349 research outputs found
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/BeSeTe heterostructures by a semiempirical
tight-binding method. Tight-binding parameters and band bowing of
BeSeTe 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/BeSeTe with conduction band minimum in the Si layer and
valence band maximum in the BeSeTe layer. The electronic
structure and optical properties of various (Si/(BeSeTe [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 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 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
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