Dynamical studies of periodic and disordered systems

The time evolution of two classes of systems is studied with real time molecular dynamics simulations. The first consists of a coupled electron-lattice system. For a periodic system, we present results for the time evolution of a one-dimensional system consisting of an electron, described by a tight-binding Hamiltonian, and a harmonic lattice, coupled by a deformation-type potential. We solve numerically the nonlinear system of equations of motion for this model in order to study the effects of varying the electronic effective mass for several initial conditions and coupling strengths. A large effective mass favors localized polaron formation for initially localized electrons. For initially extended electronic states, increasing the effective mass of an electron initially close to the bottom of the band makes localization more difficult, while for an initially highly excited electron, localized polaron formation is possible only when the electronic effective mass and the atomic masses of the lattice become of the same order. For a small parameter range, we find an impressive recurrence, a periodic and a complete exchange between the electronic and vibrational degrees of freedom of a small part of the initial electronic energy. The disordered case, described by a tight-binding model exhibiting metal-insulator transition (the diagonal matrix elements having a spatial variation incommensurate with the lattice), demonstrates the combined effects of disorder and electron-phonon interaction. The el-ph interaction has profound effects, especially on one-electron extended states just above the mobility edge, where the electronic states change from extended to localized. Polaron formation is facilitated close to the mobility edge and, in most cases, the localization length (lc) decreases upon increasing the disorder or el-ph coupling, as expected. However, for strongly localized states due to disorder or el-ph interaction, increase of el-ph coupling or disorder, respectively, results in an increase of lc. This increase is due to phonon assisted hopping. The second class of systems studied consists of carbon and hydrogen. We calculate phonon anharmonic effects in diamond and graphite using a tight-binding molecular dynamics scheme. Using one-phonon spectral intensities that have been calculated through the Fourier transform of the velocity-velocity correlation function, we study the temperature dependence of the phonon frequency shift and phonon linewidth. In the case of the zone-center optical mode of diamond where experimental data are available, our results are in good agreement with experiment. A tight-binding model for carbon-hydrogen interaction is developed and used in molecular dynamics simulations. The parameters are obtained by fitting to the electronic and vibrational properties of methane. The results obtained for hydrocarbon molecules are in good agreement with experimental data and first-principles results. Interstitial hydrogen in diamond is also studied with this model and the results are compared with available experimental and ab initio results. The case of hydrogenated amorphous carbon is considered as well

Softening of ultra-nanocrystalline diamond at low grain sizes

Ultra-nanocrystalline diamond is a polycrystalline material, having crystalline diamond grains of sizes in the nanometer regime. We study the structure and mechanical properties of this material as a function of the average grain size, employing atomistic simulations. From the calculated elastic constants and the estimated hardness, we observe softening of the material as the size of its grains decreases. We attribute the observed softening to the enhanced fraction of interfacial atoms as the average grain size becomes smaller. We provide a fitting formula for the scaling of the cohesive energy and bulk modulus with respect to the average grain size. We find that they both scale as quadratic polynomials of the inverse grain size. Our formulae yield correct values for bulk diamond in the limit of large grain sizes.Comment: 5 pages, 3 figures, to be published in Acta Materiali

Standing wave instabilities in a chain of nonlinear coupled oscillators

We consider existence and stability properties of nonlinear spatially periodic or quasiperiodic standing waves (SWs) in one-dimensional lattices of coupled anharmonic oscillators. Specifically, we consider Klein-Gordon (KG) chains with either soft (e.g., Morse) or hard (e.g., quartic) on-site potentials, as well as discrete nonlinear Schroedinger (DNLS) chains approximating the small-amplitude dynamics of KG chains with weak inter-site coupling. The SWs are constructed as exact time-periodic multibreather solutions from the anticontinuous limit of uncoupled oscillators. In the validity regime of the DNLS approximation these solutions can be continued into the linear phonon band, where they merge into standard harmonic SWs. For SWs with incommensurate wave vectors, this continuation is associated with an inverse transition by breaking of analyticity. When the DNLS approximation is not valid, the continuation may be interrupted by bifurcations associated with resonances with higher harmonics of the SW. Concerning the stability, we identify one class of SWs which are always linearly stable close to the anticontinuous limit. However, approaching the linear limit all SWs with nontrivial wave vectors become unstable through oscillatory instabilities, persisting for arbitrarily small amplitudes in infinite lattices. Investigating the dynamics resulting from these instabilities, we find two qualitatively different regimes for wave vectors smaller than or larger than pi/2, respectively. In one regime persisting breathers are found, while in the other regime the system rapidly thermalizes.Comment: 57 pages, 21 figures, to be published in Physica D. Revised version: Figs. 5 and 12 (f) replaced, some new results added to Sec. 5, Sec.7 (Conclusions) extended, 3 references adde

Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices

In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of analyticity versus wave amplitude is observed. As a consequence of the discreteness, oscillatory linear instabilities, persisting for arbitrarily small amplitude in infinite lattices, appear for all wave numbers Q not equal to zero or \pi. Incommensurate analytic SWs with |Q|>\pi/2 may however appear as 'quasi-stable', as their instability growth rate is of higher order.Comment: 4 pages, 6 figures, to appear in Phys. Rev. Let

All-optical header processing in a 42.6Gb/s optoelectronic firewall

A novel architecture to enable future network security systems to provide effective protection in the context of continued traffic growth and the need to minimise energy consumption is proposed. It makes use of an all-optical pre-filtering stage operating at the line rate under software control to distribute incoming packets to specialised electronic processors. An experimental system that integrates software controls and electronic interfaces with an all-optical pattern recognition system has demonstrated the key functions required by the new architecture. As an example, the ability to sort packets arriving in a 42.6Gb/s data stream according to their service type was shown experimentally

Dynamical studies of periodic and disordered systems

The time evolution of two classes of systems is studied with real time molecular dynamics simulations. The first consists of a coupled electron-lattice system. For a periodic system, we present results for the time evolution of a one-dimensional system consisting of an electron, described by a tight-binding Hamiltonian, and a harmonic lattice, coupled by a deformation-type potential. We solve numerically the nonlinear system of equations of motion for this model in order to study the effects of varying the electronic effective mass for several initial conditions and coupling strengths. A large effective mass favors localized polaron formation for initially localized electrons. For initially extended electronic states, increasing the effective mass of an electron initially close to the bottom of the band makes localization more difficult, while for an initially highly excited electron, localized polaron formation is possible only when the electronic effective mass and the atomic masses of the lattice become of the same order. For a small parameter range, we find an impressive recurrence, a periodic and a complete exchange between the electronic and vibrational degrees of freedom of a small part of the initial electronic energy. The disordered case, described by a tight-binding model exhibiting metal-insulator transition (the diagonal matrix elements having a spatial variation incommensurate with the lattice), demonstrates the combined effects of disorder and electron-phonon interaction. The el-ph interaction has profound effects, especially on one-electron extended states just above the mobility edge, where the electronic states change from extended to localized. Polaron formation is facilitated close to the mobility edge and, in most cases, the localization length (lc) decreases upon increasing the disorder or el-ph coupling, as expected. However, for strongly localized states due to disorder or el-ph interaction, increase of el-ph coupling or disorder, respectively, results in an increase of lc. This increase is due to phonon assisted hopping. The second class of systems studied consists of carbon and hydrogen. We calculate phonon anharmonic effects in diamond and graphite using a tight-binding molecular dynamics scheme. Using one-phonon spectral intensities that have been calculated through the Fourier transform of the velocity-velocity correlation function, we study the temperature dependence of the phonon frequency shift and phonon linewidth. In the case of the zone-center optical mode of diamond where experimental data are available, our results are in good agreement with experiment. A tight-binding model for carbon-hydrogen interaction is developed and used in molecular dynamics simulations. The parameters are obtained by fitting to the electronic and vibrational properties of methane. The results obtained for hydrocarbon molecules are in good agreement with experimental data and first-principles results. Interstitial hydrogen in diamond is also studied with this model and the results are compared with available experimental and ab initio results. The case of hydrogenated amorphous carbon is considered as well.</p

Shape-Dependent Single-Electron Levels for Au Nanoparticles

The shape of metal nanoparticles has a crucial role in their performance in heterogeneous catalysis as well as photocatalysis. We propose a method of determining the shape of nanoparticles based on measurements of single-electron quantum levels. We first consider nanoparticles in two shapes of high symmetry: cube and sphere. We then focus on Au nanoparticles in three characteristic shapes that can be found in metal/inorganic or metal/organic compounds routinely used in catalysis and photocatalysis. We describe the methodology we use to solve the Schrödinger equation for arbitrary nanoparticle shape. The method gives results that agree well with analytical solutions for the high-symmetry shapes. When we apply our method in realistic gold nanoparticle models, which are obtained from Wulff construction based on first principles calculations, the single-electron levels and their density of states exhibit distinct shape-dependent features. Results for clean-surface nanoparticles are closer to those for cubic particles, while CO-covered nanoparticles have energy levels close to those of a sphere. Thiolate-covered nanoparticles with multifaceted polyhedral shape have distinct levels that are in between those for sphere and cube. We discuss how shape-dependent electronic structure features could be identified in experiments and thus guide catalyst design

Electronic and optical properties of a-c from tight-binding molecular dynamics simulations

Although the structural and mechanical properties of a-C have been theoretically investigated in detail, this is not so for the optoelectronic properties. Many issues remain unclear, such as the influence of disorder and intrinsic defects on the localization of the electron states and on the optical transitions. Here, as a first step towards solving this kind of problems, we present a computational approach to the study of the optoelectronic properties of a-C. This is based on tight-binding (TB) molecular dynamics (TBMD) simulations using a reliable environment-dependent Hamiltonian. The a-C networks were generated by quenching from the liquid. The electronic density of states of all simulated networks show that the material is semiconducting, and that the gap is clearly controlled by the separation of the π and π* peaks. A Tauc gap analysis shows that the optical gap varies between 2.7 and 0.3 eV. We analyze the dielectric functions as a function of the sp3 fraction. We also compare the computational results with experimental dielectric function spectra revealing considerable consistency between theory and experiment

Physical trends in amorphous carbon: a tight-binding molecular-dynamics study

Tight-binding molecular dynamics simulations reveal interesting physical trends in amorphous carbon networks. The variation of sp3 fraction, or mean coordination, is found to be linear over the whole possible range of densities. The density at the floppy transition is ∼0.5 g cm-3, while the density of "amorphous diamond" is ∼3.3 g cm -3. The bulk modulus vanishes at the floppy transition, having a critical coordination near 2.4, and its variation with the mean coordination has a scaling exponent of 1.5, confirming the constraint-counting model of Phillips and Thorpe. A hypothetical fully tetrahedral network has a bulk modulus of 360 GPa, about 15% lower than diamond's. The bulk modulus is also found to vary with the average bond length d̄ as (d̄)35. The homopolar gap of "amorphous diamond" is ∼11.5 eV, compared to ∼14 eV for diamond