One-dimensional Carbon Chains Research Articles

Ab initio electron-lattice downfolding: Potential energy landscapes, anharmonicity, and molecular dynamics in charge density wave materials

The interplay of electronic and nuclear degrees of freedom presents an outstanding problem in condensed matter physics and chemistry. Computational challenges arise especially for large systems, long time scales, in nonequilibrium, or in systems with strong correlations. In this work, we show how downfolding approaches facilitate complexity reduction on the electronic side and thereby boost the simulation of electronic properties and nuclear motion-in particular molecular dynamics (MD) simulations. Three different downfolding strategies based on constraining, unscreening, and combinations thereof are benchmarked against full density functional calculations for selected charge density wave (CDW) systems, namely 1H-TaS_22, 1T-TiSe_22, 1H-NbS_22, and a one-dimensional carbon chain. We find that the downfolded models can reproduce potential energy surfaces on supercells accurately and facilitate computational speedup in MD simulations by about five orders of magnitude in comparison to purely ab initio calculations. For monolayer 1H-TaS_22 we report classical and path integral replica exchange MD simulations, revealing the impact of thermal and quantum fluctuations on the CDW transition.

Hamiltonian formulation and symplectic split-operator schemes for time-dependent density-functional-theory equations of electron dynamics in molecules

We revisit Kohn–Sham time-dependent density-functional theory (TDDFT) equations and show that they derive from a canonical Hamiltonian formalism. We use this geometric description of the TDDFT dynamics to define families of symplectic split-operator schemes that accurately and efficiently simulate the time propagation for certain classes of DFT functionals. We illustrate these with numerical simulations of the far-from-equilibrium electronic dynamics of a one-dimensional carbon chain. In these examples, we find that an optimized 4th order scheme provides a good compromise between the numerical complexity of each time step and the accuracy of the scheme. We also discuss how the Hamiltonian structure changes when using a basis set to discretize TDDFT and the challenges this raises for using symplectic split-operator propagation schemes.

One-dimensional carbon chains encapsulated in hollandite

One-dimensional carbon chains are highly reactive allotropes that are stabilized inside the protective environment of carbon nanotubes. Here we show that carbon chains can be encapsulated in metal oxides containing open structural channels, exemplified by hollandite α-MnO2. The α-MnO2 channels stabilize cumulene chains due to their structural commensurability, whereas the triple bonds in polyyne chains exhibit excessive steric repulsion to the oxide ions bordering the channel. Cumulene exhibits an interaction energy of only 0.065 eV per carbon atom, obtained by first-principles calculations, which is significantly more favorable than for encapsulation in a similarly sized carbon nanotube. Encapsulation of carbon chains is associated with lateral expansion of the α-MnO2 channel and polarization of the manganese and oxygen charge densities adjacent to the chains. Accordingly, the interaction energy is governed by a balance between van der Waals attraction and steric repulsion between the materials.

Study of the energy spectrum of a few one-dimensional and quasi one-dimensional lattices through tight binding and density functional theory

A graphene nanoribbon (GNR) is a strip of carbon atoms having sp2 hybridization. It has wide application in nanoelectronics and opto-electronics. Usual fields of application are found in field effect transistors, interconnects, logic gates, sensors, energy storage, and photovoltaics. A single unit graphene nanoribbon is a long strip of graphene rings. Such a GNR structure may be seen as two one-dimensional carbon chains that are suitable connected with bonds. We have done tight binding calculations and density functional theory simulation of carbon chains. We study the single bond and double bond one-dimensional carbon chain and the alternate bond (t1-t2), also called a bond order system in one dimension and quasi one-dimensional chain. We find evidence for the emergence of multiple gaps in the energy spectrum of these systems. We have mapped the alternate bond system to the Su–Schrieffer–Heeger model (with a small modification) in one dimension and quasi one dimension. This is the first time such a mapping has been attempted and a comprehensive theoretical and computational study of these chains has been performed.

Surface hopping dynamics in periodic solid-state materials with a linear vibronic coupling model.

We report a surface hopping approach in which the implemented linear vibronic coupling Hamiltonian is constructed and the electronic wavefunction is propagated in the reciprocal space. The parameters of the linear vibronic coupling model, including onsite energies, phonon frequencies, and electron-phonon couplings, are calculated with density-functional theory and density-functional perturbation theory and interpolated in fine sampling points of the Brillouin zone with maximally localized Wannier functions. Using this approach, we studied the relaxation dynamics of the photo-excited hot carrier in a one-dimensional periodic carbon chain. The results show that the completeness of the number of Hilbert space k points and the number of phonon q points plays an important role in the hot carrier relaxation processes. By calculating the relaxation times of hot carriers under different reciprocal space sampling and extrapolating with the stretched-compressed exponential function, the relaxation times of hot electrons and holes in the quasi-continuous energy band are obtained. By considering the feedback effect in the hopping processes and analyzing the time-dependent phonon energy in different normal modes, we found that the long-wave longitudinal optical phonons play a major role in the relaxation dynamics of hot electrons and holes. We, therefore, provided herein an efficient and accurate approach for modeling the photophysical processes in periodic solid-state material systems.

Excitonic-insulator instability and Peierls distortion in one-dimensional semimetals

The charge density wave instability in one-dimensional semimetals is usually explained through a Peierls-like mechanism, where the coupling of electrons and phonons induces a periodic lattice distortion along certain modes of vibration, leading to a gap opening in the electronic band structure and to a lowering of the symmetry of the lattice. In this work, we study two prototypical Peierls systems: the one-dimensional carbon chain and the monatomic hydrogen chain with accurate ab initio calculations based on quantum Monte Carlo and hybrid density functional theory. We demonstrate that in one-dimensional semimetals at $T=0$, a purely electronic instability can exist independently of a lattice distortion. It is induced by spontaneous formation of low energy electron-hole pairs resulting in the electronic band gap opening, i.e., the destabilization of the semimetallic phase is due to an excitonic mechanism.

Inelastic light scattering by self-formed linear-chain aggregates of carbon atoms in gold island films

The study of the optical response of gold island films revealed an intense line in the light scattering spectrum near 2100 cm-1. Some possible reasons for the appearance of this line are considered. Comparison of the results obtained for films obtained by various technologies, light scattering spectra on other types of samples, as well as comparison with the results of other authors allow us to interpret the line as the result of inelastic light scattering by one-dimensional carbon chains. Keywords: inelastic light scattering, gold films, SERS, one-dimensional carbon chains.

Неупругое рассеяние света самосформированными линейно-цепочными агрегатами углеродных атомов в островковых пленках золота

The study of the optical response of gold island films revealed an intense line in the light scattering spectrum near 2100 cm-1. Some possible reasons for the appearance of this line are considered. Comparison of the results obtained for films obtained by various technologies, light scattering spectra on other types of samples, as well as comparison with the results of other authors allow us to interpret the line as the result of inelastic light scattering by one-dimensional carbon chains.

Occurrence of nonohmic trend in the ballistic transport mode of a modelled low dimensional device capable of performing electronic functions

Abstract Electronic transport mechanism has been investigated through a modelled one-dimensional carbon chain consisting of four atoms, connected to two identical planar zigzag graphene nanoribbons (ZGNR) electrodes. Non equilibrium green's function (NGEF) formalism, coupled with density functional theory (DFT) is employed in stabilizing the geometry of the constructed device and in calculating the electronic transmission (conduction) at room temperature. The primitive pristine carbon chain device shows three distinct behaviours in the context of negative differential resistance (NDR) within a small voltage range 0.0–2.0 V. The first nonlinear trend shows a sharp NDR feature. It appears within an extremely low operating voltage range 0.0–0.5 V. Doping with nitrogen and boron atoms in different parts of the device (scattering and electrode region) tends to alter the transport behaviour differently. It is exciting to observe the functioning of the device upon doping in two different ways. Doping in scattering region of the device keeps the shape of I–V curve same in forward and reverse bias operation. However, doping in the electrode region results in altering the shape of I–V curve on biasing differently. Eventually in former case doping in scattering region enhances (amplify) the magnitude of current and in later, doping in electrode region makes it suitable for rectification. Analysis of the computational data generated by the, extremely small device gives exceptionally high values of PVR (peak to value ratio) and rectification ratio. Devices demonstrating high values of these two parameters are of outmost importance and often desired, as they are suitable in performing useful electronic functions. The advantage of the present device over enormous number of similar devices reported in past, being small consisting of only four atoms long carbon chain and short electrodes, its performance potential is comparatively high. The proposed carbon chain device reported here can be utilized as a nano transistor in miniaturized electronic circuitry. Uniqueness of the reported device is its small size coupled with multiple NDR, owing to smallness of dimensions the packing density of such transistors on a single chip operational capability can be increased manifold thereby enhancing its functional performance.

Irradiation-enhanced torsional buckling capacity of carbon nanotube bundles

Molecular dynamics simulations are used to understand the torsional buckling of pristine and irradiated carbon nanotube (CNT) bundles. Irradiation-induced inter-tube defects are shown to significantly increase the critical buckling torque and critical buckling angle, while slightly increasing the torsional stiffness. In contrast, intra-tube defects are found to degrade the torsional properties. Such competing interactions cause irradiation enhancement to occur in large bundles where significant inter-tube bonding can occur. However, the irradiation enhancement effect becomes weak for very large bundles in which enhanced inter-tube interactions already exist in unirradiated bundles. In pristine CNT bundles of all sizes under torsional loading, CNTs can slip via the weakly interacting van der Waals force, whereas in the irradiated bundles, the inter-tube defects prevent slipping. The study further shows that the formation of one-dimensional carbon chain defects contributes to enhanced friction under slipping.

Bond-Scission-Induced Structural Transformation from Cumulene to Diyne Moiety and Formation of Semiconducting Organometallic Polyyne.

The structural transformation from symmetric cumulene to broken-symmetry polyyne within a one-dimensional (1-D) atomic carbon chain is a signature of Peierls distortion. Direct observation of such a structural transformation with single-bond resolution is, however, still challenging. Herein, we design a molecule with a cumulene moiety (Br2C═C═C═CBr2) and employ STM tip manipulation to achieve the molecular skeleton rearrangement from a cumulene to a diyne moiety (Br-C≡C-C≡C-Br). Furthermore, by an on-surface reaction strategy, thermally induced entire debromination (:C═C═C═C:) leads to the formation of a 1-D organometallic polyyne (-C≡C-C≡C-Au-) with a semiconducting characteristic, which implies that a Peierls-like transition may occur in a rationally designed molecular system with limited length.

First-principle study of structure stability and electronic structures of graphyne derivatives

A new carbon allotropegraphyne has attracted a lot of attention in the field of material sciences and condensed-matter physics due to its unique structure and excellent electronic, optical and mechanical properties. First-principles calculations based on the density functional theory (DFT) are performed to investigate the structures, energetic stabilities and electronic structures of -graphyne derivatives ( -N). The studied -graphyne derivative consists of hexagon carbon rings connected by onedimensional carbon chains with various numbers of carbon atoms (N=1-6) on the chain. The calculation results show that the parity of number of carbon atoms on the carbon chains has a great influence on the structural configuration, the structural stability and the electronic property of the system. The -graphyne derivatives with odd-numbered carbon chains possess continuous CC double bonds, energetically less stable than those with even-numbered carbon chains which have alternating single and triple CC bonds. The electronic structure calculations indicate that -graphyne derivatives can be either metallic (when N is odd) or direct band gap semiconducting (when N is even). The existence of direct band gap can promote the efficient conversion of photoelectric energy, which indicates the advantage of -graphyne in the optoelectronic device. The band gaps of -2, 4, 6 are between 0.94 eV and 0.84 eV, the gap decreases with the number of triple CC bonds increasing, and increases with the augment of length of carbon chains in -2, 4, 6. Our first-principles studies show that introducing carbon chains between the hexagon carbon rings of graphene gives us a method to switch between metallic and semiconducting electronic structures by tuning the number of carbon atoms on the chains and provides a theoretical basis for designing and preparing the tunable s-p hybridized two-dimensional materials and nanoelectronic devices based on carbon atoms.

Origin of a Raman scattering peak generated in single-walled carbon nanotubes by X-ray irradiation and subsequent thermal annealing

We have found that a Raman scattering (RS) peak around 1870 cm−1 was produced by the annealing of the X-ray irradiated film of single-walled carbon nanotubes (SWNTs) at 450 oC. The intensity of 1870-cm−1 peak showed a maximum at the probe energy of 2.3 eV for the RS spectroscopy with various probe lasers. Both the peak position and the probe-energy dependence were almost identical to those of the one-dimensional carbon chains previously reported in multi-walled carbon nanotubes. Consequently, we concluded that the 1870-cm−1 peak found in the present study is attributed to carbon chains. The formation of carbon chains by the annealing at temperature lower than 500 oC is firstly reported by the present study. The carbon chains would be formed by aggregation of the interstitial carbons, which are formed as a counterpart of carbon vacancies by X-ray irradiation diffused on SWNT walls. The result indicates that the combination of X-ray irradiation and subsequent thermal annealing is a feasible tool for generating new nanostructures in SWNT.

Quasiparticle and excitonic gaps of one-dimensional carbon chains.

We report diffusion quantum Monte Carlo (DMC) calculations of the quasiparticle and excitonic gaps of hydrogen-terminated oligoynes and extended polyyne. The electronic gaps are found to be very sensitive to the atomic structure in these systems. We have therefore optimised the geometry of polyyne by directly minimising the DMC energy with respect to the lattice constant and the Peierls-induced carbon-carbon bond-length alternation. We find the bond-length alternation of polyyne to be 0.136(2) Å and the excitonic and quasiparticle gaps to be 3.30(7) and 3.4(1) eV, respectively. The DMC zone-centre longitudinal optical phonon frequency of polyyne is 2084(5) cm(-1), which is consistent with Raman spectroscopic measurements for large oligoynes.

Laser synthesis and stability of one-dimensional polyynic carbon chains in liquid media

The results on femtosecond laser formation of polyynic linear carbon chains (LCCs) are reported. To reduce the oxidation and degradation of carbon chains, the synthesis of LCCs was performed in liquid media. The flakes of graphite were suspended in water or in hexane and ultrasonicated to obtain a suspension of micron-size graphite particles. This suspension was irradiated by pulses of Ti:sapphire laser. The spectral lines at 189, 199, 215, 225, 262, 276, 284, 299, 323, 342, and 368 nm in the optical absorption spectrum of the irradiated graphite suspension were clearly distinguished. They were attributed to the absorption of polyynic carbon chains CnH2, where n=2 to 20. The stability of the synthesized one-dimensional carbon chains suspended in water and hexane was defined based on the intensity of the optical absorption bands. Its half-life time was estimated to be 20 h at room temperature for water, and 7 and 25 days for hexane at 60°C and 5°C, respectively.

Ballistic Thermal Transport in Carbyne and Cumulene with Micron-Scale Spectral Acoustic Phonon Mean Free Path.

The elastic modulus of carbyne, a one-dimensional carbon chain, was recently predicted to be much higher than graphene. Inspired by this discovery and the fundamental correlation between elastic modulus and thermal conductivity, we investigate the intrinsic thermal transport in two carbon allotropes: carbyne and cumulene. Using molecular dynamics simulations, we discover that thermal conductivities of carbyne and cumulene at the quantum-corrected room temperature can exceed 54 and 148 kW/m/K, respectively, much higher than that for graphene. Such conductivity is attributed to high phonon energies and group velocities, as well as reduced scattering from non-overlapped acoustic and optical phonon modes. The prolonged spectral acoustic phonon lifetime of 30–110 ps and mean free path of 0.5–2.5 μm exceed those for graphene, and allow ballistic phonon transport along micron-length carbon chains. Tensile extensions can enhance the thermal conductivity of carbyne due to the increased phonon density of states in the acoustic modes and the increased phonon lifetime from phonon bandgap opening. These findings provide fundamental insights into phonon transport and band structure engineering through tensile deformation in low-dimensional materials, and will inspire studies on carbyne, cumulene, and boron nitride chains for their practical deployments in nano-devices.

First-principles study of electron-phonon coupling and superconductivity in compound Li2C2

One-dimensional carbon chains are expected to show outstanding optical and mechanical properties. But synthesis of the compounds containing one-dimensional carbon chains is a challenging work, because of the difficulty in saturating the dangling bonds of carbon atoms. Recently, the transition from the Immm phase to the Cmcm one at a transition pressure 5 GPa has been predicted for Li2C2 by density-functional theory calculations. In Cmcm-Li2C2, there are one-dimensional zigzag carbon chains caged by lithium atoms. Under ambient pressure, the electronic structure of Cmcm-Li2C2 is as follows: The hybridization among 2s, 2py, and 2pz orbitals of carbon atoms results in three sp2-hybridized orbitals that are coplanar with the zigzag chains of these carbon atoms, denoted as the y-z plane. The sp2-hybridized orbitals along y-axis (perpendicular to the zigzag chain) overlap with each other and form one πup-bonding band and one πup ^*-antibonding band. Likewise, the 2p_x orbitals of carbon atoms will provide also one πup-bonding band and one π*-antibonding band. These two π*-antibonding bands cross the Fermi level and contribute to the metallicity of Cmcm-Li2C2. The other two sp2-hybridized orbitals will give two σ-bonding bands, whose band tops are about 5 eV below the Fermi energy level. These two fully occupied σ bands are the framework of the zigzag carbon chains. The changes in electronic structure of Cmcm-Li2C2 under 5 GPa are negligible, compared with that in case of ambient pressure. To our best knowledge, there is no report upon the superconductivity for compounds containing one dimensional carbon chains. We choose Cmcm-Li2C2 as a model system to investigate its electron-phonon coupling and phonon-mediated superconductivity. To determine the phonon-mediated superconductivity, the electron-phonon coupling constant λ and logarithmic average frequency ωlog are calculated based on density functional perturbation theory and Eliashberg equations. We find that λ and ωlog are equal to 0.63 and 53.8 meV respectively at ambient pressure for Cmcm-Li2C2. In comparison, both the phonon density of states and the Eliashberg spectral function α2F(ω) are slightly blue-shifted at a pressure of 5 GPa. Correspondingly, λ and ωlog are calculated to be 0.56 and 58.2 meV at 5 GPa. Utilizing McMillian-Allen-Dynes formula, we find that the superconducting transition temperatures (Tc) for Cmcm-Li2C2 are 13.2 K and 9.8 K, respectively, at ambient pressure and 5 GPa. We also find that two phonon modes B1g and Ag at Γ point have strong coupling with π* electrons. Among lithium carbide compounds, the superconductivity is only observed in LiC2 below 1.9 K. Besides LiC2, theoretical calculations also predicted superconductivity in mono-layer LiC6, with Tc being 8.1 K. So if the superconductivity of Cmcm-Li2C2 is confirmed by experiment, it will be the first superconducting compound containing one dimensional carbon chains and its Tc will be the highest one among lithium carbide compounds. Thus experimental research to explore the possible superconductivity in Cmcm-Li2C2 is called for.

Effects of substrate defects on the carbon cluster formation in graphene growth on Ni(111) surface

Abstract The growth of graphene by chemical vapor deposition on transition metal has shown promise in this regard. The main hurdle for further improvement is the lack of complete understanding of the atomistic processes involved in the early growth stages, which is conceivable because there are too many factors affecting the growth process. Using first-principles calculations, we investigate the effect of substrate defects on the graphene nucleation on the Ni(111) surface. Our calculations reveal that the defects on substrates can induce the carbon aggregation, and the corresponding structures are completely different from that on the perfect Ni surface. We also compare the critical cluster sizes for the transition from one-dimensional carbon chains to two-dimensional graphene flakes in the growth sequence. Our investigations on the effects of substrate defects would be extremely useful for the future experimental synthesis of high-quality graphene.

Electronic properties of linear carbon chains: Resolving the controversy

Literature values for the energy gap of long one-dimensional carbon chains vary from as little as 0.2 eV to more than 4 eV. To resolve this discrepancy, we use the GW many-body approach to calculate the band gap E(g) of an infinite carbon chain. We also compute the energy dependence of the attenuation coefficient β governing the decay with chain length of the electrical conductance of long chains and compare this with recent experimental measurements of the single-molecule conductance of end-capped carbon chains. For long chains, we find E(g) = 2.16 eV and an upper bound for β of 0.21 Å(-1).

Formation of atomic carbon chains from graphene nanoribbons

The formation of one-dimensional carbon chains from graphene nanoribbons is investigated using it ab initio molecular dynamics. We show under what conditions it is possible to obtain a linear atomic chain via pulling of the graphene nanoribbons. The presence of dimers composed of two-coordinated carbon atoms at the edge of the ribbons is necessary for the formation of the linear chains, otherwise there is simply the full rupture of the structure. The presence of Stone-Wales defects close to these dimers may lead to the formation of longer chains. The local atomic configuration of the suspended atoms indicates the formation of single and triple bonds, which is a characteristic of polyynes.