimetal behavior of the zigzag carbon chain.

Molecular Self-Assembly in a Poorly Screened Environment: F4TCNQ on Graphene/BN

We report a scanning tunneling microscopy and noncontact atomic force microscopy study of close-packed 2D islands of tetrafluorotetracyanoquinodimethane (F4TCNQ) molecules at the surface of a graphene layer supported by boron nitride. While F4TCNQ molecules are known to form cohesive 3D solids, the intermolecular interactions that are attractive for F4TCNQ in 3D are repulsive in 2D. Our experimental observation of cohesive molecular behavior for F4TCNQ on graphene is thus unexpected. This self-assembly behavior can be explained by a novel solid formation mechanism that occurs when charged molecules are placed in a poorly screened environment. As negatively charged molecules coalesce, the local work function increases, causing electrons to flow into the coalescing molecular island and increase its cohesive binding energy.

Nanostructured Carbon Allotropes with Weyl-like Loops and Points

Carbon allotropes are subject of intense investigations for their superb structural, electronic, and chemical properties, but not for topological band properties because of the lack of strong spin-orbit coupling (SOC). Here, we show that conjugated p-orbital interactions, common to most carbon allotropes, can in principle produce a new type of topological band structure, forming the so-called Weyl-like semimetal in the absence of SOC. Taking a structurally stable interpenetrated graphene network (IGN) as example, we show, by first-principles calculations and tight-binding modeling, that its Fermi surface is made of two symmetry-protected Weyl-like loops with linear dispersion along perpendicular directions. These loops are reduced to Weyl-like points upon breaking of the inversion symmetry. Because of the topological properties of these band-structure anomalies, remarkably, at a surface terminated by vacuum there emerges a flat band in the loop case and two Fermi arcs in the point case. These topological carbon materials may also find applications in the fields of catalysts.

Calculation of the specific heat of optimally K-doped BaFe₂As₂

The calculated specific heat of optimally K-doped BaFe2As2 in density functional theory is about five times smaller than that found in the experiment. We report that by adjusting the potential on the iron atom to be slightly more repulsive for electrons improves the calculated heat capacity as well as the electronic band structure of Ba0.6K0.4Fe2As2. In addition, structural and magnetic properties are moved in the direction of experimental values. Applying the same correction to the antiferromagnetic state, we find that the electron-phonon coupling is strongly enhanced.

Carbon kagome lattice and orbital-frustration-induced metal-insulator transition for optoelectronics

A three-dimensional elemental carbon kagome lattice, made of only fourfold-coordinated carbon atoms, is proposed based on first-principles calculations. Despite the existence of 60° bond angles in the triangle rings, widely perceived to be energetically unfavorable, the carbon kagome lattice is found to display exceptional stability comparable to that of C(60). The system allows us to study the effects of triangular frustration on the electronic properties of realistic solids, and it demonstrates a metal-insulator transition from that of graphene to a direct gap semiconductor in the visible blue region. By minimizing s-p orbital hybridization, which is an intrinsic property of carbon, not only the band edge states become nearly purely frustrated p states, but also the band structure is qualitatively different from any known bulk elemental semiconductors. For example, the optical properties are similar to those of direct-gap semiconductors GaN and ZnO, whereas the effective masses are comparable to or smaller than those of Si.

Surface atom motion to move iron nanocrystals through constrictions in carbon nanotubes under the action of an electric current

Under the application of electrical currents, metal nanocrystals inside carbon nanotubes can be bodily transported. We examine experimentally and theoretically how an iron nanocrystal can pass through a constriction in the carbon nanotube with a smaller cross-sectional area than the nanocrystal itself. Remarkably, through in situ transmission electron imaging and diffraction, we find that, while passing through a constriction, the nanocrystal remains largely solid and crystalline and the carbon nanotube is unaffected. We account for this behavior by a pattern of iron atom motion and rearrangement on the surface of the nanocrystal. The nanocrystal motion can be described with a model whose parameters are nearly independent of the nanocrystal length, area, temperature, and electromigration force magnitude. We predict that metal nanocrystals can move through complex geometries and constrictions, with implications for both nanomechanics and tunable synthesis of metal nanoparticles.

Multiparticle Exciton Ionization in Shallow Doped Carbon Nanotubes

Shallow hole doping in small-diameter semiconducting carbon nanotubes with a valley degeneracy is predicted to result in the resonant ionization of excitons into free electron-hole pairs. This mechanism, which relies on the chirality of the electronic states, causes excitons to decay with high efficiencies where the rate scales as the square of the dopant density. Moreover, multiparticle exciton ionization can account for delocalized fluorescence quenching when a few holes per micrometer of tube length are present.

Effects of charge doping and constrained magnetization on the electronic structure of an FeSe monolayer

The electronic structural properties in the presence of constrained magnetization and a charged background are studied for a monolayer of FeSe in non-magnetic, checkerboard- and striped-antiferromagnetic (AFM) spin configurations. First-principles techniques based on the pseudopotential density functional approach and the local spin density approximation are utilized. Our findings show that the experimentally observed shape of the Fermi surface is best described by the checkerboard AFM spin pattern. To explore the underlying pairing mechanism, we study the evolution of the non-magnetic to the AFM-ordered structure under constrained magnetization. We estimate the strength of electronic coupling to magnetic excitations involving an increase in local moment and, separately, a partial moment transfer from one Fe atom to another. We also show that the charge doping in the FeSe can lead to an increase in the density of states at the Fermi level.

Quasiparticle semiconductor band structures including spin-orbit interactions

We present first-principles calculations of the quasiparticle band structure of the group IV materials Si and Ge and the group III-V compound semiconductors AlP, AlAs, AlSb, InP, InAs, InSb, GaP, GaAs and GaSb. Calculations are performed using the plane wave pseudopotential method and the 'one-shot' GW method, i.e. G(0)W(0). Quasiparticle band structures, augmented with the effects of spin-orbit, are obtained via a Wannier interpolation of the obtained quasiparticle energies and calculated spin-orbit matrix. Our calculations explicitly treat the shallow semicore states of In and Ga, which are known to be important in the description of the electronic properties, as valence states in the quasiparticle calculation. Our calculated quasiparticle energies, combining both the ab initio evaluation of the electron self-energy and the vector part of the pseudopotential representing the spin-orbit effects, are in generally very good agreement with experimental values. These calculations illustrate the predictive power of the methodology as applied to group IV and III-V semiconductors.

Evidence for the R8 phase of germanium

The formation of R8 germanium is reported. The β-Sn phase is first induced by the indentation of amorphous germanium (a-Ge) and the resultant phases on pressure release are characterized by Raman scattering. The expected Raman line frequencies for the various phases of Ge are determined from first-principles calculations using density functional perturbation theory of the zone-center phonons in the diamond, ST12, BC8, and R8 Ge phases. In addition to the R8 phase, traces of BC8 may also be present following pressure release.

The design and conduct of clinical trials to limit missing data

This article summarizes recommendations on the design and conduct of clinical trials of a National Research Council study on missing data in clinical trials. Key findings of the study are that (a) substantial missing data is a serious problem that undermines the scientific credibility of causal conclusions from clinical trials; (b) the assumption that analysis methods can compensate for substantial missing data is not justified; hence (c) clinical trial design, including the choice of key causal estimands, the target population, and the length of the study, should include limiting missing data as one of its goals; (d) missing-data procedures should be discussed explicitly in the clinical trial protocol; (e) clinical trial conduct should take steps to limit the extent of missing data; (f) there is no universal method for handling missing data in the analysis of clinical trials - methods should be justified on the plausibility of the underlying scientific assumptions; and (g) when alternative assumptions are plausible, sensitivity analysis should be conducted to assess robustness of findings to these alternatives. This article focuses on the panel's recommendations on the design and conduct of clinical trials to limit missing data. A companion paper addresses the panel's findings on analysis methods.

Raman spectroscopy study of rotated double-layer graphene: misorientation-angle dependence of electronic structure

We present a systematic Raman study of unconventionally stacked double-layer graphene, and find that the spectrum strongly depends on the relative rotation angle between layers. Rotation-dependent trends in the position, width and intensity of graphene 2D and G peaks are experimentally established and accounted for theoretically. Our theoretical analysis reveals that changes in electronic band structure due to the interlayer interaction, such as rotational-angle dependent Van Hove singularities, are responsible for the observed spectral features. Our combined experimental and theoretical study provides a deeper understanding of the electronic band structure of rotated double-layer graphene, and leads to a practical way to identify and analyze rotation angles of misoriented double-layer graphene.

Phonon-assisted optical absorption in silicon from first principles

The phonon-assisted interband optical absorption spectrum of silicon is calculated at the quasiparticle level entirely from first principles. We make use of the Wannier interpolation formalism to determine the quasiparticle energies, as well as the optical transition and electron-phonon coupling matrix elements, on fine grids in the Brillouin zone. The calculated spectrum near the onset of indirect absorption is in very good agreement with experimental measurements for a range of temperatures. Moreover, our method can accurately determine the optical absorption spectrum of silicon in the visible range, an important process for optoelectronic and photovoltaic applications that cannot be addressed with simple models. The computational formalism is quite general and can be used to understand the phonon-assisted absorption processes in general.

First principles study of phosphorus and boron substitutional defects in Si-XII

We present a first principles study of boron and phosphorus substitutional defects in Si-XII. Recent results from nanoindentation experiments reveal that the Si-XII phase is semiconducting and has the interesting property that it can be doped n- and p-type at room temperature without an annealing step. Using the hybrid functional of Heyd, Scuseria and Ernzerhof (HSE), we examine the formation energies of the B and P defects at the two distinct atomic sites in Si-XII to find on which site the substitutional defects are more easily accommodated. We also estimate the thermodynamic transition levels of each defect in its relevant charge states. The hybrid calculations also give an independent prediction that Si-XII is semiconducting, in agreement with recent experimental data.

Simple approximate physical orbitals for GW quasiparticle calculations

Generating unoccupied orbitals within density functional theory (DFT) for use in GW calculations of quasiparticle energies becomes prohibitive for large systems. We show that, without any loss of accuracy, the unoccupied orbitals may be replaced by a set of simple approximate physical orbitals made from appropriately prepared plane waves and localized basis DFT orbitals that represent the continuum and resonant states of the system, respectively. This approach allows for accurate quasiparticle calculations using only a very small number of unoccupied DFT orbitals, resulting in an order of magnitude gain in speed.

Electrodynamic and excitonic intertube interactions in semiconducting carbon nanotube aggregates

The optical properties of selectively aggregated, nearly single chirality single-wall carbon nanotubes were investigated by both continuous-wave and time-resolved spectroscopies. With reduced sample heterogeneities, we have resolved aggregation-dependent reductions of the excitation energy of the S(1) exciton and enhanced electron-hole pair absorption. Photoluminescence spectra revealed a spectral splitting of S(1) and simultaneous reductions of the emission efficiencies and nonradiative decay rates. The observed strong deviations from isolated tube behavior are accounted for by enhanced screening of the intratube Coulomb interactions, intertube exciton tunneling, and diffusion-driven exciton quenching. We also provide evidence that density gradient ultracentrifugation can be used to structurally sort single-wall carbon nanotubes by aggregate size as evident by a monotonic dependence of the aforementioned optical properties on buoyant density.

Electron-phonon renormalization of the direct band gap of diamond

We calculate from first principles the temperature-dependent renormalization of the direct band gap of diamond arising from electron-phonon interactions. The calculated temperature dependence is in good agreement with spectroscopic ellipsometry measurements, and the zero-point renormalization of the band gap is found to be as large as 0.6 eV. We also calculate the temperature-dependent broadening of the direct absorption edge and find good agreement with experiment. Our work calls for a critical revision of the band structures of other carbon-based materials calculated by neglecting electron-phonon interactions.

Quasiparticle band gap of ZnO: high accuracy from the conventional G⁰W⁰ approach

Contrary to previous reports, we show that the conventional GW (the so-called G⁰W⁰) approximation can be used to calculate accurately the experimental band gap (∼3.6  eV) of ZnO. The widely discussed underestimate of the quasiparticle gap of ZnO within the GW method is a result of an inadequate treatment of the semicore electrons and the slow and nonuniform convergence in the calculation of the Coulomb-hole self-energy in previous studies. In addition, an assumed small kinetic energy cutoff for the dielectric matrix may result in a false convergence behavior for the quasiparticle self-energy.

Calcium-decorated graphene-based nanostructures for hydrogen storage

We report a first-principles study of hydrogen storage media consisting of calcium atoms and graphene-based nanostructures. We find that Ca atoms prefer to be individually adsorbed on the zigzag edge of graphene with a Ca-Ca distance of 10 A without clustering of the Ca atoms, and up to six H(2) molecules can bind to a Ca atom with a binding energy of approximately 0.2 eV/H(2). A Ca-decorated zigzag graphene nanoribbon (ZGNR) can reach the gravimetric capacity of approximately 5 wt % hydrogen. We also consider various edge geometries of the graphene for Ca dispersion.

Spatial resolution of a type II heterojunction in a single bipolar molecule

Bipolar molecules incorporating donor and acceptor components within a single molecule create exciting device opportunities due to their possible use as nanoscale p-n heterojunctions. Here we report a direct characterization of the internal electronic structure of a single bipolar molecular heterojunction, including subnanometer features of the intramolecular donor-acceptor interface. Angstrom-resolved scanning tunneling spectroscopy was used to map the energy levels and spatial extent of molecular orbitals across the surface of an individual bipolar molecule, bithiophene naphthalene diimide (BND). We find that individual BND molecules exhibit type II heterojunction behavior with orbital energy shifts occurring over subnanometer intramolecular interface distances. Comparison of this behavior with first-principles theoretical modeling provides new insights into the optimization of these molecular systems.

Angle-resolved photoemission spectra of graphene from first-principles calculations

Angle-resolved photoemission spectroscopy (ARPES) is a powerful experimental technique for directly probing electron dynamics in solids. The energy versus momentum dispersion relations and the associated spectral broadenings measured by ARPES provide a wealth of information on quantum many-body interaction effects. In particular, ARPES allows studies of the Coulomb interaction among electrons (electron-electron interactions) and the interaction between electrons and lattice vibrations (electron-phonon interactions). Here, we report ab initio simulations of the ARPES spectra of graphene including both electron-electron and electron-phonon interactions on the same footing. Our calculations reproduce some of the key experimental observations related to many-body effects, including the indication of a mismatch between the upper and lower halves of the Dirac cone.

Excitonic effects on the optical response of graphene and bilayer graphene

We present first-principles calculations of many-electron effects on the optical response of graphene, bilayer graphene, and graphite employing the GW-Bethe Salpeter equation approach. We find that resonant excitons are formed in these two-dimensional semimetals. The resonant excitons give rise to a prominent peak in the absorption spectrum near 4.5 eV with a different line shape and significantly redshifted peak position from those of an absorption peak arising from interband transitions in an independent quasiparticle picture. In the infrared regime, our calculated optical absorbance per graphene layer is approximately a constant, 2.4%, in agreement with recent experiments; additional low frequency features are found for bilayer graphene because of band structure effects.

Optimizing anharmonicity in nanoscale weak link Josephson junction oscillators

We compute the current phase relation for superconducting weak links, with dimensions comparable to the zero temperature coherence length, connected to two and three dimensional superconducting electrodes. Our results indicate that 50-100 nm long aluminum nanobridges with three dimensional banks have sufficient anharmonicity for realizing low noise amplifiers and quantum bits. Such weak link junctions thus present a practical new route for realizing sensitive quantum circuits with potentially higher quality factor than tunnel junction devices due to the absence of a lossy oxide layer.

Landau levels and quantum Hall effect in graphene superlattices

We show that, when graphene is subjected to an appropriate one-dimensional external periodic potential, additional branches of massless fermions are generated with nearly the same electron-hole crossing energy as that at the original Dirac point of graphene. Because of these new zero-energy branches, the Landau levels at charge neutral filling become 4(2N + 1)-fold degenerate (with N = 0, 1, 2, ..., tunable by the potential strength and periodicity) with the corresponding Hall conductivity sigma_{xy} showing a step of size 4(2N + 1)e;{2}/h. These theoretical findings are robust against variations in the details of the external potential and provide measurable signatures of the unusual electronic structure of graphene superlattices.

Role of fluorine in the iron pnictides: phonon softening and effective hole doping

Using a first-principles approach, we investigate the influence of fluorine doping on the electronic structure, lattice dynamics, and electron-phonon coupling in LaFeAsO. In order to explore properties which are not described by the virtual crystal approximation, we explicitly simulate the F doping using a supercell model. Our analysis reveals that the relaxation of the crystal lattice around the dopant modifies the lattice dynamics in agreement with recent experimental data. In addition, we find that the doped electronic charge does not localize on the two-dimensional Fe plane. The net charge variation in this plane upon doping corresponds instead to a slight hole doping.

Graphene at the edge: stability and dynamics

Although the physics of materials at surfaces and edges has been extensively studied, the movement of individual atoms at an isolated edge has not been directly observed in real time. With a transmission electron aberration-corrected microscope capable of simultaneous atomic spatial resolution and 1-second temporal resolution, we produced movies of the dynamics of carbon atoms at the edge of a hole in a suspended, single atomic layer of graphene. The rearrangement of bonds and beam-induced ejection of carbon atoms are recorded as the hole grows. We investigated the mechanism of edge reconstruction and demonstrated the stability of the "zigzag" edge configuration. This study of an ideal low-dimensional interface, a hole in graphene, exhibits the complex behavior of atoms at a boundary.

First-principles study of electron linewidths in graphene

We present first-principles calculations of the linewidths of low-energy quasiparticles in n-doped graphene arising from both the electron-electron and the electron-phonon interactions. The contribution to the electron linewidth arising from the electron-electron interactions varies significantly with wave vector at fixed energy; in contrast, the electron-phonon contribution is virtually wave vector independent. These two contributions are comparable in magnitude at a binding energy of approximately 0.2 eV, corresponding to the optical phonon energy. The calculated linewidths, with both electron-electron and electron-phonon interactions included, explain to a large extent the linewidths seen in recent photoemission experiments.

Essay: fifty years of condensed matter physics

Since the birth of Physical Review Letters fifty years ago, condensed matter physics has seen considerable growth, and both the journal and the field have flourished during this period. In this essay, I begin with some general comments about condensed matter physics and then give some personal views on the conceptual development of the field and list some highlights. The focus is mostly on theoretical developments.

Electron-phonon interactions in graphene, bilayer graphene, and graphite

Using first-principles techniques, we calculate the renormalization of the electron Fermi velocity and the vibrational lifetimes arising from electron-phonon interactions in doped bilayer graphene and in graphite and compare the results with the corresponding quantities in graphene. For similar levels of doping, the Fermi velocity renormalization in bilayer graphene and in graphite is found to be approximately 30% larger than that in graphene. In the case of bilayer graphene, this difference is shown to arise from the interlayer interaction. We discuss our findings in the light of recent photoemission and Raman spectroscopy experiments.