494 research outputs found
A Characterization of Completely Reachable Automata
A complete deterministic finite automaton in which every non-empty subset of
the state set occurs as the image of the whole state set under the action of a
suitable input word is called completely reachable. We characterize completely
reachable automata in terms of certain directed graphs.Comment: 12 pages, 3 figures, submitted to DLT 201
First-principles study of vibrational and dielectric properties of {\beta}-Si3N4
First-principles calculations have been conducted to study the structural,
vibrational and dielectric properties of {\beta}-Si3N4. Calculations of the
zone-center optical-mode frequencies (including LO-TO splittings), Born
effective charge tensors for each atom, dielectric constants, using density
functional perturbation theory, are reported. The fully relaxed structural
parameters are found to be in good agreement with experimental data. All optic
modes are identified and agreement of theory with experiment is excellent. The
static dielectric tensor is decomposed into contributions arising from
individual infrared-active phonon modes. It is found that high-frequency modes
mainly contribute to the lattice dielectric constant.Comment: 15pages, 1 figure, 5 table
Non-linear optical susceptibilities, Raman efficiencies and electrooptic tensors from first-principles density functional perturbation theory
The non-linear response of infinite periodic solids to homogenous electric
fields and collective atomic displacements is discussed in the framework of
density functional perturbation theory. The approach is based on the 2n + 1
theorem applied to an electric-field-dependent energy functional. We report the
expressions for the calculation of the non-linear optical susceptibilities,
Raman scattering efficiencies and electrooptic coefficients. Different
formulations of third-order energy derivatives are examined and their
convergence with respect to the k-point sampling is discussed. We apply our
method to a few simple cases and compare our results to those obtained with
distinct techniques. Finally, we discuss the effect of a scissors correction on
the EO coefficients and non-linear optical susceptibilities
Theory of structural response to macroscopic electric fields in ferroelectric systems
We have developed and implemented a formalism for computing the structural
response of a periodic insulating system to a homogeneous static electric field
within density-functional perturbation theory (DFPT). We consider the
thermodynamic potentials E(R,eta,e) and F(R,eta,e) whose minimization with
respect to the internal structural parameters R and unit cell strain eta yields
the equilibrium structure at fixed electric field e and polarization P,
respectively. First-order expansion of E(R,eta,e) in e leads to a useful
approximation in which R(P) and eta(P) can be obtained by simply minimizing the
zero-field internal energy with respect to structural coordinates subject to
the constraint of a fixed spontaneous polarization P. To facilitate this
minimization, we formulate a modified DFPT scheme such that the computed
derivatives of the polarization are consistent with the discretized form of the
Berry-phase expression. We then describe the application of this approach to
several problems associated with bulk and short-period superlattice structures
of ferroelectric materials such as BaTiO3 and PbTiO3. These include the effects
of compositionally broken inversion symmetry, the equilibrium structure for
high values of polarization, field-induced structural phase transitions, and
the lattice contributions to the linear and the non-linear dielectric
constants.Comment: 19 pages, with 15 postscript figures embedded. Uses REVTEX4 and epsf
macros. Also available at
http://www.physics.rutgers.edu/~dhv/preprints/sai_pol/index.htm
Origin of magnetism and quasiparticles properties in Cr-doped TiO
Combining LSDA+ and an analysis of superexchange interactions beyond DFT,
we describe the magnetic ground states in rutile and anatase Cr-doped TiO.
In parallel, we correct our LSDA+ ground state through GW corrections
(@LSDA+) that reproduce the position of impurity states and the band
gaps in satisfying agreement with experiments. Because of the different
topological coordinations of Cr-Cr bonds in the ground states of rutile and
anatase, superexchange interactions induce either ferromagnetic or
antiferromagnetic couplings of Cr ions. In Cr-doped anatase, this interaction
leads to a new mechanism which stabilizes a ferromagnetic ground state, in
keeping with experimental evidence, without the need to invoke F-center
exchange.Comment: 5<pages, 4 figure
High-order density-matrix perturbation theory
We present a simple formalism for the calculation of the derivatives of the
electronic density matrix at any order, within density functional theory. Our
approach, contrary to previous ones, is not based on the perturbative expansion
of the Kohn-Sham wavefunctions. It has the following advantages: (i) it allows
a simple derivation for the expression for the high order derivatives of the
density matrix; (ii) in extended insulators, the treatment of
uniform-electric-field perturbations and of the polarization derivatives is
straightforward.Comment: 4 page
First-principles study of the electrooptic effect in ferroelectric oxides
We present a method to compute the electrooptic tensor from first principles,
explicitly taking into account the electronic, ionic and piezoelectric
contributions. It allows us to study the non-linear optic behavior of three
ferroelectric ABO_3 compounds : LiNbO_3, BaTiO_3 and PbTiO_3. Our calculations
reveal the dominant contribution of the soft mode to the electrooptic
coefficients in LiNbO_3 and BaTiO_3 and identify the coupling between the
electric field and the polar atomic displacements along the B-O chains as the
origin of the large electrooptic response in these compounds.Comment: accepted for publication in Phys. Rev. Let
A First-Principles Approach to Insulators in Finite Electric Fields
We describe a method for computing the response of an insulator to a static,
homogeneous electric field. It consists of iteratively minimizing an electric
enthalpy functional expressed in terms of occupied Bloch-like states on a
uniform grid of k points. The functional has equivalent local minima below a
critical field E_c that depends inversely on the density of k points; the
disappearance of the minima at E_c signals the onset of Zener breakdown. We
illustrate the procedure by computing the piezoelectric and nonlinear
dielectric susceptibility tensors of III-V semiconductors.Comment: 4 pages, with 1 postscript figure embedded. Uses REVTEX and epsf
macros. Also available at
http://www.physics.rutgers.edu/~dhv/preprints/is_ef/index.htm
Nanotube Piezoelectricity
We combine ab initio, tight-binding methods and analytical theory to study
piezoelectric effect of boron nitride nanotubes. We find that piezoelectricity
of a heteropolar nanotube depends on its chirality and diameter and can be
understood starting from the piezoelectric response of an isolated planar
sheet, along with a structure specific mapping from the sheet onto the tube
surface. We demonstrate that coupling between the uniaxial and shear
deformation are only allowed in the nanotubes with lower chiral symmetry. Our
study shows that piezoelectricity of nanotubes is fundamentally different from
its counterpart in three dimensional (3D) bulk materials.Comment: 4 pages, with 3 postscript figures embedded. Uses REVTEX4 macros.
Also available at
http://www.physics.upenn.edu/~nsai/preprints/bn_piezo/index.htm
First principles study of strain/electronic interplay in ZnO; Stress and temperature dependence of the piezoelectric constants
We present a first-principles study of the relationship between stress,
temperature and electronic properties in piezoelectric ZnO. Our method is a
plane wave pseudopotential implementation of density functional theory and
density functional linear response within the local density approximation. We
observe marked changes in the piezoelectric and dielectric constants when the
material is distorted. This stress dependence is the result of strong, bond
length dependent, hybridization between the O and Zn electrons. Our
results indicate that fine tuning of the piezoelectric properties for specific
device applications can be achieved by control of the ZnO lattice constant, for
example by epitaxial growth on an appropriate substrate.Comment: accepted for publication in Phys. Rev.
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