On vanishing theorems for Higgs bundles

We introduce the notion of Hermitian Higgs bundle as a natural generalization of the notion of Hermitian vector bundle and we study some vanishing theorems concerning Hermitian Higgs bundles when the base manifold is a compact complex manifold. We show that a first vanishing result, proved for these objects when the base manifold was K\"ahler, also holds when the manifold is compact complex. From this fact and some basic properties of Hermitian Higgs bundles, we conclude several results. In particular we show that, in analogy to the classical case, there are vanishing theorems for invariant sections of tensor products of Higgs bundles. Then, we prove that a Higgs bundle admits no nonzero invariant sections if there is a condition of negativity on the greatest eigenvalue of the Hitchin-Simpson mean curvature. Finally, we prove that invariant sections of certain tensor products of a weak Hermitian-Yang-Mills Higgs bundle are all parallel in the classical sense.Comment: 10 Pages, some typos corrected and minor change

Nitrate uptake across biomes and the influence of elemental stoichiometry: A new look at LINX II

Considering recent increases in anthropogenic N loading, it is essential to identify the controls on N removal and retention in aquatic ecosystems because the fate of N has consequences for water quality in streams and downstream ecosystems. Biological uptake of nitrate (NO3−) is a major pathway by which N is removed from these ecosystems. Here we used data from the second Lotic Intersite Nitrogen eXperiment (LINX II) in a multivariate analysis to identify the primary drivers of variation in NO3− uptake velocity among biomes. Across 69 study watersheds in North America, dissolved organic carbon:NO3− ratios and photosynthetically active radiation were identified as the two most important predictor variables in explaining NO3− uptake velocity. However, within a specific biome the predictor variables of NO3− uptake velocity varied and included various physical, chemical, and biological attributes. Our analysis demonstrates the broad control of elemental stoichiometry on NO3− uptake velocity as well as the importance of biome-specific predictors. Understanding this spatial variation has important implications for biome-specific watershed management and the downstream export of NO3−, as well as for development of spatially explicit global models that describe N dynamics in streams and rivers

Approximate Hermitian-Yang-Mills structures and semistability for Higgs bundles. II: Higgs sheaves and admissible structures

We study the basic properties of Higgs sheaves over compact K\"ahler manifolds and we establish some results concerning the notion of semistability; in particular, we show that any extension of semistable Higgs sheaves with equal slopes is semistable. Then, we use the flattening theorem to construct a regularization of any torsion-free Higgs sheaf and we show that it is in fact a Higgs bundle. Using this, we prove that any Hermitian metric on a regularization of a torsion-free Higgs sheaf induces an admissible structure on the Higgs sheaf. Finally, using admissible structures we proved some properties of semistable Higgs sheaves.Comment: 18 pages; some typos correcte

Electroreflectance spectroscopy in self-assembled quantum dots: lens symmetry

Modulated electroreflectance spectroscopy $\Delta R/R$ of semiconductor self-assembled quantum dots is investigated. The structure is modeled as dots with lens shape geometry and circular cross section. A microscopic description of the electroreflectance spectrum and optical response in terms of an external electric field (${\bf F}$) and lens geometry have been considered. The field and lens symmetry dependence of all experimental parameters involved in the $\Delta R/R$ spectrum have been considered. Using the effective mass formalism the energies and the electronic states as a function of ${\bf F}$ and dot parameters are calculated. Also, in the framework of the strongly confined regime general expressions for the excitonic binding energies are reported. Optical selection rules are derived in the cases of the light wave vector perpendicular and parallel to $$. Detailed calculation of the Seraphin coefficients and electroreflectance spectrum are performed for the InAs and CdSe nanostructures. Calculations show good agreement with measurements recently performed on CdSe/ZnSe when statistical distribution on size is considered, explaining the main observed characteristic in the electroreflectance spectra

Chemical Raman Enhancement of Organic Adsorbates on Metal Surfaces

Using a combination of first-principles theory and experiments, we provide a quantitative explanation for chemical contributions to surface-enhanced Raman spectroscopy for a well-studied organic molecule, benzene thiol, chemisorbed on planar Au(111) surfaces. With density functional theory calculations of the static Raman tensor, we demonstrate and quantify a strong mode-dependent modification of benzene thiol Raman spectra by Au substrates. Raman active modes with the largest enhancements result from stronger contributions from Au to their electron-vibron coupling, as quantified through a deformation potential, a well-defined property of each vibrational mode. A straightforward and general analysis is introduced that allows extraction of chemical enhancement from experiments for specific vibrational modes; measured values are in excellent agreement with our calculations.Comment: 5 pages, 4 figures and Supplementary material included as ancillary fil

Electron-phonon renormalization of the absorption edge of the cuprous halides

Compared to most tetrahedral semiconductors, the temperature dependence of the absorption edges of the cuprous halides (CuCl, CuBr, CuI) is very small. CuCl and CuBr show a small increase of the gap $E_0$ with increasing temperature, with a change in the slope of $E_0$ vs. $T$ at around 150 K: above this temperature, the variation of $E_0$ with $T$ becomes even smaller. This unusual behavior has been clarified for CuCl by measurements of the low temperature gap vs. the isotopic masses of both constituents, yielding an anomalous negative shift with increasing copper mass. Here we report the isotope effects of Cu and Br on the gap of CuBr, and that of Cu on the gap of CuI. The measured isotope effects allow us to understand the corresponding temperature dependences, which we also report, to our knowledge for the first time, in the case of CuI. These results enable us to develop a more quantitative understanding of the phenomena mentioned for the three halides, and to interpret other anomalies reported for the temperature dependence of the absorption gap in copper and silver chalcogenides; similarities to the behavior observed for the copper chalcopyrites are also pointed out.Comment: 14 pages, 5 figures, submitted to Phys. Rev.

Electronic, vibrational, and thermodynamic properties of ZnS (zincblende and rocksalt structure)

We have measured the specific heat of zincblende ZnS for several isotopic compositions and over a broad temperature range (3 to 1100 K). We have compared these results with calculations based on ab initio electronic band structures, performed using both LDA and GGA exchange- correlation functionals. We have compared the lattice dynamics obtained in this manner with experimental data and have calculated the one-phonon and two-phonon densities of states. We have also calculated mode Grueneisen parameters at a number of high symmetry points of the Brillouin zone. The electronic part of our calculations has been used to investigate the effect of the 3d core electrons of zinc on the spin-orbit splitting of the top valence bands. The effect of these core electrons on the band structure of the rock salt modification of ZnS is also discussed.Comment: 33pages, 16 Figures, submitted to Phys. Rev.