Phonon Localization in One-Dimensional Quasiperiodic Chains

Quasiperiodic long range order is intermediate between spatial periodicity and disorder, and the excitations in 1D quasiperiodic systems are believed to be transitional between extended and localized. These ideas are tested with a numerical analysis of two incommensurate 1D elastic chains: Frenkel-Kontorova (FK) and Lennard-Jones (LJ). The ground state configurations and the eigenfrequencies and eigenfunctions for harmonic excitations are determined. Aubry's "transition by breaking the analyticity" is observed in the ground state of each model, but the behavior of the excitations is qualitatively different. Phonon localization is observed for some modes in the LJ chain on both sides of the transition. The localization phenomenon apparently is decoupled from the distribution of eigenfrequencies since the spectrum changes from continuous to Cantor-set-like when the interaction parameters are varied to cross the analyticity--breaking transition. The eigenfunctions of the FK chain satisfy the "quasi-Bloch" theorem below the transition, but not above it, while only a subset of the eigenfunctions of the LJ chain satisfy the theorem.Comment: This is a revised version to appear in Physical Review B; includes additional and necessary clarifications and comments. 7 pages; requires revtex.sty v3.0, epsf.sty; includes 6 EPS figures. Postscript version also available at http://lifshitz.physics.wisc.edu/www/koltenbah/koltenbah_homepage.htm

Atomistic simulations of self-trapped exciton formation in silicon nanostructures: The transition from quantum dots to nanowires

Using an approximate time-dependent density functional theory method, we calculate the absorption and luminescence spectra for hydrogen passivated silicon nanoscale structures with large aspect ratio. The effect of electron confinement in axial and radial directions is systematically investigated. Excited state relaxation leads to significant Stokes shifts for short nanorods with lengths less than 2 nm, but has little effect on the luminescence intensity. The formation of self-trapped excitons is likewise observed for short nanostructures only; longer wires exhibit fully delocalized excitons with neglible geometrical distortion at the excited state minimum.Comment: 10 pages, 4 figure

A comparative ab initio study of the Si2_2C4_4, Si3_3C3_3, Si4_4C2_2 clusters

Various structural possibilities for the Si$_2$C$_4$ and Si$_4$C$_2$ clusters are investigated by employing a basis set of triple-zeta plus polarization quality; electron correlation is generally accounted for by second-order M0ller-Plesset and, in certain instances, by higher-order perturbation (CASPT2) approaches. The building-up principle recently suggested from an analysis of Si$_3$C$_3$ clusters is found to be fully operative for Si$_2$C$_4$ and Si$_4$C$_2$ clusters. A comparison of the structure and stability of various geometrical arrangements in the series C$_6$ , Si$_2$C$_4$ , Si$_3$C$_3$ , Si$_4$C$_2$, and Si$_6$ shows that linear and planar structures become rapidly less stable if carbons are replaced by silicons and that the three-dimensional bipyramidal forms become less favorable as soon as silicons are exchanged by carbons in the parent Si$_6$ structure. The effects can be rationalized in qualitative terms based on differences in silicon and carbon bonding

Structural and static electric response properties of highly symmetric lithiated silicon cages: Theoretical predictions

cited By 16International audienceIt is shown by density functional theory calculations that high symmetry silicon cages can be designed by coating with Li atoms. The resulting highly symmetric lithiated silicon cages (up to D 5d symmetry) are low-lying true minima of the energy hypersurface with binding energies of the order of 4.6 eV per Si atom and moderate highest occupied molecular orbital-lowest unoccupied molecular orbital gaps. Moreover, relying on a systematic study of the electric response properties obtained by ab initio (Hartree-Fock, MP2, and configuration interaction singles (CIS)) and density functional (B3LYP, B2PLYP, and CAM-B3LYP) methods, it is shown that lithium coating has a large impact on the magnitude of their second hyperpolarizabilities resulting to highly hyperpolarizable species. Such hyperpolarizable character is directly connected to the increase in the density of the low-lying excited states triggered by the interaction between the Si cage and the surrounding Li atoms. Copyright © 2012 Wiley Periodicals, Inc