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