Magnetic edge-state excitons in zigzag graphene nanoribbons

We present first-principles calculations of the optical properties of zigzag-edged graphene nanoribbons (ZGNRs) employing the GW-Bethe-Salpeter equation approach with the spin interaction included. Optical response of the ZGNRs is found to be dominated by magnetic edge-state-derived excitons with large binding energy. The absorption spectrum is composed of a characteristic series of exciton states, providing a possible signature for identifying the ZGNRs. The edge-state excitons are charge-transfer excitations with the excited electron and hole located on opposite edges; they moreover induce a spin transfer across the ribbon, resulting in a photoreduction of the magnetic ordering. These novel characteristics are potentially useful in the applications.     

Valence charge distribution and electric field gradients in GaAsAlAs mixed crystals

Electric field gradients at the arsenic sites in the GaAsAlAs mixed compounds are calculated using the self-consistent pseudo-potential method. The result is in good agreement with recent nuclear quadrupole resonance (NQR) experiments and supports the interpretation that the NQR splittings arise from an Al ion relacing one of the four Ga ions near an As site.     

Dynamics of lateral modes in broad aperture injection lasers

The dynamics of optical filaments in broad aperture semiconductor lasers was studied. We use the model where one longitudinal mode is taken into account. The spectrum and the instabilities of lateral modes joined with the above mentioned longitudinal mode were investigated. The structures arise due to instability of various number of lateral modes. On the background of these modes we found a new type of modulation with a frequency depending on the laser aperture width. This frequency is smaller than the electron-photon resonance one. The existence of the modulation was confirmed by experimental investigations of broad aperture laser noise spectra.     

Diffraction from stepped surfaces: I. Reversible surfaces

In electron or atom diffraction experiments on surfaces, the angular shapes of the diffracted beams depend upon the distribution of steps over the surface. In this paper we analyze diffracted beam profiles from stepped surfaces that are reversible. A reversible surface is one in which the pair correlation function over the surface is symmetric with respect to positive and negative directions. We show that the intensity profile across a diffracted beam can be separated into a sharp central spike due to the limit of the correlation function at large separation plus wings or shoulders due to the finite extent of the step disorder. Simple functional expressions for these angular profiles are obtained by a Markov method of treating a one-dimensional geometric distribution of steps. The result explicitly displays the deep structure found for the general case. The method reduces the calculation to a simple eigenvalue problem so that even the continuously changing step distributions that occur in epitaxial growth can be treated easily. As in the general case, the resulting intensity profile is a sharp central spike plus a step-broadened term which now is a sum of Lorentzians. The widths of the Lorentzians are the logarithms of the eigenvalues of the matrix of probabilities which describe the step distribution over the surface. This matrix method, which treats the surface as a Markov chain, also points the correct way to account for correlations between surface atoms for two-dimensional distributions of steps. For a two-dimensional surface one must consider a Markov Random Field as opposed to a simple multiplication of two one-dimensional results. We compare the results of the general calculation to the Si epitaxy experiments of Gronwald and Henzler. The coverage and momentum transfer dependencies of the shapes of the calculated profiles agree with their measurements. The calculation is also applied to the RHEED measurements of Van Hove et al. during GaAs MBE. The measured intensity oscillations can be accounted for by a cyclically changing one-dimensional geometric distribution of steps among three layers in which the third-layer scattering increases with time.     

A rank-three condition for invariant (1, 2)-symplectic almost Hermitian structures on flag manifolds

This paper considers invariant (1, 2)-symplectic almost Hermitian structures on the maximal flag manifod associated to a complex semi-simple Lie group G. The concept of cone-free invariant almost complex structure is introduced. It involves the rank-three subgroups of G, and generalizes the cone-free property for tournaments related to 𝕊l (n,ℂ) case. It is proved that the cone-free property is necessary for an invariant almost-complex structure to take part in an invariant (1, 2)-symplectic almost Hermitian structure. It is also sufficient if the Lie group is not B _l , l ≥ 3, G ₂ or F ₄. For B _l and F ₄ a close condition turns out to be sufficient. Received: 28 October 2001     

Hermite and Smith normal form algorithms over Dedekind domains

We show how the usual algorithms valid over Euclidean domains, such as the Hermite Normal Form, the modular Hermite Normal Form and the Smith Normal Form can be extended to Dedekind rings. In a sequel to this paper, we will explain the use of these algorithms for computing in relative extensions of number fields.