Range separated hybrid exchange-correlation functional analyses of W and/or N(S) (co)doped anatase TiO_2

Electronic properties and atomic structures of W, N, S, W/N, and W/S dopings of anatase TiO_2 have been systematically investigated using the density functional theory (DFT). The exchange and correlation effects have been treated with Heyd, Scuseria and Ernzerhof (HSE) hybrid functional. Mixing traditional semi-local and non-local screened Hartree-Fock (HF) exchange energies, the HSE method corrects the band gap and also improves the description of anion/cation derived gap states. Enhanced charge carrier dynamics, observed for W/N codoped titania, can partly be explained by the passivative modifications of N 2p and W 5d states on its electronic structure. Following this trend we have found an apparent band gap narrowing of 1.03 eV for W/S codoping. This is due to the large dispersion of S 3p states at the valance band (VB) top extending its edge to higher energies and Ti--S--W hybridized states appearing at the bottom of the conduction band (CB). W/S-TiO_2 might show strong visible light response comparable to W/N codoped anatase catalysts.Comment: 8 pages, 5 figures and 3 table

An estimate for the average spectral measure of random band matrices

For a class of random band matrices of band width $W$, we prove regularity of the average spectral measure at scales $\epsilon \geq W^{-0.99}$, and find its asymptotics at these scales.Comment: 19 pp., revised versio

Eigenvector localization for random band matrices with power law band width

It is shown that certain ensembles of random matrices with entries that vanish outside a band around the diagonal satisfy a localization condition on the resolvent which guarantees that eigenvectors have strong overlap with a vanishing fraction of standard basis vectors, provided the band width $W$ raised to a power $\mu$ remains smaller than the matrix size $N$. For a Gaussian band ensemble, with matrix elements given by i.i.d. centered Gaussians within a band of width $W$, the estimate $\mu \le 8$ holds.Comment: 30 pages; corrected typo

Development of Lumped Element Kinetic Inductance Detectors for the W-Band

We are developing a Lumped Element Kinetic Inductance Detector (LEKID) array able to operate in the W-band (75-110 GHz) in order to perform ground-based Cosmic Microwave Background (CMB) and mm-wave astronomical observations. The W-band is close to optimal in terms of contamination of the CMB from Galactic synchrotron, free-free, and thermal interstellar dust. In this band, the atmosphere has very good transparency, allowing interesting ground-based observations with large (>30 m) telescopes, achieving high angular resolution (<0.4 arcmin). In this work we describe the startup measurements devoted to the optimization of a W-band camera/spectrometer prototype for large aperture telescopes like the 64 m SRT (Sardinia Radio Telescope). In the process of selecting the best superconducting film for the LEKID, we characterized a 40 nm thick Aluminum 2-pixel array. We measured the minimum frequency able to break CPs (i.e. $h\nu=2\Delta\left(T_{c}\right)=3.5k_{B}T_{c}$) obtaining $\nu=95.5$ GHz, that corresponds to a critical temperature of 1.31 K. This is not suitable to cover the entire W-band. For an 80 nm layer the minimum frequency decreases to 93.2 GHz, which corresponds to a critical temperature of 1.28 K; this value is still suboptimal for W-band operation. Further increase of the Al film thickness results in bad performance of the detector. We have thus considered a Titanium-Aluminum bi-layer (10 nm thick Ti + 25 nm thick Al, already tested in other laboratories), for which we measured a critical temperature of 820 mK and a cut-on frequency of 65 GHz: so this solution allows operation in the entire W-band.Comment: 16th International Workshop on Low Temperature Detectors, Grenoble 20-24 July 2015, Journal of Low Temperature Physics, Accepte

Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model

We consider Hermitian and symmetric random band matrices $H$ in $d \geq 1$ dimensions. The matrix elements $H_{xy}$, indexed by $x,y \in \Lambda \subset \Z^d$, are independent, uniformly distributed random variables if \abs{x-y} is less than the band width $W$, and zero otherwise. We prove that the time evolution of a quantum particle subject to the Hamiltonian $H$ is diffusive on time scales $t\ll W^{d/3}$. We also show that the localization length of an arbitrarily large majority of the eigenvectors is larger than a factor $W^{d/6}$ times the band width. All results are uniform in the size \abs{\Lambda} of the matrix.Comment: Minor corrections, Sections 4 and 11 update