21,026 research outputs found
Scaling behavior of spin transport in hydrogenated graphene
We calculate the spin transport of hydrogenated graphene using the
Landauer-B\"uttiker formalism with a spin-dependent tight-binding Hamiltonian.
The advantages of using this method is that it simultaneously gives information
on sheet resistance and localization length as well as spin relaxation length.
Furthermore, the Landauer-B\"uttiker formula can be computed very efficiently
using the recursive Green's function technique. Previous theoretical results on
spin relaxation time in hydrogenated graphene have not been in agreement with
experiments. Here, we study magnetic defects in graphene with randomly aligned
magnetic moments, where interference between spin-channels is explicitly
included. We show that the spin relaxation length and sheet resistance scale
nearly linearly with the impurity concentration. Moreover, the spin relaxation
mechanism in hydrogenated graphene is Markovian only near the charge neutrality
point or in the highly dilute impurity limit
Dirac model of electronic transport in graphene antidot barriers
In order to use graphene for semiconductor applications, such as transistors
with high on/off ratios, a band gap must be introduced into this otherwise
semimetallic material. A promising method of achieving a band gap is by
introducing nanoscale perforations (antidots) in a periodic pattern, known as a
graphene antidot lattice (GAL). A graphene antidot barrier (GAB) can be made by
introducing a 1D GAL strip in an otherwise pristine sheet of graphene. In this
paper, we will use the Dirac equation (DE) with a spatially varying mass term
to calculate the electronic transport through such structures. Our approach is
much more general than previous attempts to use the Dirac equation to calculate
scattering of Dirac electrons on antidots. The advantage of using the DE is
that the computational time is scale invariant and our method may therefore be
used to calculate properties of arbitrarily large structures. We show that the
results of our Dirac model are in quantitative agreement with tight-binding for
hexagonal antidots with armchair edges. Furthermore, for a wide range of
structures, we verify that a relatively narrow GAB, with only a few antidots in
the unit cell, is sufficient to give rise to a transport gap
Electronic and optical properties of graphene antidot lattices: Comparison of Dirac and tight-binding models
The electronic properties of graphene may be changed from semimetallic to
semiconducting by introducing perforations (antidots) in a periodic pattern.
The properties of such graphene antidot lattices (GALs) have previously been
studied using atomistic models, which are very time consuming for large
structures. We present a continuum model that uses the Dirac equation (DE) to
describe the electronic and optical properties of GALs. The advantages of the
Dirac model are that the calculation time does not depend on the size of the
structures and that the results are scalable. In addition, an approximation of
the band gap using the DE is presented. The Dirac model is compared with
nearest-neighbour tight-binding (TB) in order to assess its accuracy. Extended
zigzag regions give rise to localized edge states, whereas armchair edges do
not. We find that the Dirac model is in quantitative agreement with TB for GALs
without edge states, but deviates for antidots with large zigzag regions.Comment: 15 pages, 7 figures. Accepted by Journal of Physics: Condensed matte
Faraday effect revisited: sum rules and convergence issues
This is the third paper of a series revisiting the Faraday effect. The
question of the absolute convergence of the sums over the band indices entering
the Verdet constant is considered. In general, sum rules and traces per unit
volume play an important role in solid state physics, and they give rise to
certain convergence problems widely ignored by physicists. We give a complete
answer in the case of smooth potentials and formulate an open problem related
to less regular perturbations.Comment: Dedicated to the memory of our late friend Pierre Duclos. Accepted
for publication in Journal of Physics A: Mathematical and Theoretical
Conditional expectations associated with quantum states
An extension of the conditional expectations (those under a given subalgebra
of events and not the simple ones under a single event) from the classical to
the quantum case is presented. In the classical case, the conditional
expectations always exist; in the quantum case, however, they exist only if a
certain weak compatibility criterion is satisfied. This compatibility criterion
was introduced among others in a recent paper by the author. Then,
state-independent conditional expectations and quantum Markov processes are
studied. A classical Markov process is a probability measure, together with a
system of random variables, satisfying the Markov property and can equivalently
be described by a system of Markovian kernels (often forming a semigroup). This
equivalence is partly extended to quantum probabilities. It is shown that a
dynamical (semi)group can be derived from a given system of quantum observables
satisfying the Markov property, and the group generators are studied. The
results are presented in the framework of Jordan operator algebras, and a very
general type of observables (including the usual real-valued observables or
self-adjoint operators) is considered.Comment: 10 pages, the original publication is available at http://www.aip.or
Clar Sextet Analysis of Triangular, Rectangular and Honeycomb Graphene Antidot Lattices
Pristine graphene is a semimetal and thus does not have a band gap. By making
a nanometer scale periodic array of holes in the graphene sheet a band gap may
form; the size of the gap is controllable by adjusting the parameters of the
lattice. The hole diameter, hole geometry, lattice geometry and the separation
of the holes are parameters that all play an important role in determining the
size of the band gap, which, for technological applications, should be at least
of the order of tenths of an eV. We investigate four different hole
configurations: the rectangular, the triangular, the rotated triangular and the
honeycomb lattice. It is found that the lattice geometry plays a crucial role
for size of the band gap: the triangular arrangement displays always a sizable
gap, while for the other types only particular hole separations lead to a large
gap. This observation is explained using Clar sextet theory, and we find that a
sufficient condition for a large gap is that the number of sextets exceeds one
third of the total number of hexagons in the unit cell. Furthermore, we
investigate non-isosceles triangular structures to probe the sensitivity of the
gap in triangular lattices to small changes in geometry
Synthesis and analysis of jet fuel from shale oil and coal syncrudes
Thirty-two jet fuel samples of varying properties were produced from shale oil and coal syncrudes, and analyzed to assess their suitability for use. TOSCO II shale oil and H-COAL and COED syncrudes were used as starting materials. The processes used were among those commonly in use in petroleum processing-distillation, hydrogenation and catalytic hydrocracking. The processing conditions required to meet two levels of specifications regarding aromatic, hydrogen, sulfur and nitrogen contents at two yield levels were determined and found to be more demanding than normally required in petroleum processing. Analysis of the samples produced indicated that if the more stringent specifications of 13.5% hydrogen (min.) and 0.02% nitrogen (max.) were met, products similar in properties to conventional jet fuels were obtained. In general, shale oil was easier to process (catalyst deactivation was seen when processing coal syncrudes), consumed less hydrogen and yielded superior products. Based on these considerations, shale oil appears to be preferred to coal as a petroleum substitute for jet fuel production
Commuting self-adjoint extensions of symmetric operators defined from the partial derivatives
We consider the problem of finding commuting self-adjoint extensions of the
partial derivatives {(1/i)(\partial/\partial x_j):j=1,...,d} with domain
C_c^\infty(\Omega) where the self-adjointness is defined relative to
L^2(\Omega), and \Omega is a given open subset of R^d. The measure on \Omega is
Lebesgue measure on R^d restricted to \Omega. The problem originates with I.E.
Segal and B. Fuglede, and is difficult in general. In this paper, we provide a
representation-theoretic answer in the special case when \Omega=I\times\Omega_2
and I is an open interval. We then apply the results to the case when \Omega is
a d-cube, I^d, and we describe possible subsets \Lambda of R^d such that
{e^(i2\pi\lambda \dot x) restricted to I^d:\lambda\in\Lambda} is an orthonormal
basis in L^2(I^d).Comment: LaTeX2e amsart class, 18 pages, 2 figures; PACS numbers 02.20.Km,
02.30.Nw, 02.30.Tb, 02.60.-x, 03.65.-w, 03.65.Bz, 03.65.Db, 61.12.Bt,
61.44.B
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