2,548 research outputs found
First-principles envelope-function theory for lattice-matched semiconductor heterostructures
In this paper a multi-band envelope-function Hamiltonian for lattice-matched
semiconductor heterostructures is derived from first-principles norm-conserving
pseudopotentials. The theory is applicable to isovalent or heterovalent
heterostructures with macroscopically neutral interfaces and no spontaneous
bulk polarization. The key assumption -- proved in earlier numerical studies --
is that the heterostructure can be treated as a weak perturbation with respect
to some periodic reference crystal, with the nonlinear response small in
comparison to the linear response. Quadratic response theory is then used in
conjunction with k.p perturbation theory to develop a multi-band effective-mass
Hamiltonian (for slowly varying envelope functions) in which all interface
band-mixing effects are determined by the linear response. To within terms of
the same order as the position dependence of the effective mass, the quadratic
response contributes only a bulk band offset term and an interface dipole term,
both of which are diagonal in the effective-mass Hamiltonian. Long-range
multipole Coulomb fields arise in quantum wires or dots, but have no
qualitative effect in two-dimensional systems beyond a dipole contribution to
the band offsets.Comment: 25 pages, no figures, RevTeX4; v3: final published versio
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Least action principle for envelope functions in abrupt heterostructures
We apply the envelope function approach to abrupt heterostructures starting
with the least action principle for the microscopic wave function. The
interface is treated nonperturbatively, and our approach is applicable to
mismatched heterostructure. We obtain the interface connection rules for the
multiband envelope function and the short-range interface terms which consist
of two physically distinct contributions. The first one depends only on the
structure of the interface, and the second one is completely determined by the
bulk parameters. We discover new structure inversion asymmetry terms and new
magnetic energy terms important in spintronic applications.Comment: 4 pages, 1 figur
Quadratic response theory for spin-orbit coupling in semiconductor heterostructures
This paper examines the properties of the self-energy operator in
lattice-matched semiconductor heterostructures, focusing on nonanalytic
behavior at small values of the crystal momentum, which gives rise to
long-range Coulomb potentials. A nonlinear response theory is developed for
nonlocal spin-dependent perturbing potentials. The ionic pseudopotential of the
heterostructure is treated as a perturbation of a bulk reference crystal, and
the self-energy is derived to second order in the perturbation. If spin-orbit
coupling is neglected outside the atomic cores, the problem can be analyzed as
if the perturbation were a local spin scalar, since the nonlocal spin-dependent
part of the pseudopotential merely renormalizes the results obtained from a
local perturbation. The spin-dependent terms in the self-energy therefore fall
into two classes: short-range potentials that are analytic in momentum space,
and long-range nonanalytic terms that arise from the screened Coulomb potential
multiplied by a spin-dependent vertex function. For an insulator at zero
temperature, it is shown that the electronic charge induced by a given
perturbation is exactly linearly proportional to the charge of the perturbing
potential. These results are used in a subsequent paper to develop a
first-principles effective-mass theory with generalized Rashba spin-orbit
coupling.Comment: 20 pages, no figures, RevTeX4; v2: final published versio
Finite Sized Atomistic Simulations of Screw Dislocations
The interaction of screw dislocations with an applied stress is studied using
atomistic simulations in conjunction with a continuum treatment of the role
played by the far field boundary condition. A finite cell of atoms is used to
consider the response of dislocations to an applied stress and this introduces
an additional force on the dislocation due to the presence of the boundary.
Continuum mechanics is used to calculate the boundary force which is
subsequently accounted for in the equilibrium condition for the dislocation.
Using this formulation, the lattice resistance curve and the associated Peierls
stress are calculated for screw dislocations in several close packed metals. As
a concrete example of the boundary force method, we compute the bow out of a
pinned screw dislocation; the line-tension of the dislocation is calculated
from the results of the atomistic simulations using a variational principle
that explicitly accounts for the boundary force.Comment: LaTex, 20 pages, 11 figure
Statics and Dynamics of an Inhomogeneously-Nonlinear Lattice
We introduce an inhomogeneously-nonlinear Schr{\"o}dinger lattice, featuring
a defocusing segment, a focusing segment and a transitional interface between
the two. We illustrate that such inhomogeneous settings present vastly
different dynamical behavior than the one expected in their homogeneous
counterparts in the vicinity of the interface. We analyze the relevant
stationary states, as well as their stability by means of perturbation theory
and linear stability analysis. We find good agreement with the numerical
findings in the vicinity of the anti-continuum limit. For larger values of the
coupling, we follow the relevant branches numerically and show that they
terminate at values of the coupling strength which are larger for more extended
solutions. The dynamical development of relevant instabilities is also
monitored in the case of unstable solutions.Comment: 14 pages, 4 figure
Accurate quadratic-response approximation for the self-consistent pseudopotential of semiconductor nanostructures
Quadratic-response theory is shown to provide a conceptually simple but
accurate approximation for the self-consistent one-electron potential of
semiconductor nanostructures. Numerical examples are presented for GaAs/AlAs
and InGaAs/InP (001) superlattices using the local-density approximation to
density-functional theory and norm-conserving pseudopotentials without
spin-orbit coupling. When the reference crystal is chosen to be the
virtual-crystal average of the two bulk constituents, the absolute error in the
quadratic-response potential for Gamma(15) valence electrons is about 2 meV for
GaAs/AlAs and 5 meV for InGaAs/InP. Low-order multipole expansions of the
electron density and potential response are shown to be accurate throughout a
small neighborhood of each reciprocal lattice vector, thus providing a further
simplification that is confirmed to be valid for slowly varying envelope
functions. Although the linear response is about an order of magnitude larger
than the quadratic response, the quadratic terms are important both
quantitatively (if an accuracy of better than a few tens of meV is desired) and
qualitatively (due to their different symmetry and long-range dipole effects).Comment: 16 pages, 20 figures; v2: new section on limitations of theor
A high stability semiconductor laser system for a Sr-based optical lattice clock
We describe a frequency stabilized diode laser at 698 nm used for high
resolution spectroscopy of the 1S0-3P0 strontium clock transition. For the
laser stabilization we use state-of-the-art symmetrically suspended optical
cavities optimized for very low thermal noise at room temperature. Two-stage
frequency stabilization to high finesse optical cavities results in measured
laser frequency noise about a factor of three above the cavity thermal noise
between 2 Hz and 11 Hz. With this system, we demonstrate high resolution remote
spectroscopy on the 88Sr clock transition by transferring the laser output over
a phase-noise-compensated 200 m-long fiber link between two separated
laboratories. Our dedicated fiber link ensures a transfer of the optical
carrier with frequency stability of 7 \cdot 10^{-18} after 100 s integration
time, which could enable the observation of the strontium clock transition with
an atomic Q of 10^{14}. Furthermore, with an eye towards the development of
transportable optical clocks, we investigate how the complete laser system
(laser+optics+cavity) can be influenced by environmental disturbances in terms
of both short- and long-term frequency stability.Comment: 9 pages, 9 figures, submitted to Appl. Phys.
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