Importance of van der Waals interactions for ab initio studies of topological insulators

We investigate the lattice and electronic structures of the bulk and surface of the prototypical layered topological insulators Bi$_2$Se$_3$ and Bi$_2$Te$_3$ using ab initio density functional methods, and systematically compare the results of different methods of including van der Waals (vdW) interactions. We show that the methods utilizing semi-empirical energy corrections yield accurate descriptions of these materials, with the most precise results obtained by properly accounting for the long-range tail of the vdW interactions. The bulk lattice constants, distances between quintuple layers and the Dirac velocity of the topological surface states (TSS) are all in excellent agreement with experiment. In Bi$_2$Te$_3$, hexagonal warping of the energy dispersion leads to complex spin textures of the TSS at moderate energies, while in Bi$_2$Se$_3$ these states remain almost perfectly helical away from the Dirac point, showing appreciable signs of hexagonal warping at much higher energies, above the minimum of the bulk conduction band. Our results establish a framework for unified and systematic self-consistent first principles calculations of topological insulators in bulk, slab and interface geometries, and provides the necessary first step towards ab initio modeling of topological heterostructures.Comment: 26 pages, 7 figures. This is the Accepted Manuscript version of an article accepted for publication in Journal of Physics: Condensed Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://dx.doi.org/10.1088/1361-648X/abbdb

Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and hausdorff dimension

Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal ows on homogeneous spaces nG, where G is any connected semisimple Lie group of real rank 1 with nite center, and is any nonuniform lattice in G. We show that this bound is sharp, and apply the methods used to establish bounds for the Hausdorff dimension of the set of points which diverge on average

Escape of mass and entropy for diagonal flows in real rank one situations

Let G be a connected semisimple Lie group of real rank 1 with finite center, let be a non-uniform lattice in G and a any diagonalizable element in G. We investigate the relation between the metric entropy of a acting on the homogeneous space \G and escape of mass. Moreover, we provide bounds on the escaping mass and, as an application, we show that the Hausdorff dimension of the set of orbits (under iteration of a) which miss a fixed open set is not full

The fine art of euclidean geometry Viviani’s theorem . . . and a cousin

‘‘ I think it is said that Gauss had ten different proofs for the law of quadratic reciprocity. Any good theorem should have several proofs, the more the better. For two reasons: usually, different proofs have different strengths and weaknesses, and they generalise in different directions — they are not just repetitions of each other. ’’ Sir Michael Atiyah, interview in European Mathematical Society Newsletter, September 2004

Solvent free synthesis of n-alkylated imino indoline-2-one derivatives under microwave irradiation

The solvent-free microwave-assisted syntheses of N-alkyl isatin Schiff base derivatives are reported. These isatin derivatives are obtained as a result of the condensation of an isatin compound with a benzyl halide and an aniline derivatives using microwave irradiation condition in high yield and short reaction time.               KEY WORDS: Microwave, Isatin derivatives, Solvent free, Combinatorial synthesis Bull. Chem. Soc. Ethiop. 2018, 32(2), 393-398.DOI: https://dx.doi.org/10.4314/bcse.v32i2.1

Angiopoietin-2 predicts morbidity in adults with Fontan physiology.

Morbidity in patients with single-ventricle Fontan circulation is common and includes arrhythmias, edema, and pulmonary arteriovenous malformations (PAVM) among others. We sought to identify biomarkers that may predict such complications. Twenty-five patients with Fontan physiology and 12 control patients with atrial septal defects (ASD) that underwent cardiac catheterization were included. Plasma was collected from the hepatic vein and superior vena cava and underwent protein profiling for a panel of 20 analytes involved in angiogenesis and endothelial dysfunction. Ten (40%) of Fontan patients had evidence of PAVM, eighteen (72%) had a history of arrhythmia, and five (20%) were actively in arrhythmia or had a recent arrhythmia. Angiopoietin-2 (Ang-2) was higher in Fontan patients (8,875.4 ± 3,336.9 pg/mL) versus the ASD group (1,663.6 ± 587.3 pg/mL, p < 0.0001). Ang-2 was higher in Fontan patients with active or recent arrhythmia (11,396.0 ± 3,457.7 vs 8,118.2 ± 2,795.1 pg/mL, p < 0.05). A threshold of 8,500 pg/mL gives Ang-2 a negative predictive value of 100% and positive predictive value of 42% in diagnosing recent arrhythmia. Ang-2 is elevated among adults with Fontan physiology. Ang-2 level is associated with active or recent arrhythmia, but was not found to be associated with PAVM