GW band structure of InAs and GaAs in the wurtzite phase

We report the first quasiparticle calculations of the newly observed wurtzite polymorph of InAs and GaAs. The calculations are performed in the GW approximation using plane waves and pseudopotentials. For comparison we also report the study of the zinc-blende phase within the same approximations. In the InAs compound the In 4d electrons play a very important role: whether they are frozen in the core or not, leads either to a correct or a wrong band ordering (negative gap) within the Local Density Appproximation (LDA). We have calculated the GW band structure in both cases. In the first approach, we have estimated the correction to the pd repulsion calculated within the LDA and included this effect in the calculation of the GW corrections to the LDA spectrum. In the second case, we circumvent the negative gap problem by first using the screened exchange approximation and then calculating the GW corrections starting from the so obtained eigenvalues and eigenfunctions. This approach leads to a more realistic band-structure and was also used for GaAs. For both InAs and GaAs in the wurtzite phase we predict an increase of the quasiparticle gap with respect to the zinc-blende polytype.Comment: 9 pages, 6 figures, 3 table

Optical Study of GaAs quantum dots embedded into AlGaAs nanowires

We report on the photoluminescence characterization of GaAs quantum dots embedded into AlGaAs nano-wires. Time integrated and time resolved photoluminescence measurements from both an array and a single quantum dot/nano-wire are reported. The influence of the diameter sizes distribution is evidenced in the optical spectroscopy data together with the presence of various crystalline phases in the AlGaAs nanowires.Comment: 5 page, 5 figure

On the top eigenvalue of heavy-tailed random matrices

We study the statistics of the largest eigenvalue lambda_max of N x N random matrices with unit variance, but power-law distributed entries, P(M_{ij})~ |M_{ij}|^{-1-mu}. When mu > 4, lambda_max converges to 2 with Tracy-Widom fluctuations of order N^{-2/3}. When mu < 4, lambda_max is of order N^{2/mu-1/2} and is governed by Fr\'echet statistics. The marginal case mu=4 provides a new class of limiting distribution that we compute explicitely. We extend these results to sample covariance matrices, and show that extreme events may cause the largest eigenvalue to significantly exceed the Marcenko-Pastur edge. Connections with Directed Polymers are briefly discussed.Comment: 4 pages, 2 figure

Local semicircle law at the spectral edge for Gaussian β\beta-ensembles

We study the local semicircle law for Gaussian $\beta$-ensembles at the edge of the spectrum. We prove that at the almost optimal level of $n^{-2/3+\epsilon}$, the local semicircle law holds for all $\beta \geq 1$ at the edge. The proof of the main theorem relies on the calculation of the moments of the tridiagonal model of Gaussian $\beta$-ensembles up to the $p_n$-moment where $p_n = O(n^{2/3-\epsilon})$. The result is the analogous to the result of Sinai and Soshnikov for Wigner matrices, but the combinatorics involved in the calculations are different.Comment: 16 pages, 2 figure

Increasing subsequences and the hard-to-soft edge transition in matrix ensembles

Our interest is in the cumulative probabilities Pr(L(t) \le l) for the maximum length of increasing subsequences in Poissonized ensembles of random permutations, random fixed point free involutions and reversed random fixed point free involutions. It is shown that these probabilities are equal to the hard edge gap probability for matrix ensembles with unitary, orthogonal and symplectic symmetry respectively. The gap probabilities can be written as a sum over correlations for certain determinantal point processes. From these expressions a proof can be given that the limiting form of Pr(L(t) \le l) in the three cases is equal to the soft edge gap probability for matrix ensembles with unitary, orthogonal and symplectic symmetry respectively, thereby reclaiming theorems due to Baik-Deift-Johansson and Baik-Rains.Comment: LaTeX, 19 page

HRTEM study of growth-correlated properties of (Si,Ge) islands

This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Peer Reviewe

Subcritical multiplicative chaos for regularized counting statistics from random matrix theory

For an N×N random unitary matrix U_N, we consider the random field defined by counting the number of eigenvalues of U_N in a mesoscopic arc of the unit circle, regularized at an N-dependent scale Ɛ_N>0. We prove that the renormalized exponential of this field converges as N → ∞ to a Gaussian multiplicative chaos measure in the whole subcritical phase. In addition, we show that the moments of the total mass converge to a Selberg-like integral and by taking a further limit as the size of the arc diverges, we establish part of the conjectures in [55]. By an analogous construction, we prove that the multiplicative chaos measure coming from the sine process has the same distribution, which strongly suggests that this limiting object should be universal. The proofs are based on the asymptotic analysis of certain Toeplitz or Fredholm determinants using the Borodin-Okounkov formula or a Riemann-Hilbert problem for integrable operators. Our approach to the L¹-phase is based on a generalization of the construction in Berestycki [5] to random fields which are only asymptotically Gaussian. In particular, our method could have applications to other random fields coming from either random matrix theory or a different context

Determinantal point processes associated with Hilbert spaces of holomorphic functions

International audienceWe study determinantal point processes on C induced by the reproducing kernels of generalized Fock spaces as well as those on the unit disc D induced by the reproducing kernels of generalized Bergman spaces. In the first case, we show that all reduced Palm measures of the same order are equivalent. The Radon-Nikodym derivatives are computed explicitly using regularized multiplicative functionals. We also show that these determinantal point processes are rigid in the sense of Ghosh and Peres, hence reduced Palm measures of different orders are singular. In the second case, we show that all reduced Palm measures, of all orders, are equivalent. The Radon-Nikodym derivatives are computed using regularized multiplicative function-als associated with certain Blaschke products. The quasi-invariance of these deter-minantal point processes under the group of diffeomorphisms with compact supports follows as a corollary

Growth of SiC films by the method of substitution of atoms on porous Si (100) and (111) substrates

The mechanisms of growth of silicon carbide (SiC) films by the method of substitution of atoms on macro- and mesoporous silicon substrates (Si) of p- and n-type conduction are investigated. Significant dependence of the rate and the mechanism of nucleation of SiC layers on Si on the type of Si doping and its crystallographic orientation is experimentally found. Comparison of the experimental data with the theoretical results obtained earlier is performed. It is shown that the presence of the system of pores on the surface allows one to significantly increase the thickness of silicon transformed into SiC during the process of synthesis by the method of substitution of atoms, which was equal to 115 microns in our experiments. The obtained samples are studied by methods of scanning electron microscopy, micro-Raman spectroscopy, and X-ray diffraction analysis. Numerical simulation of the distribution of elastic stresses caused by the difference in thermal expansion coefficients (TEC) in the heterostructures of GaN/SiC/porous Si/Si is conducted. It is revealed that the presence of pores in the near-surface layers of Si leads to considerable relaxation of elastic stresses in GaN films caused by differences in the TEC between GaN and Si

Burden of injury along the development spectrum: Associations between the Socio-demographic Index and disability-adjusted life year estimates from the Global Burden of Disease Study 2017

Background: The epidemiological transition of non-communicable diseases replacing infectious diseases as the main contributors to disease burden has been well documented in global health literature. Less focus, however, has been given to the relationship between sociodemographic changes and injury. The aim of this study was to examine the association between disability-adjusted life years (DALYs) from injury for 195 countries and territories at different levels along the development spectrum between 1990 and 2017 based on the Global Burden of Disease (GBD) 2017 estimates. Methods: Injury mortality was estimated using the GBD mortality database, corrections for garbage coding and CODEm-the cause of death ensemble modelling tool. Morbidity estimation was based on surveys and inpatient and outpatient data sets for 30 cause-of-injury with 47 nature-of-injury categories each. The Socio-demographic Index (SDI) is a composite indicator that includes lagged income per capita, average educational attainment over age 15 years and total fertility rate. Results: For many causes of injury, age-standardised DALY rates declined with increasing SDI, although road injury, interpersonal violence and self-harm did not follow this pattern. Particularly for self-harm opposing patterns were observed in regions with similar SDI levels. For road injuries, this effect was less pronounced. Conclusions: The overall global pattern is that of declining injury burden with increasing SDI. However, not all injuries follow this pattern, which suggests multiple underlying mechanisms influencing injury DALYs. There is a need for a detailed understanding of these patterns to help to inform national and global efforts to address injury-related health outcomes across the development spectrum