20,246 research outputs found
Corner effects on the perturbation of an electric potential
We consider the perturbation of an electric potential due to an insulating
inclusion with corners. This perturbation is known to admit a multipole
expansion whose coefficients are linear combinations of generalized
polarization tensors. We define new geometric factors of a simple planar domain
in terms of a conformal mapping associated with the domain. The geometric
factors share properties of the generalized polarization tensors and are the
Fourier series coefficients of a kind of generalized external angle of the
inclusion boundary. Since the generalized external angle contains the Dirac
delta singularity at corner points, we can determine the criterion for the
existence of corner points on the inclusion boundary in terms of the geometric
factors. We illustrate and validate our results with numerical examples
computed to a high degree of precision using integral equation techniques,
Nystr\"om discretization, and recursively compressed inverse preconditioning.Comment: 25 pages, 6 figure
Dynamical control of correlated states in a square quantum dot
In the limit of low particle density, electrons confined to a quantum dot
form strongly correlated states termed Wigner molecules, in which the Coulomb
interaction causes the electrons to become highly localized in space. By using
an effective model of Hubbard-type to describe these states, we investigate how
an oscillatory electric field can drive the dynamics of a two-electron Wigner
molecule held in a square quantum dot. We find that, for certain combinations
of frequency and strength of the applied field, the tunneling between various
charge configurations can be strongly quenched, and we relate this phenomenon
to the presence of anti-crossings in the Floquet quasi-energy spectrum. We
further obtain simple analytic expressions for the location of these
anti-crossings, which allows the effective parameters for a given quantum dot
to be directly measured in experiment, and suggests the exciting possibility of
using ac-fields to control the time evolution of entangled states in mesoscopic
devices.Comment: Replaced with version to be published in Phys. Rev.
A Scanned Perturbation Technique For Imaging Electromagnetic Standing Wave Patterns of Microwave Cavities
We have developed a method to measure the electric field standing wave
distributions in a microwave resonator using a scanned perturbation technique.
Fast and reliable solutions to the Helmholtz equation (and to the Schrodinger
equation for two dimensional systems) with arbitrarily-shaped boundaries are
obtained. We use a pin perturbation to image primarily the microwave electric
field amplitude, and we demonstrate the ability to image broken time-reversal
symmetry standing wave patterns produced with a magnetized ferrite in the
cavity. The whole cavity, including areas very close to the walls, can be
imaged using this technique with high spatial resolution over a broad range of
frequencies.Comment: To be published in Review of Scientific Instruments,September, 199
Analysis of a combined influence of substrate wetting and surface electromigration on a thin film stability and dynamical morphologies
A PDE-based model combining surface electromigration and wetting is developed
for the analysis of morphological stability of ultrathin solid films. Adatom
mobility is assumed anisotropic, and two directions of the electric field
(parallel and perpendicular to the surface) are discussed and contrasted.
Linear stability analyses of small-slope evolution equations are performed,
followed by computations of fully nonlinear parametric evolution equations that
permit surface overhangs. The results reveal parameter domains of instability
for wetting and non-wetting films and variable electric field strength,
nonlinear steady-state solutions in certain cases, and interesting coarsening
behavior for strongly wetting films.Comment: Submitted to the special issue "Nanoscale wetting of solids on
solids" of the journal Comptes Rendus Physique (Olivier Pierre-Louis, Univ.
Lyon, Editor
Steric engineering of metal-halide perovskites with tunable optical band gaps
Owing to their high energy-conversion efficiency and inexpensive fabrication
routes, solar cells based on metal-organic halide perovskites have rapidly
gained prominence as a disruptive technology. An attractive feature of
perovskite absorbers is the possibility of tailoring their properties by
changing the elemental composition through the chemical precursors. In this
context, rational in silico design represents a powerful tool for mapping the
vast materials landscape and accelerating discovery. Here we show that the
optical band gap of metal-halide perovskites, a key design parameter for solar
cells, strongly correlates with a simple structural feature, the largest
metal-halide-metal bond angle. Using this descriptor we suggest continuous
tunability of the optical gap from the mid-infrared to the visible. Precise
band gap engineering is achieved by controlling the bond angles through the
steric size of the molecular cation. Based on these design principles we
predict novel low-gap perovskites for optimum photovoltaic efficiency, and we
demonstrate the concept of band gap modulation by synthesising and
characterising novel mixed-cation perovskites.Comment: This manuscript was submitted for publication on March 6th, 2014.
Many of the results presented in this manuscript were presented at the
International Conference on Solution processed Semiconductor Solar Cells,
held in Oxford, UK, on 10-12 September 2014. The manuscript is 37 pages long
and contains 8 figure
Bound States in Sharply Bent Waveguides: Analytical and Experimental Approach
Quantum wires and electromagnetic waveguides possess common features since
their physics is described by the same wave equation. We exploit this analogy
to investigate experimentally with microwave waveguides and theoretically with
the help of an effective potential approach the occurrence of bound states in
sharply bent quantum wires. In particular, we compute the bound states, study
the features of the transition from a bound to an unbound state caused by the
variation of the bending angle and determine the critical bending angles at
which such a transition takes place. The predictions are confirmed by
calculations based on a conventional numerical method as well as experimental
measurements of the spectra and electric field intensity distributions of
electromagnetic waveguides
In-plane magnetoelectric response in bilayer graphene
A graphene bilayer shows an unusual magnetoelectric response whose magnitude
is controlled by the valley-isospin density, making it possible to link
magnetoelectric behavior to valleytronics. Complementary to previous studies,
we consider the effect of static homogeneous electric and magnetic fields that
are oriented parallel to the bilayer's plane. Starting from a tight-binding
description and using quasi-degenerate perturbation theory, the low-energy
Hamiltonian is derived including all relevant magnetoelectric terms whose
prefactors are expressed in terms of tight-binding parameters. We confirm the
existence of an expected axion-type pseudoscalar term, which turns out to have
the same sign and about twice the magnitude of the previously obtained
out-of-plane counterpart. Additionally, small anisotropic corrections to the
magnetoelectric tensor are found that are fundamentally related to the skew
interlayer hopping parameter . We discuss possible ways to identify
magnetoelectric effects by distinctive features in the optical conductivity.Comment: 14 pages, 7 figure
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