Alexander V. Savin

Suppression of thermal conductivity in graphene nanoribbons with rough edges

We analyze numerically thermal conductivity of graphene nanoribbons with perfect and rough edges. We demonstrate that edge roughness can suppress thermal conductivity by two orders of magnitude. This effect is associated with the edge-induced energy localization and suppression of the phonon transport, and it becomes more pronounced for longer nanoribbons and low temperatures.

Nonlinear dynamics of topological solitons in DNA

Dynamics of topological solitons describing open states in the DNA double helix are studied in the framework of a model that takes into account asymmetry of the helix. It is shown that three types of topological solitons can occur in the DNA double chain. Interaction between the solitons, their interactions with the chain inhomogeneities, and stability of the solitons with respect to thermal oscillations are investigated.

Vibrational Tamm states at the edges of grapheme nanoribbons

We study vibrational states localized at the edges of graphene nanoribbons. Such surface oscillations can be considered as a phonon analog of Tamm states in the electronic theory. We consider both armchair and zigzag graphene stripes and demonstrate that surface modes correspond to phonons localized at the edges of the graphene nanoribbon, and they can be classified as in-plane and out-of-plane modes. In armchair nanoribbons anharmonic edge modes can experience longitudinal localization in the form of self-localized nonlinear modes or surface breather solitons.

Discrete breather on the edge of the graphene sheet with the armchair orientation

Linear and nonlinear vibrations of a graphene nanoribbon with free armchair edges subjected to tensile deformation have been studied by atomistic simulation methods. It has been shown that the phonon modes are split into two subsets. Atoms in some (XY) modes vibrate in the nanoribbon plane and in other (Z) modes vibrate along the normal to this plane. The possibility of the excitation of a gap discrete breather in an extended nanoribbon in the spectrum of the Z modes, the frequency of which lies in the gap of the spectrum of the XY modes, has been demonstrated. This breather is a large-amplitude vibrational mode in the XY plane localized on the four atoms on the nanoribbon edge. The breather is unstable with respect to small perturbations in the form of displacements of atoms out of the nanoribbon plane. Nevertheless, the discrete breather decays slowly owing to its weak interaction with the Z modes, so that its lifetime can be on the order of 103 vibrational periods.

Heat conduction in one-dimensional lattices with on-site potential

The process of heat conduction in one-dimensional lattices with on-site potential is studied by means of numerical simulation. Using the discrete Frenkel-Kontorova, phi(4), and sinh-Gordon models we demonstrate that contrary to previously expressed opinions the sole anharmonicity of the on-site potential is insufficient to ensure the normal heat conductivity in these systems. The character of the heat conduction is determined by the spectrum of nonlinear excitations peculiar for every given model and therefore depends on the concrete potential shape and the temperature of the lattice. The reason is that the peculiarities of the nonlinear excitations and their interactions prescribe the energy scattering mechanism in each model. For sine-Gordon and phi(4) models, phonons are scattered at a dynamical lattice of topological solitons; for sinh-Gordon and for phi(4) in a different parameter regime the phonons are scattered at localized high-frequency breathers (in the case of phi(4) the scattering mechanism switches with the growth of the temperature).

Surface solitons at the edges of graphene nanoribbons

We demonstrate numerically that armchair graphene nanoribbons can support vibrational localized states in the form of surface solitons. Such localized states appear through self-localization of the vibrational energy along the edge of the graphene nanoribbon, and they decay rapidly inside the structure. We find five types of such solitary waves including in-plane and out-of-plane edge breathers and moving envelope solitons.

Semiquantum molecular dynamics simulation of thermal properties and heat transport in low-dimensional nanostructures

We present a detailed description of the semi-quantum approach to the molecular dynamics simulation of stochastic dynamics of a system of interacting particles. Within this approach, the dynamics of the system is described with the use of classical Newtonian equations of motion in which the quantum effects are introduced through random Langevin-like forces with a specific power spectral density (the color noise). The color noise describes the interaction of the molecular system with the thermostat. We apply this technique to the simulation of the thermal properties of different low-dimensional nanostructures. Within this approach, we simulate the specific heat and heat transport in carbon nanotubes, as well as the thermal transport in a molecular nanoribbon with rough edges and in a nanoribbon with a strongly anharmonic periodic interatomic potential. We show that the existence of rough edges and quantum statistics of phonons change drastically the thermal conductivity of the rough-edge nanoribbon in comparison with that of the nanoribbon with ideal (atomically smooth) edges and classical dynamics. We show how the combination of strong nonlinearity of the interatomic potentials with quantum statistics of phonons changes the low-temperature thermal conductivity of the nanoribbon with periodic interatomic potentials. Molecular dynamics is a method of numerical modeling of molecular systems based on classical Newtonian mechanics. It does not allow for the description of pure quantum effects such as freezing out of high-frequency oscillations at low temperatures and the related decrease to zero of heat capacity for T → 0. In classical molecular dynamics, each dynamical degree of freedom possesses the same energy kBT, where kB is Boltzmann constant. Therefore, in classical statistics the specific heat of a solid almost does not depend on temperature when only relatively small changes, caused the anharmonicity of the potential, can be taken into account [1]). On the other hand, because of its complexity, a pure quantum-mechanical description does not allow in general the detailed modeling of the dynamics of many-body systems. To overcome these obstacles, different semiclassical methods, which allow to take into an account quantum effects in the dynamics of molecular systems, have been proposed [2–8]. The most convenient for the numerical modeling is the use of the Langevin equations with color-noise random forces [5, 7]. In this approximation, the dynamics of the system is described with the use of classical Newtonian equations of motion, while the quantum effects are introduced through random Langevin-like forces with a specific power spectral density (color noise), which describe the interaction of the molecular system with the thermostat. Below we give a detailed description of this semi-quantum approach, in application to the simulation of specific heat and heat transport in different low-dimensional nanostructures.

Discrete breathers in carbon nanotubes

We study large-amplitude oscillations of carbon nanotubes with chiralities (m, 0) and (m, m) and predict the existence of spatially localized nonlinear modes in the form of discrete breathers. In nanotubes with the index (m, 0) we find three types of discrete breathers associate with longitudinal, radial, and torsion anharmonic vibrations, however only the twisting breathers are found to be nonradiating nonlinear modes which survive in a curved geometry described by a three-dimensional microscopic model and remain long-lived modes even in the presence of thermal fluctuations.

Stability range for a flat graphene sheet subjected to in-plane deformation

The effects of the elastic deformation on the mechanical and physical properties of graphene are a subject of intensive current studies. Nevertheless, the stability range for a flat graphene sheet subjected to in-plane deformation is still unknown. Here, this problem is solved by atomistic simulations. In the three-dimensional space corresponding to the ɛxx, ɛyy, and ɛxy components of the planar strain tensor, the surface bounding the stability range for a flat graphene sheet has been constructed disregarding the thermal vibrations and the effects of boundary conditions. For the points of this surface, force components Tx, Ty, and Txy have been calculated. It is shown that graphene is structurally stable up to strains on the order of 0.3–0.4, but it is unstable with respect to the shear in the absence of stretching forces. In addition, graphene cannot preserve its flat shape under the effect of a compressive force since it has zero flexural stiffness.

Two-phase stretching of molecular chains

Although stretching of most polymer chains leads to rather featureless force-extension diagrams, some, notably DNA, exhibit nontrivial behavior with a distinct plateau region. Here, we propose a unified theory that connects force-extension characteristics of the polymer chain with the convexity properties of the extension energy profile of its individual monomer subunits. Namely, if the effective monomer deformation energy as a function of its extension has a nonconvex (concave up) region, the stretched polymer chain separates into two phases: the weakly and strongly stretched monomers. Simplified planar and 3D polymer models are used to illustrate the basic principles of the proposed model. Specifically, we show rigorously that, when the secondary structure of a polymer is mostly caused by weak noncovalent interactions, the stretching is two phase, and the force-stretching diagram has the characteristic plateau. We then use realistic coarse-grained models to confirm the main findings and make direct connection to the microscopic structure of the monomers. We show in detail how the two-phase scenario is realized in the α-helix and DNA double helix. The predicted plateau parameters are consistent with single-molecules experiments. Detailed analysis of DNA stretching shows that breaking of Watson–Crick bonds is not necessary for the existence of the plateau, although some of the bonds do break as the double helix extends at room temperature. The main strengths of the proposed theory are its generality and direct microscopic connection.