PT−{\cal PT}-Symmetric Dimers with Time-Periodic Gain/Loss Function

${\mathcal PT}-$symmetric dimers with a time-periodic gain/loss function in a balanced configuration where the amount of gain equals that of loss are investigated analytically and numerically. Two prototypical dimers in the linear regime are investigated: a system of coupled classical oscillators, and a Schr\"{o}dinger dimer representing the coupling of field amplitudes; each system representing a wide class of physical models. Through a thorough analysis of their stability behaviour, we find that turning on the coupling parameter in the classical dimer system, leads initially to decreased stability but then to re-entrant transitions from the exact to the broken ${\mathcal PT}-$phase and vice versa, as it is increased beyond a critical value. On the other hand, the Schr\"{o}dinger dimer behaves more like a single oscillator with time-periodic gain/loss. In addition, we are able to identify the conditions under which the behaviour of the two dimer systems coincides and/or reduces to that of a single oscillator.Comment: 9 pages, 9 figures, META14 Conference, subm. Special Issue Appl. Phys.

Electron-electron interaction effects on the photophysics of metallic single-walled carbon nanotubes

Single-walled carbon nanotubes are strongly correlated systems with large Coulomb repulsion between two electrons occupying the same $p_z$ orbital. Within a molecular Hamiltonian appropriate for correlated $\pi$-electron systems, we show that optical excitations polarized parallel to the nanotube axes in the so-called metallic single-walled carbon nanotubes are to excitons. Our calculated absolute exciton energies in twelve different metallic single-walled carbon nanotubes, with diameters in the range 0.8 - 1.4 nm, are in nearly quantitative agreement with experimental results. We have also calculated the absorption spectrum for the (21,21) single-walled carbon nanotube in the E$_{22}$ region. Our calculated spectrum gives an excellent fit to the experimental absorption spectrum. In all cases our calculated exciton binding energies are only slightly smaller than those of semiconducting nanotubes with comparable diameters, in contradiction to results obtained within the {\it ab initio} approach, which predicts much smaller binding energies. We ascribe this difference to the difficulty of determining the behavior of systems with strong on-site Coulomb interactions within theories based on the density functional approach. As in the semiconducting nanotubes we predict in the metallic nanotubes a two-photon exciton above the lowest longitudinally polarized exciton that can be detected by ultrafast pump-probe spectroscopy. We also predict a subgap absorption polarized perpendicular to the nanotube axes below the lowest longitudinal exciton, blueshifted from the exact midgap by electron-electron interactions

Indium clusters on the Ge(5x5) wetting layer of Si(111)-7x7

The adsorption of In on the Si(111)−Ge(5×5) surface reconstruction has been studied with scanning tunneling microscopy and ab initio calculations to investigate the possibility of using this reconstruction as a template for cluster formation. As with In adsorption on Si(111)−7×7 at low substrate temperatures and low In fluences, the In adatoms are found to preferentially adsorb on the faulted half-unit cell. However, in contrast to In adsorption on Si(111)−7×7, the In adatoms are also frequently found in the unfaulted half-unit cell at low coverages. The filling of unfaulted unit cell halves is primarily due to the formation of large clusters that span multiple substrate half-unit cells. Moreover, many of the faulted half-unit cells have a streaked appearance that indicates that surface atoms within them are mobile

Patterned growth of nanoscale in clusters on the Si(111)-7x7 and Si(111)-ge(5x5) reconstructions

Results of a study designed to investigate the possibility of using the Si(111)- Ge(5×5) surface reconstruction as a template for In cluster growth are described. As with Si(111)-7×7, the In adatoms preferentially adsorb in the faulted half-unit cell, but on Si(111)- Ge(5×5) a richer variety of cluster geometries are found. In addition to the clusters that occupy the faulted half-unit cell, clusters that span two and four half-unit cells are found. The latter have a triangular shape spanning one unfaulted and three, nearest neighbor, faulted half-unit cells, Triangular clusters in the opposite orientation were not found. Many of the faulted halfunit cells have a streaked appearance consistent with adatom mobility