61 research outputs found
Compositional uniformity, domain patterning and the mechanism underlying nano-chessboard arrays
We propose that systems exhibiting compositional patterning at the nanoscale,
so far assumed to be due to some kind of ordered phase segregation, can be
understood instead in terms of coherent, single phase ordering of minority
motifs, caused by some constrained drive for uniformity. The essential features
of this type of arrangements can be reproduced using a superspace construction
typical of uniformity-driven orderings, which only requires the knowledge of
the modulation vectors observed in the diffraction patterns. The idea is
discussed in terms of a simple two dimensional lattice-gas model that simulates
a binary system in which the dilution of the minority component is favored.
This simple model already exhibits a hierarchy of arrangements similar to the
experimentally observed nano-chessboard and nano-diamond patterns, which are
described as occupational modulated structures with two independent modulation
wave vectors and simple step-like occupation modulation functions.Comment: Preprint. 11 pages, 11 figure
Topological quantum chemistry
The past decade's apparent success in predicting and experimentally
discovering distinct classes of topological insulators (TIs) and semimetals
masks a fundamental shortcoming: out of 200,000 stoichiometric compounds extant
in material databases, only several hundred of them are topologically
nontrivial. Are TIs that esoteric, or does this reflect a fundamental problem
with the current piecemeal approach to finding them? To address this, we
propose a new and complete electronic band theory that highlights the link
between topology and local chemical bonding, and combines this with the
conventional band theory of electrons. Topological Quantum Chemistry is a
description of the universal global properties of all possible band structures
and materials, comprised of a graph theoretical description of momentum space
and a dual group theoretical description in real space. We classify the
possible band structures for all 230 crystal symmetry groups that arise from
local atomic orbitals, and show which are topologically nontrivial. We show how
our topological band theory sheds new light on known TIs, and demonstrate the
power of our method to predict a plethora of new TIs.Comment: v1: 8 pages + 40 pages supplemenetary material. Previously submitted
v2: ~ Published version. 11 pages + 79 pages supplementary material.
Descriptions of the data used in this paper can be found in arXiv:1706.08529
and arXiv:1706.09272. All data can be accessed via the Bilbao
Crystallographic Server (http://cryst.ehu.es). Two additional papers
elaborating on the general theory currently in pre
Graph Theory Data for Topological Quantum Chemistry
Topological phases of noninteracting particles are distinguished by global
properties of their band structure and eigenfunctions in momentum space. On the
other hand, group theory as conventionally applied to solid-state physics
focuses only on properties which are local (at high symmetry points, lines, and
planes) in the Brillouin zone. To bridge this gap, we have previously [B.
Bradlyn et al., Nature 547, 298--305 (2017)] mapped the problem of constructing
global band structures out of local data to a graph construction problem. In
this paper, we provide the explicit data and formulate the necessary algorithms
to produce all topologically distinct graphs. Furthermore, we show how to apply
these algorithms to certain "elementary" band structures highlighted in the
aforementioned reference, and so identified and tabulated all orbital types and
lattices that can give rise to topologically disconnected band structures.
Finally, we show how to use the newly developed BANDREP program on the Bilbao
Crystallographic Server to access the results of our computation.Comment: v1: 29 Pages, 13 Figures. Explains how to access the data presented
in arXiv:1703.02050 v2: Accepted version. References updated, figures
improve
Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
The link between chemical orbitals described by local degrees of freedom and
band theory, which is defined in momentum space, was proposed by Zak several
decades ago for spinless systems with and without time-reversal in his theory
of "elementary" band representations. In Nature 547, 298-305 (2017), we
introduced the generalization of this theory to the experimentally relevant
situation of spin-orbit coupled systems with time-reversal symmetry and proved
that all bands that do not transform as band representations are topological.
Here, we give the full details of this construction. We prove that elementary
band representations are either connected as bands in the Brillouin zone and
are described by localized Wannier orbitals respecting the symmetries of the
lattice (including time-reversal when applicable), or, if disconnected,
describe topological insulators. We then show how to generate a band
representation from a particular Wyckoff position and determine which Wyckoff
positions generate elementary band representations for all space groups. This
theory applies to spinful and spinless systems, in all dimensions, with and
without time reversal. We introduce a homotopic notion of equivalence and show
that it results in a finer classification of topological phases than approaches
based only on the symmetry of wavefunctions at special points in the Brillouin
zone. Utilizing a mapping of the band connectivity into a graph theory problem,
which we introduced in Nature 547, 298-305 (2017), we show in companion papers
which Wyckoff positions can generate disconnected elementary band
representations, furnishing a natural avenue for a systematic materials search.Comment: 15+9 pages, 4 figures; v2: minor corrections; v3: updated references
(published version
Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem
The conventional theory of solids is well suited to describing band
structures locally near isolated points in momentum space, but struggles to
capture the full, global picture necessary for understanding topological
phenomena. In part of a recent paper [B. Bradlyn et al., Nature 547, 298
(2017)], we have introduced the way to overcome this difficulty by formulating
the problem of sewing together many disconnected local "k-dot-p" band
structures across the Brillouin zone in terms of graph theory. In the current
manuscript we give the details of our full theoretical construction. We show
that crystal symmetries strongly constrain the allowed connectivities of energy
bands, and we employ graph-theoretic techniques such as graph connectivity to
enumerate all the solutions to these constraints. The tools of graph theory
allow us to identify disconnected groups of bands in these solutions, and so
identify topologically distinct insulating phases.Comment: 19 pages. Companion paper to arXiv:1703.02050 and arXiv:1706.08529
v2: Accepted version, minor typos corrected and references added. Now
19+epsilon page
On the possibility of magnetic Weyl fermions in non-symmorphic compound PtFeSb
Weyl fermions are expected to exhibit exotic physical properties such as the
chiral anomaly, large negative magnetoresistance or Fermi arcs. Recently a new
platform to realize these fermions has been introduced based on the appearance
of a three-fold band crossing at high symmetry points of certain space groups.
These band crossings are composed of two linearly dispersed bands that are
topologically protected by a Chern number, and a at band with no topological
charge. In this paper we present a new way of inducing two kinds of Weyl
fermions, based on two- and three-fold band crossings, in the non-symmorphic
magnetic material PtFeSb. By means of density functional theory calculations
and group theory analysis we show that magnetic order can split a six-fold
degeneracy enforced by non-symmoprhic symmetry to create three-fold or two-fold
degenerate Weyl nodes. We also report on the synthesis of a related phase
potentially containing two-fold degenerate magnetic Weyl points and extend our
group theory analysis to that phase. This is the first study showing that
magnetic ordering has the potential to generate new threefold degenerate Weyl
nodes, advancing the understanding of magnetic interactions in topological
materials.Comment: 8 pages, 5 figure
Catalogue of topological phonon materials
Phonons play a crucial role in many properties of solid state systems, such
as thermal and electrical conductivity, neutron scattering and associated
effects or superconductivity. Hence, it is expected that topological phonons
will also lead to rich and unconventional physics and the search of materials
hosting topological phonons becomes a priority in the field. In electronic
crystalline materials, a large part of the topological properties of Bloch
states can be indicated by their symmetry eigenvalues in reciprocal space. This
has been adapted to the high-throughput calculations of topological materials,
and more than half of the stoichiometric materials on the databases are found
to be topological insulators or semi-metals. Based on the existing phonon
materials databases, here we have performed the first catalogue of topological
phonon bands for more than ten thousand three-dimensional crystalline
materials. Using topological quantum chemistry, we calculate the band
representations, compatibility relations, and band topologies of each isolated
set of phonon bands for the materials in the phonon databases. We have also
calculated the real space invariants for all the topologically trivial bands
and classified them as atomic and obstructed atomic bands. In particular,
surface phonon modes (dispersion) are calculated on different cleavage planes
for all the materials. Remarkably, we select more than one thousand "ideal"
non-trivial phonon materials to fascinate the future experimental studies. All
the data-sets obtained in the the high-throughput calculations are used to
build a Topological Phonon Database.Comment: 8+535 pages, 187 figures, 21 tables. The Topological Phonon Database
is available at https://www.topologicalquantumchemistry.com/topophonons or
https://www.topologicalquantumchemistry.fr/topophonon
The diagnostic value of endoscopy and Helicobacter pylori tests for peptic ulcer patients in late post-treatment setting
BACKGROUND: Guidelines for management of peptic ulcer patients after the treatment are largely directed to detection of H. pylori infection using only non-invasive tests. We compared the diagnostic value of non-invasive and endoscopy based H. pylori tests in a late post-treatment setting. METHODS: Altogether 34 patients with dyspeptic complaints were referred for gastroscopy 5 years after the treatment of peptic ulcer using a one-week triple therapy scheme. The endoscopic and histologic findings were evaluated according to the Sydney classification. Bacteriological, PCR and cytological investigations and (13)C-UBT tests were performed. RESULTS: Seventeen patients were defined H. pylori positive by (13)C-UBT test, PCR and histological examination. On endoscopy, peptic ulcer persisted in 4 H. pylori positive cases. Among the 6 cases with erosions of the gastric mucosa, only two patients were H. pylori positive. Mucosal atrophy and intestinal metaplasia were revealed both in the H. pylori positive and H. pylori negative cases. Bacteriological examination revealed three clarithromycin resistant H. pylori strains. Cytology failed to prove validity for diagnosing H. pylori in a post-treatment setting. CONCLUSIONS: In a late post-treatment setting, patients with dyspepsia should not be monitored only by non-invasive investigation methods; it is also justified to use the classical histological evaluation of H. pylori colonisation, PCR and bacteriology as they have shown good concordance with (13)C-UBT. Moreover, endoscopy and histological investigation of a gastric biopsy have proved to be the methods with an additional diagnostic value, providing the physician with information about inflammatory, atrophic and metaplastic lesions of the stomach in dyspeptic H. pylori positive and negative patients. Bacteriological methods are suggested for detecting the putative antimicrobial resistance of H. pylori, aimed at successful eradication of infection in persistent peptic ulcer cases
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