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 $m_{1-x} M_x$ 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 $0.5<x<0.7$, 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 $^{13}{\rm C}$-enriched carbon sublattice. \cite{Rohmfeld00,Rohmfeld01}Comment: 29 pages, 9 figures, 2 tables, submitted to PR

The structural properties of the multi-layer graphene/4H-SiC(000-1) system as determined by Surface X-ray Diffraction

We present a structural analysis of the multi-layer graphene-4HSiC(000-1}) system using Surface X-Ray Reflectivity. We show for the first time that graphene films grown on the C-terminated (000-1}) surface have a graphene-substrate bond length that is very short (0.162nm). The measured distance rules out a weak Van der Waals interaction to the substrate and instead indicates a strong bond between the first graphene layer and the bulk as predicted by ab-initio calculations. The measurements also indicate that multi-layer graphene grows in a near turbostratic mode on this surface. This result may explain the lack of a broken graphene symmetry inferred from conduction measurements on this system [C. Berger et al., Science 312, 1191 (2006)].Comment: 9 pages with 6 figure

The Computational Complexity of Knot and Link Problems

We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted, capable of being continuously deformed without self-intersection so that it lies in a plane. We show that this problem, {\sc unknotting problem} is in {\bf NP}. We also consider the problem, {\sc unknotting problem} of determining whether two or more such polygons can be split, or continuously deformed without self-intersection so that they occupy both sides of a plane without intersecting it. We show that it also is in NP. Finally, we show that the problem of determining the genus of a polygonal knot (a generalization of the problem of determining whether it is unknotted) is in {\bf PSPACE}. We also give exponential worst-case running time bounds for deterministic algorithms to solve each of these problems. These algorithms are based on the use of normal surfaces and decision procedures due to W. Haken, with recent extensions by W. Jaco and J. L. Tollefson.Comment: 32 pages, 1 figur

Raman spectra of epitaxial graphene on SiC and of epitaxial graphene transferred to SiO2

Raman spectra were measured for mono-, bi- and trilayer graphene grown on SiC by solid state graphitization, whereby the number of layers was pre-assigned by angle-resolved ultraviolet photoemission spectroscopy. It was found that the only unambiguous fingerprint in Raman spectroscopy to identify the number of layers for graphene on SiC(0001) is the linewidth of the 2D (or D*) peak. The Raman spectra of epitaxial graphene show significant differences as compared to micromechanically cleaved graphene obtained from highly oriented pyrolytic graphite crystals. The G peak is found to be blue-shifted. The 2D peak does not exhibit any obvious shoulder structures but it is much broader and almost resembles a single-peak even for multilayers. Flakes of epitaxial graphene were transferred from SiC onto SiO2 for further Raman studies. A comparison of the Raman data obtained for graphene on SiC with data for epitaxial graphene transferred to SiO2 reveals that the G peak blue-shift is clearly due to the SiC substrate. The broadened 2D peak however stems from the graphene structure itself and not from the substrate.Comment: 27 pages, 8 figure

Mechanisms of Manganese-Assisted Nonradiative Recombination in Cd(Mn)Se/Zn(Mn)Se Quantum Dots

Mechanisms of nonradiative recombination of electron-hole complexes in Cd(Mn)Se/Zn(Mn)Se quantum dots accompanied by interconfigurational excitations of Mn$^{2+}$ ions are analyzed within the framework of single electron model of deep {\it 3d}-levels in semiconductors. In addition to the mechanisms caused by Coulomb and exchange interactions, which are related because of the Pauli principle, another mechanism due to {\it sp-d} mixing is considered. It is shown that the Coulomb mechanism reduces to long-range dipole-dipole energy transfer from photoexcited quantum dots to Mn$^{2+}$ ions. The recombination due to the Coulomb mechanism is allowed for any states of Mn$^{2+}$ ions and {\it e-h} complexes. In contrast, short-range exchange and ${\it sp-d}$ recombinations are subject to spin selection rules, which are the result of strong {\it lh-hh} splitting of hole states in quantum dots. Estimates show that efficiency of the {\it sp-d} mechanism can considerably exceed that of the Coulomb mechanism. The phonon-assisted recombination and processes involving upper excited states of Mn$^{2+}$ ions are studied. The increase in PL intensity of an ensemble of quantum dots in a magnetic field perpendicular to the sample growth plane observed earlier is analyzed as a possible manifestation of the spin-dependent recombination.Comment: 14 pages, 2 figure

Directed self-organization of graphene nanoribbons on SiC

Realization of post-CMOS graphene electronics requires production of semiconducting graphene, which has been a labor-intensive process. We present tailoring of silicon carbide crystals via conventional photolithography and microelectronics processing to enable templated graphene growth on 4H-SiC{1-10n} (n = 8) crystal facets rather than the customary {0001} planes. This allows self-organized growth of graphene nanoribbons with dimensions defined by those of the facet. Preferential growth is confirmed by Raman spectroscopy and high-resolution transmission electron microscopy (HRTEM) measurements, and electrical characterization of prototypic graphene devices is presented. Fabrication of > 10,000 top-gated graphene transistors on a 0.24 cm2 SiC chip demonstrates scalability of this process and represents the highest density of graphene devices reported to date.Comment: 13 pages, 5 figure

Editorial: The Mammary Stroma in Normal Development and Function

The mammary gland can no longer be simply viewed as an organ composed of epithelial cells within a passive stromal microenvironment. Many lines of evidence have evolved to reinforce the notion that mammary epithelial cell growth, differentiation, lactation and progression to cancer involves bidirectional interactions between the epithelial population and its surrounding stroma. Within this stroma are numerous systems that are all capable of modulating epithelial function. In this context, the mammary stroma is not simply a depot of adipose tissue in which mammary epithelial cells undertake a unique growth and differentiation process, although adipocytes can impart numerous modulatory signals to epithelial cells, and vice versa. Rather, the stromal environment constitutes and supports a critical vasculature that supplies nutrients and endocrine cues, a lymphatic system that not only removes metabolites but also provides an intimate interface with the immune system, and an extracellular matrix scaffold in which epithelial cells grow, differentiate and regress. Ultimately all of these components play a critical role in directing the epithelial phenotype during normal mammary gland growth and function. An increasing appreciation for these different systems demands a view of mammary epithelial cells in a much different light, and further necessitates the development of model systems that incorporate and integrate increasing complexity

Electronic structure and the minimum conductance of a graphene layer on SiO2 from density-functional methods.

The effect of the SiO$_2$ substrate on a graphene film is investigated using realistic but computationally convenient energy-optimized models of the substrate supporting a layer of graphene. The electronic bands are calculated using density-functional methods for several model substrates. This provides an estimate of the substrate-charge effects on the behaviour of the bands near $E_F$, as well as a variation of the equilibrium distance of the graphene sheet. A model of a wavy graphene layer is examined as a possible candidate for understanding the nature of the minimally conducting states in graphene.Comment: 6 pages, 5 figure

The Optical Design and Characterization of the Microwave Anisotropy Probe

The primary goal of the MAP satellite, now in orbit, is to make high fidelity polarization sensitive maps of the full sky in five frequency bands between 20 and 100 GHz. From these maps we will characterize the properties of the cosmic microwave background (CMB) anisotropy and Galactic and extragalactic emission on angular scales ranging from the effective beam size, <0.23 degree, to the full sky. MAP is a differential microwave radiometer. Two back-to-back shaped offset Gregorian telescopes feed two mirror symmetric arrays of ten corrugated feeds. We describe the prelaunch design and characterization of the optical system, compare the optical models to the measurements, and consider multiple possible sources of systematic error.Comment: ApJ in press; 22 pages with 11 low resolution figures; paper is available with higher quality figures at http://map.gsfc.nasa.gov/m_mm/tp_links.htm