Optical matrix elements in tight-binding models with overlap

We investigate the effect of orbital overlap on optical matrix elements in empirical tight-binding models. Empirical tight-binding models assume an orthogonal basis of (atomiclike) states and a diagonal coordinate operator which neglects the intra-atomic part. It is shown that, starting with an atomic basis which is not orthogonal, the orthogonalization process induces intra-atomic matrix elements of the coordinate operator and extends the range of the effective Hamiltonian. We analyze simple tight-binding models and show that non-orthogonality plays an important role in optical matrix elements. In addition, the procedure gives formal justification to the nearest-neighbor spin-orbit interaction introduced by Boykin [Phys. Rev \textbf{B} 57, 1620 (1998)] in order to describe the Dresselahaus term which is neglected in empirical tight-binding models.Comment: 16 pages 6 figures, to appear in Phys. Rev.

Threshold Error Penalty for Fault Tolerant Computation with Nearest Neighbour Communication

The error threshold for fault tolerant quantum computation with concatenated encoding of qubits is penalized by internal communication overhead. Many quantum computation proposals rely on nearest-neighbour communication, which requires excess gate operations. For a qubit stripe with a width of L+1 physical qubits implementing L levels of concatenation, we find that the error threshold of 2.1x10^-5 without any communication burden is reduced to 1.2x10^-7 when gate errors are the dominant source of error. This ~175X penalty in error threshold translates to an ~13X penalty in the amplitude and timing of gate operation control pulses.Comment: minor correctio

Electronic and optical properties of beryllium chalcogenides/silicon heterostructures

We have calculated electronic and optical properties of Si/BeSe$_{0.41}$Te$_{0.59}$ heterostructures by a semiempirical $sp^{3}s^{*}$ tight-binding method. Tight-binding parameters and band bowing of BeSe$_{0.41}$Te$_{0.59}$ are considered through a recent model for highly mismatched semiconductor alloys. The band bowing and the measurements of conduction band offset lead to a type II heterostucture for Si/BeSe$_{0.41}$Te$_{0.59}$ with conduction band minimum in the Si layer and valence band maximum in the BeSe$_{0.41}$Te$_{0.59}$ layer. The electronic structure and optical properties of various (Si$_{2})_{n }$/(BeSe$_{0.41}$Te$_{0.59})_{m}$ [001] superlattices have been considered. Two bands of interface states were found within the bandgap of bulk Si. Our calculations indicate that the optical edges are below the fundamental bandgap of bulk Si and the transitions are optically allowed.Comment: 16 pager, 7 figure

The Importance of Racial Socialization: Schoolâ Based Racial Discrimination and Racial Identity Among African American Adolescent Boys and Girls

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149540/1/jora12383_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149540/2/jora12383.pd

Constructing Mutually Unbiased Bases in Dimension Six

The density matrix of a qudit may be reconstructed with optimal efficiency if the expectation values of a specific set of observables are known. In dimension six, the required observables only exist if it is possible to identify six mutually unbiased complex 6x6 Hadamard matrices. Prescribing a first Hadamard matrix, we construct all others mutually unbiased to it, using algebraic computations performed by a computer program. We repeat this calculation many times, sampling all known complex Hadamard matrices, and we never find more than two that are mutually unbiased. This result adds considerable support to the conjecture that no seven mutually unbiased bases exist in dimension six.Comment: As published version. Added discussion of the impact of numerical approximations and corrected the number of triples existing for non-affine families (cf Table 3

Investigation of ripple-limited low-field mobility in large-scale graphene nanoribbons

Combining molecular dynamics and quantum transport simulations, we study the degradation of mobility in graphene nanoribbons caused by substrate-induced ripples. First, the atom coordinates of large-scale structures are relaxed such that surface properties are consistent with those of graphene on a substrate. Then, the electron current and low-field mobility of the resulting non-flat nanoribbons are calculated within the Non-equilibrium Green\u27s Function formalism in the coherent transport limit. An accurate tight-binding basis coupling the sigma- and pi-bands of graphene is used for this purpose. It is found that the presence of ripples decreases the mobility of graphene nanoribbons on SiO2 below 3000 cm(2)/Vs, which is comparable to experimentally reported values. (C) 2013 AIP Publishing LLC

Balloon-borne coded aperture telescope for arc-minute angular resolution at hard x-ray energies

We are working on the development of a new balloon-borne telescope, MARGIE (minute-of-arc resolution gamma ray imaging experiment). It will be a coded aperture telescope designed to image hard x-rays (in various configurations) over the 20 - 600 keV range with an angular resolution approaching one arc minute. MARGIE will use one (or both) of two different detection plane technologies, each of which is capable of providing event locations with sub-mm accuracies. One such technology involves the use of cadmium zinc telluride (CZT) strip detectors. We have successfully completed a series of laboratory measurements using a prototype CZT detector with 375 micron pitch. Spatial location accuracies of better than 375 microns have been demonstrated. A second type of detection plane would be based on CsI microfiber arrays coupled to a large area silicon CCD readout array. This approach would provide spatial resolutions comparable to that of the CZT prototype. In one possible configuration, the coded mask would be 0.5 mm thick tungsten, with 0.5 mm pixels at a distance of 1.5 m from the central detector giving an angular resolution of 1 arc-minute and a fully coded field of view of 12 degrees. We review the capabilities of the MARGIE telescope and report on the status of our development efforts and our plans for a first balloon flight

The Lie Algebraic Significance of Symmetric Informationally Complete Measurements

Examples of symmetric informationally complete positive operator valued measures (SIC-POVMs) have been constructed in every dimension less than or equal to 67. However, it remains an open question whether they exist in all finite dimensions. A SIC-POVM is usually thought of as a highly symmetric structure in quantum state space. However, its elements can equally well be regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the resulting structure constants, which are calculated from the traces of the triple products of the SIC-POVM elements and which, it turns out, characterize the SIC-POVM up to unitary equivalence. We show that the structure constants have numerous remarkable properties. In particular we show that the existence of a SIC-POVM in dimension d is equivalent to the existence of a certain structure in the adjoint representation of gl(d,C). We hope that transforming the problem in this way, from a question about quantum state space to a question about Lie algebras, may help to make the existence problem tractable.Comment: 56 page

Consequences of local gauge symmetry in empirical tight-binding theory

A method for incorporating electromagnetic fields into empirical tight-binding theory is derived from the principle of local gauge symmetry. Gauge invariance is shown to be incompatible with empirical tight-binding theory unless a representation exists in which the coordinate operator is diagonal. The present approach takes this basis as fundamental and uses group theory to construct symmetrized linear combinations of discrete coordinate eigenkets. This produces orthogonal atomic-like "orbitals" that may be used as a tight-binding basis. The coordinate matrix in the latter basis includes intra-atomic matrix elements between different orbitals on the same atom. Lattice gauge theory is then used to define discrete electromagnetic fields and their interaction with electrons. Local gauge symmetry is shown to impose strong restrictions limiting the range of the Hamiltonian in the coordinate basis. The theory is applied to the semiconductors Ge and Si, for which it is shown that a basis of 15 orbitals per atom provides a satisfactory description of the valence bands and the lowest conduction bands. Calculations of the dielectric function demonstrate that this model yields an accurate joint density of states, but underestimates the oscillator strength by about 20% in comparison to a nonlocal empirical pseudopotential calculation.Comment: 23 pages, 7 figures, RevTeX4; submitted to Phys. Rev.

Tight-binding study of the influence of the strain on the electronic properties of InAs/GaAs quantum dots

We present an atomistic investigation of the influence of strain on the electronic properties of quantum dots (QD's) within the empirical $s p^{3} s^{*}$ tight-binding (ETB) model with interactions up to 2nd nearest neighbors and spin-orbit coupling. Results for the model system of capped pyramid-shaped InAs QD's in GaAs, with supercells containing $10^{5}$ atoms are presented and compared with previous empirical pseudopotential results. The good agreement shows that ETB is a reliable alternative for an atomistic treatment. The strain is incorporated through the atomistic valence force field model. The ETB treatment allows for the effects of bond length and bond angle deviations from the ideal InAs and GaAs zincblende structure to be selectively removed from the electronic-structure calculation, giving quantitative information on the importance of strain effects on the bound state energies and on the physical origin of the spatial elongation of the wave functions. Effects of dot-dot coupling have also been examined to determine the relative weight of both strain field and wave function overlap.Comment: 22 pages, 7 figures, submitted to Phys. Rev. B (in press) In the latest version, added Figs. 3 and 4, modified Fig. 5, Tables I and II,.and added new reference