Monoatomic Chains Research Articles

Static structures of strained carbon chains: DFT-modeling vs classical modeling of the chain with Lennard-Jones potential

We proved earlier that in the strained monoatomic chains with Lennard-Jones potential there can exist an equilibrium static bi-structure, which corresponds to N - 1 equal short interatomic bonds and one long bond with inversion in its center (N is the number of atoms of the chain). In the present work, we investigate with the aid of the density functional theory (DFT modeling) similar structures that can exist in the strained carbon chains. In contrast to the Lennard-Jones model, the bi-structures in this case are inhomogeneous (they have short bonds of different lengths) and appear abruptly when the strain exceeds a certain critical value $\eta_c$ as a result of a hard bifurcation of the equilibrium state (an analogue of the first-order phase transition). Such a bifurcation is associated with two different parts of potential, in which the Lennard-Jones forces can be quite small (this is the vicinity of the potential minimum and the potential tail) and, therefore, the forces acting on the particle between the long and short bonds can be equal. Since practically all interatomic potentials possess such features, the above bifurcation is universal, i.e. it must occur for any monoatomic chain. We have studied in detail the properties of the above structures, in particular, the behavior of their parameters with increasing N. With the help of DFT-modeling, the electron density of the above structures near the bifurcation point is investigated.

Topological properties of a bipartite lattice of domain wall states

We propose a generalization of the Su-Schrieffer-Heeger (SSH) model of the bipartite lattice, consisting of a periodic array of domain walls. The low-energy description is governed by the superposition of localized states at each domain wall, forming an effective mono-atomic chain at a larger scale. When the domain walls are dimerized, topologically protected edge states can appear, just like in the original SSH model. These new edge states are formed exclusively by soliton-like states and therefore, the new topological states are qualitatively different from the regular SSH edge states. They posses a much longer localization length and are more resistant to on-site disorder, in marked contrast to the standard SSH case.

Electronic and vibrational properties of PbI2 : From bulk to monolayer

Using first-principles calculations, we study the dependence of the electronic and vibrational properties of multi-layered PbI 2 crystals on the number of layers and focus on the electronic-band structure and the Raman spectrum. Electronic-band structure calculations reveal that the direct or indirect semiconducting behavior of PbI 2 is strongly influenced by the number of layers. We find that at 3L-thickness there is a direct-to-indirect band gap transition (from bulk-to-monolayer). It is shown that in the Raman spectrum two prominent peaks, A 1g and E g , exhibit phonon hardening with increasing number of layers due to the inter-layer van der Waals interaction. Moreover, the Raman activity of the A 1g mode significantly increases with increasing number of layers due to the enhanced out-of-plane dielectric constant in the few-layer case. We further characterize rigid-layer vibrations of low-frequency inter-layer shear (C) and breathing (LB) modes in few-layer PbI 2 . A reduced mono-atomic (linear) chain model (LCM) provides a fairly accurate picture of the number of layers dependence of the low-frequency modes and it is shown also to be a powerful tool to study the inter-layer coupling strength in layered PbI 2 .

Tuning frequency band gaps of tensegrity mass-spring chains with local and global prestress

This work studies the acoustic band structure of tensegrity mass-spring chains, and the possibility to tune the dispersion relation of such systems by suitably varying local and global prestress variables. Building on established results of the Bloch–Floquet theory, the paper first investigates the linearized response of chains composed of tensegrity units and lumped masses, which undergo small oscillations around an initial equilibrium state. The stiffness of the units in such a state varies with an internal self-stress induced by prestretching the cables forming the tensegrity units, and the global prestress induced by the application of compression forces to the terminal bases. The given results show that frequency band gaps of monoatomic and biatomic chains can be effectively altered by the fine tuning of local and global prestress parameters, while keeping material properties unchanged. Numerical results on the wave dynamics of chains under moderately large displacements confirm the presence of frequency band gaps of the examined systems in the elastically hardening regime. Novel engineering uses of the examined systems are discussed.

Controllable wave propagation in a weakly nonlinear monoatomic lattice chain with nonlocal interaction and active control

The one-dimensional monoatomic lattice chain connected by nonlinear springs is investigated, and the asymptotic solution is obtained through the Lindstedt-Poincar´e perturbation method. The dispersion relation is derived with the consideration of both the nonlocal and the active control effects. The numerical results show that the nonlocal effect can effectively enhance the frequency in the middle part of the dispersion curve. When the nonlocal effect is strong enough, zero and negative group velocities will be evoked at different points along the dispersion curve, which will provide different ways of transporting energy including the forward-propagation, localization, and backwardpropagation of wavepackets related to the phase velocity. Both the nonlinear effect and the active control can enhance the frequency, but neither of them is able to produce zero or negative group velocities. Specifically, the active control enhances the frequency of the dispersion curve including the point at which the reduced wave number equals zero, and therefore gives birth to a nonzero cutoff frequency and a band gap in the low frequency range. With a combinational adjustment of all these effects, the wave propagation behaviors can be comprehensively controlled, and energy transferring can be readily manipulated in various ways.

Numerical and Experimental Study on the Dynamic Interaction Between Highly Nonlinear Solitary Waves and Pressurized Balls

This paper discusses the dynamic interaction between a monoatomic chain of solid particles and a thin-walled spherical pressure vessel. The objective is to find a relationship between the highly nonlinear solitary waves (HNSWs) propagating within the chain and the internal pressure of the vessel. The paper introduces first a general finite element model to predict the abovementioned interaction, and then a specific application to tennis balls. The scope is to demonstrate a new nondestructive testing (NDT) method to infer the internal pressure of the balls. The overarching idea is that a mechanically induced solitary pulse propagating within the chain interacts with the thin-walled ball to be probed. At the chain–ball interface, the acoustic pulse is partially reflected back to the chain and partially deforms the rubber giving rise to secondary pulses. The research hypothesis is that one or more features of the reflected waves are monotonically dependent on the internal pressure. Both numerical and experimental results demonstrate a monotonic relationship between the time of flight (TOF) of the solitary waves and the internal pressure of the tennis balls. In addition, the pressure inferred nondestructively with the HNSWs matches very well the pressure measured destructively with an ad hoc pressure gauge needle. In the future, the results presented in this study could be used to develop a portable device to infer anytime anywhere the internal pressure of deformable systems (including biological systems) for which conventional pressure gages cannot be used noninvasively.

Discrete breathers of new type in monoatomic chains

In strained monoatomic chains with Lennard-Jones interactions, we revealed a stable static non-homogeneous structure appearing as a result of a certain phase transition. Positions of individual particles in this structure form an exact arithmetic progression whose difference depends on the value of the strain. For N-particle chain, this structure is characterized by one long and N-1 short interatomic distances (bonds). In the vicinity of the static structure, we found discrete breathers of new type which essentially differ from the traditional breathers in the form of Sievers-Takeno and Page modes. It is well known that these modes possess some staggered structures and demonstrate exponential decay of the particle amplitudes from the core to their tails. In contrast to such properties, our breathers are characterised by smooth decay and amplitudes of the particles form approximately a decreasing arithmetic progression. Core of these breathers is located on two particles with long bond in static structure. Our breathers demonstrate soft type of nonlinearity (the frequency decreases with increasing of amplitudes) and they are stable dynamical objects for amplitudes up to 20%-30% of interparticle distance of the strained equidistant chain. For infinitely small amplitudes these breathers tend to the above described static non-homogeneous structure. We studied dependence of their properties on amplitude, strain and the number of particles in the chain. There exist a reason to suppose that the above static and dynamical structures can exist in real monoatomic chains consisting of carbon, boron, and other atoms.

Tabby graphene: Dimensional magnetic crossover in fluorinated graphite

Tabby is a pattern of short irregular stripes, usually related to domestic cats. We have produced Tabby patterns on graphene by attaching fluorine atoms running as monoatomic chains in crystallographic directions. Separated by non-fluorinated sp2 carbon ribbons, sp3-hybridized carbon atoms bonded to zigzag fluorine chains produce sp2-sp3 interfaces and spin-polarized edge states localized on both sides of the chains. We have compared two kinds of fluorinated graphite samples C2Fx, with x near to 1 and x substantially below 1. The magnetic susceptibility of C2Fx (x < 1) shows a broad maximum and a thermally activated spin gap behaviour that can be understood in a two-leg spin ladder model with ferromagnetic legs and antiferromagnetic rungs; the spin gap constitutes about 450 K. Besides, stable room-temperature ferromagnetism is observed in C2Fx (x < 1) samples: the crossover to a three-dimensional magnetic behaviour is due to the onset of interlayer interactions. Similarly prepared C2Fx (x ≈ 1) samples demonstrate features of two-dimensional magnetism without signs of high-temperature magnetic ordering, but with transition to a superparamagnetic state below 40 K instead. The magnetism of the Tabby graphene is stable until 520 K, which is the temperature of the structural reconstruction of fluorinated graphite.

Nonlinear atomic vibrations and structural phase transitions in strained carbon chains

We consider longitudinal nonlinear atomic vibrations in uniformly strained carbon chains with the cumulene structure (=C=C=)n. With the aid of ab initio simulations, based on the density functional theory, we reveal the phenomenon of π-mode softening in certain range of its amplitude for the strain above the critical value ηc≈11%. Condensation of this soft mode induces the Peierls phase transition connected with doubling of the unit cell. We introduce a simple classical model without any adjustable parameters that allows one to describe quite well the properties of the π-mode softening. Besides the π-mode, two other symmetry-determined nonlinear normal modes can exist in monoatomic chains with arbitrary interparticle interactions. They correspond to tripling or quadrupling of the vibrational unit cell. Softening of these modes allows one to suppose that two new types of carbon chains (besides cumulene and polyyne) can exist with bond lengths alternation different from that of polyyne. Since the phase transitions in the strained cumulene can significantly change its electronic properties, these phenomena can be used for constructing various nanodevices.

First-principles study of the stability, magnetic and electronic properties of Fe and Co monoatomic chains encapsulated into copper nanotube

By using first-principles calculations based on density-functional theory, the stability, magnetic and electronic properties of Fe and Co monoatomic chains encapsulated into copper nanotube are systematically investigated. The binding energies of the hybrid structures are remarkably higher than those of corresponding freestanding TM chains, indicating the TM chains are significantly stabilized after encapsulating into copper nanotube. The formed bonds between outer Cu and inner TM atoms show some degree of covalent bonding character. The magnetic ground states of Fe@CuNW and Co@CuNW hybrid structures are ferromagnetic, and both spin and orbital magnetic moments of inner TM atoms have been calculated. The magnetocrystalline anisotropy energies (MAE) of the hybrid structures are enhanced by nearly fourfold compared to those of corresponding freestanding TM chains, indicating that the hybrid structures can be used in ultrahigh density magnetic storage. Furthermore, the easy magnetization axis switches from that along the axis in freestanding Fe chain to that perpendicular to the axis in Fe@CuNT hybrid structure. The large spin polarization at the Fermi level also makes the hybrid systems interesting as good potential materials for spintronic devices.

Higher-Order Dispersion, Stability, and Waveform Invariance in Nonlinear Monoatomic and Diatomic Systems

Recent studies have presented first-order multiple time scale approaches for exploring amplitude-dependent plane-wave dispersion in weakly nonlinear chains and lattices characterized by cubic stiffness. These analyses have yet to assess solution stability, which requires an analysis incorporating damping. Furthermore, due to their first-order dependence, they make an implicit assumption that the cubic stiffness influences dispersion shifts to a greater degree than the quadratic stiffness, and they thus ignore quadratic shifts. This paper addresses these limitations by carrying-out higher-order, multiple scales perturbation analyses of linearly damped nonlinear monoatomic and diatomic chains. The study derives higher-order dispersion corrections informed by both quadratic and cubic stiffness and quantifies plane wave stability using evolution equations resulting from the multiple scales analysis and numerical experiments. Additionally, by reconstructing plane waves using both homogeneous and particular solutions at multiple orders, the study introduces a new interpretation of multiple scales results in which predicted waveforms are seen to exist over all space and time, constituting an invariant, multiharmonic wave of infinite extent analogous to cnoidal waves in continuous systems. Using example chains characterized by dimensionless parameters, numerical studies confirm that the spectral content of the predicted waveforms exhibits less growth/decay over time as higher-order approximations are used in defining the simulations' initial conditions. Thus, the study results suggest that the higher-order multiple scales perturbation analysis captures long-term, nonlocalized invariant plane waves, which have the potential for propagating coherent information over long distances.

Determining alloy composition in MoxW(1 − x)S2 from low wavenumber Raman spectroscopy

Mixed alloy MoxW(1 − x)S2 (0 ≤ x ≤ 1) bulk samples are characterized by low wavenumber Raman spectroscopy. The results provide a convenient and reliable means for systematically determining the sample Mo/W composition. The absence of disorder effects in its interlayer motion (unlike for the intralayer motion) and the lack of Mo/W composition dependence of the shear mode force constants enable the facile employment of a reduced monoatomic linear chain model by treating the bulk alloy as a series of ‘single balls’ of mass (xmMo + (1 − x)mW + 2mS) attached by interlayer springs with a composition‐independent interlayer force constant of .Shear mode Raman scattering analysis may consequently be complementary to the electronic spectroscopy tools (X‐ray photoelectron spectroscopy (XPS) and energy‐dispersive X‐ray spectroscopy (EDS)), commonly used for mixed alloy bulk composition characterization. Copyright © 2017 John Wiley &amp; Sons, Ltd.

Geometric stability and electronic structure of infinite and finite phosphorus atomic chains**Project supported by the National Natural Science Foundation of China (Gant Nos. 11274380, 91433103, 11622437, and 61674171), the Fundamental Research Funds for the Central Universities, China, and the Research Funds of Renmin University of China (Grant No. 16XNLQ01). Qiao was supported by the Outstanding Innovative Talents Cultivation Funded Programs

One-dimensional mono- or few-atomic chains were successfully fabricated in a variety of two-dimensional materials, like graphene, BN, and transition metal dichalcogenides, which exhibit striking transport and mechanical properties. However, atomic chains of black phosphorus (BP), an emerging electronic and optoelectronic material, is yet to be investigated. Here, we comprehensively considered the geometry stability of six categories of infinite BP atomic chains, transitions among them, and their electronic structures. These categories include mono- and dual-atomic linear, armchair, and zigzag chains. Each zigzag chain was found to be the most stable in each category with the same chain width. The mono-atomic zigzag chain was predicted as a Dirac semi-metal. In addition, we proposed prototype structures of suspended and supported finite atomic chains. It was found that the zigzag chain is, again, the most stable form and could be transferred from mono-atomic armchair chains. An orientation dependence was revealed for supported armchair chains that they prefer an angle of roughly 35°–37° perpendicular to the BP edge, corresponding to the [110] direction of the substrate BP sheet. These results may promote successive research on mono- or few-atomic chains of BP and other two-dimensional materials for unveiling their unexplored physical properties.

Mechanics of Materials Creation: Nanotubes, Graphene, Carbyne, Borophenes

In this article, we provide brief overview of how mechanics and computations play a role in understanding materials growth, creating new low-dimensional materials and exploring structural defects. First, we introduce a concept of screw dislocation for describing carbon nanotube growth and derive a kinetic relationship between growth rate and chiral angle. Deeper analysis of the subtle balance between the kinetic and thermodynamic views reveals sharply peaked distribution of near-armchair nanotubes, explaining puzzling (n, n-1) types observed experimentally. A combination of ab initio calculations and Monte Carlo models further explains the low symmetry shapes of graphene on substrates. Being monoatomic chains of carbon, carbynes are shown to be strong yet flexible, and undergo metal-semiconductor transition under tension, offering promising innovations for future nanotechnology. We then reveal how metal substrates could facilitate the formation of boron monolayers whose bulk counterparts are non-layered and lower in energy. Further remarks are given to High Burger's vector graphene defects called D-loops and interfaces in hybrid graphene-BN materials, both with significant out-of plane distortion and impact on the mechanical properties. All of these computationally modeled systems have significant implications for the future use of these nanomaterials.

Bloch Oscillations: Inverse Problem

We use a neural network approach to explore the inverse problem of Bloch oscillations in a monoatomic linear chain: given a signal describing the path of oscillations of electrons as a function of time, we determine the strength of the applied field along the direction of motion or, equivalently, the lattice spacing. We find that the proposed approach has more than 80% of accuracy classifying the studied physical parameters.

Probing atomic structure and Majorana wavefunctions in mono-atomic Fe chains on superconducting Pb surface

AbstractMotivated by the striking promise of quantum computation, Majorana bound states (MBSs) in solid-state systems have attracted wide attention in recent years. In particular, the wavefunction localisation of MBSs is a key feature and is crucial for their future implementation as qubits. Here we investigate the spatial and electronic characteristics of topological superconducting chains of iron atoms on the surface of Pb(110) by combining scanning tunnelling microscopy and atomic force microscopy. We demonstrate that the Fe chains are mono-atomic, structured in a linear manner and exhibit zero-bias conductance peaks at their ends, which we interpret as signature for a MBS. Spatially resolved conductance maps of the atomic chains reveal that the MBSs are well localised at the chain ends (≲25 nm), with two localisation lengths as predicted by theory. Our observation lends strong support to use MBSs in Fe chains as qubits for quantum-computing devices.

Electronic and magnetic properties of spiral spin-density-wave states in transition-metal chains

The electronic and magnetic properties of one-dimensional (1D) $3d$ transition-metal nanowires are investigated in the framework of density functional theory. The relative stability of collinear and noncollinear (NC) ground-state magnetic orders in V, Mn, and Fe monoatomic chains is quantified by computing the frozen-magnon dispersion relation $\mathrm{\ensuremath{\Delta}}E(\stackrel{P\vec}{q})$ as a function of the spin-density-wave vector $\stackrel{P\vec}{q}$. The dependence on the local environment of the atoms is analyzed by varying systematically the lattice parameter $a$ of the chains. Electron correlation effects are explored by comparing local spin-density and generalized-gradient approximations to the exchange and correlation functional. Results are given for $\mathrm{\ensuremath{\Delta}}E(\stackrel{P\vec}{q})$, the local magnetic moments ${\stackrel{P\vec}{\ensuremath{\mu}}}_{i}$ at atom $i$, the magnetization-vector density $\stackrel{P\vec}{m}(\stackrel{P\vec}{r})$, and the local electronic density of states ${\ensuremath{\rho}}_{i\ensuremath{\sigma}}(\ensuremath{\varepsilon})$. The frozen-magnon dispersion relations are analyzed from a local perspective. Effective exchange interactions ${J}_{ij}$ between the local magnetic moments ${\stackrel{P\vec}{\ensuremath{\mu}}}_{i}$ and ${\stackrel{P\vec}{\ensuremath{\mu}}}_{j}$ are derived by fitting the ab initio $\mathrm{\ensuremath{\Delta}}E(\stackrel{P\vec}{q})$ to a classical 1D Heisenberg model. The dominant competing interactions ${J}_{ij}$ at the origin of the NC magnetic order are identified. The interplay between the various ${J}_{ij}$ is revealed as a function of $a$ in the framework of the corresponding magnetic phase diagrams.

Electronic energy-band structures of covalent atomic and partly ion wires A N B8–N

The thinnest nanowires represent chains with one atom in cross section. The energy-band structures of ANB8–N chains are calculated using the linear augmented cylindrical wave method. The energy-band structures of covalent monoatomic chains of the fourth group elements are characterized by the σ(s), π+, and π– bands, as well as the σ(pz)* band. The chains of C, Si, Ge, and Sn are the metallic ones. Owing to the cylindrical symmetry of the chains, the spin and the orbital motion of electrons interact in the chains, splitting the π bands, but each π+- and π– band is doubly degenerate on the spin. The energy of spin–orbit splitting varies from 1.7 meV to 0.67 eV for the C and Sn chains, respectively.

Nonlinear Phonon Modes in Second-Order Anharmonic Coupled Monoatomic Chains

We have used multiple-time-scales perturbation theory as well as the numerical methods of molecular dynamics and spectral energy density (SED) to investigate the phonon band structure of a two-chain model with second-order anharmonic interactions. We show that when one chain is linear and the other is nonlinear, the two-chain model exhibits a nonlinear resonance near a critical wave number due to mode self-interaction. The nonlinear resonance enables wave number-dependent interband energy transfer. We have also shown that there exist nonlinear modes within the spectral gap separating the lower and upper branches of the phonon band structure. These modes result from three phonon interactions between a phonon belonging to the nonlinear branch and two phonons lying on the lower branch. This phenomenon offers a mechanism for phonon splitting.

Size Dependent Heat Conduction in One-Dimensional Diatomic Lattices

We study the size dependency of heat conduction in one-dimensional diatomic FPU-β lattices and establish that for low dimensional material, contribution from optical phonons is found more effective to the thermal conductivity and enhance heat transport in the thermodynamic limit N → ∞. For the finite size, thermal conductivity of 1D diatomic lattice is found to be lower than 1D monoatomic chain of the same size made up of the constituent particle of the diatomic chain. For the present 1D diatomic chain, obtained value of power divergent exponent of thermal conductivity 0.428±0.001 and diffusion exponent 1.2723 lead to the conclusions that increase in the system size, increases the thermal conductivity and existence of anomalous energy diffusion. Existing numerical data supports our findings.