13 research outputs found
Disorder-induced phonon self-energy of semiconductors with binary isotopic composition
Self-energy effects of Raman phonons in isotopically disordered
semiconductors are deduced by perturbation theory and compared to experimental
data. In contrast to the acoustic frequency region, higher-order terms
contribute significantly to the self-energy at optical phonon frequencies. The
asymmetric dependence of the self-energy of a binary isotope system on the concentration of the heavier isotope mass x can be explained by
taking into account second- and third-order perturbation terms. For elemental
semiconductors, the maximum of the self-energy occurs at concentrations with
, depending on the strength of the third-order term. Reasonable
approximations are imposed that allow us to derive explicit expressions for the
ratio of successive perturbation terms of the real and the imaginary part of
the self-energy. This basic theoretical approach is compatible with Raman
spectroscopic results on diamond and silicon, with calculations based on the
coherent potential approximation, and with theoretical results obtained using
{\it ab initio} electronic theory. The extension of the formalism to binary
compounds, by taking into account the eigenvectors at the individual
sublattices, is straightforward. In this manner, we interpret recent
experimental results on the disorder-induced broadening of the TO (folded)
modes of SiC with a -enriched carbon sublattice.
\cite{Rohmfeld00,Rohmfeld01}Comment: 29 pages, 9 figures, 2 tables, submitted to PR
Stability of homogeneous bundles on P^3
We study the stability of some homogeneous bundles on P^3 by using their
representations of the quiver associated to the homgeneous bundles on P^3. In
particular we show that homogeneous bundles on P^3 whose support of the quiver
representation is a parallelepiped are stable, for instance the bundles E whose
minimal free resolution is of the kind 0 --> S^{l_1, l_2, l_3} V (t) --> S^{l_1
+s, l_2, l_3} V (t+s) --> E --> 0 are stable.Comment: to appear in Geometriae Dedicata
http://www.springer.com/mathematics/geometry/journal/1071