4,220 research outputs found
Gabor Frames for Quasicrystals, -theory, and Twisted Gap Labeling
We study the connection between Gabor frames for quasicrystals, the topology
of the hull of a quasicrystal and the -theory of the twisted
groupoid -algebra arising from a quasicrystal. In
particular, we construct a finitely generated projective module
\mathcal{H}_\L over related to time-frequency analysis,
and any multiwindow Gabor frame for can be used to construct an
idempotent in representing \mathcal{H}_\L in
We show for lattice subsets in dimension two, this
element corresponds to the Bott element in allowing
us to prove a twisted version of Bellissard's gap labeling theorem
There are integral heptagons, no three points on a line, no four on a circle
We give two configurations of seven points in the plane, no three points in a
line, no four points on a circle with pairwise integral distances. This answers
a famous question of Paul Erd\H{o}s.Comment: 4 pages, 1 figur
Nematicity, magnetism and superconductivity in FeSe
Iron-based superconductors are well known for their complex interplay between
structure, magnetism and superconductivity. FeSe offers a particularly
fascinating example. This material has been intensely discussed because of its
extended nematic phase, whose relationship with magnetism is not obvious.
Superconductivity in FeSe is highly tunable, with the superconducting
transition temperature, , ranging from 8 K in bulk single
crystals at ambient pressure to almost 40 K under pressure or in intercalated
systems, and to even higher temperatures in thin films. In this topical review,
we present an overview of nematicity, magnetism and superconductivity, and
discuss the interplay of these phases in FeSe. We focus on bulk FeSe and the
effects of physical pressure and chemical substitutions as tuning parameters.
The experimental results are discussed in the context of the well-studied
iron-pnictide superconductors and interpretations from theoretical approaches
are presented.Comment: Topical Review submitted to Journal of Physics: Condensed Matte
Order-Parameter Symmetries of Domain Walls in Ferroelectrics and Ferroelastics
The symmetry of boundaries between ferroelectric, ferroelastic and antiphase
domains is a key element for a theoretical understanding of their properties.
Here, we derive this symmetry from their organic relation to the symmetry of
the primary transition order parameters. The domain wall symmetries are shown
to coincide with directions of the order-parameter n-dimensional vector space,
corresponding to sum of the vectors associated with adjacent domain states.
This property is illustrated by the determination of the domain wall maximal
symmetries in BaTiO3, LaAlO3, SrTiO3 and Gd2(MoO4)3. Besides, the domain
pattern in YMnO3 is interpreted as resulting from an annihilation-creation
process, the annihilation of the antiphase domain walls creating six
ferroelectric domain walls merging at a single point.Comment: 5 pages, 3 figure
First-principles study of PbTiO under uniaxial strains and stresses
The behavior of PbTiO under uniaxial strains and stresses is investigated
from first-principles calculations within density functional theory. We show
that irrespectively of the uniaxial mechanical constraint applied, the system
keeps a purely ferroelectric ground-state, with the polarization aligned either
along the constraint direction ( phase) or along one of the pseudo-cubic
axis perpendicular to it ( phase). This contrasts with the cases of
isotropic or biaxial mechanical constraints for which novel phases combining
ferroelectic and antiferrodistortive motions have been previously reported.
Under uniaxial strain, PbTiO switched from a ground state under
compressive strain to ground-state under tensile strain, beyond a
critical strain \%. Under uniaxial stress, PbTiO
exhibits either a ground state under compression () or
a ground state under tension (). Here, however, an
abrupt jump of the structural parameters is also predicted under both
compressive and tensile stresses at critical values
GPa and GPa. This behavior appears similar to that predicted under
negative isotropic pressure and might reveal practically useful to enhance the
piezoelectric response in nanodevices.Comment: Submitted, 9 pages, 9 figure
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