A short guide to topological terms in the effective theories of condensed matter

Abstract

This article is meant as a gentle introduction to the topological terms that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples, mainly from the area of quantum magnetism and superfluids/superconductors. We then briefly discuss how these ideas are now finding incarnations in the studies of symmetry-protected topological phases, which are in a sense a generalization of the concept of topological insulators to a wider range of materials, including magnets and cold atoms.     

Influence of Mo doping on the tribological behavior of Ti3AlC2 ceramic at different temperatures

(Ti_0·8Mo_0.2)₃AlC₂ solid solutions were successfully synthesized from Ti, Al, TiC, and Mo powders using the in situ hot-pressing sintering method. The tribological properties of (Ti_0·8Mo_0.2)₃AlC₂ and the reference Ti₃AlC₂ in the temperature range 25–800 °C were evaluated in ambient air with the counterpart of Al₂O₃ balls. The results show that (Ti_0·8Mo_0.2)₃AlC₂ has improved lubricating properties and wear resistance above 400 °C compared with Ti₃AlC₂. This can be contributed to the formation of tribo-oxidation films containing MoO₃ and MoO_3-x. Structural characterization of the tribo-oxidation films was conducted using SEM, EDS, Raman spectroscopy, and XPS to evaluate the effect of Mo doping on the wear mechanisms of Ti₃AlC₂ in detail.     

Frequency and phase estimation in time series with quasi periodic components

In this article, we consider frequency and phase estimation in a noisy oscillation with potentially non‐constant phase increments resulting from an underlying non‐constant frequency. A maximum periodogram method on segments is used to estimate the time‐varying frequency and a subsequent least squares approach to estimate the phase. A key problem addressed in this article is the question how to set up a meaningful concept of asymptotic statistics for this model. This problem is solved by a special infill asymptotics concept. We use this concept to prove consistency and asymptotic normality of the estimates. Furthermore, the phase estimate is compared to the Hilbert transform in a simulation.     

Asymmetric Autocatalysis Triggered by Chiral Crystals Formed from Achiral Compounds and Chiral Isotopomers

Asymmetric autocatalysis with amplification of enantiomeric excess is found in the enantioselective addition of diisopropylzinc to pyrimidine-5-carbaldehyde using pyrimidyl alkanol as an asymmetric autocatalyst. Asymmetric autocatalysis has been employed as a method for clarifying the origin of homochirality. Circularly polarized light, inorganic chiral crystals and statistical fluctuation of enantiomeric imbalance act as chiral initiators in asymmetric autocatalysis to afford highly enantioenriched products. We have investigated asymmetric autocatalysis using chiral crystals formed from achiral and racemic compounds as an origin of chirality. Absolute control of the crystal chirality of cytosine was achieved by the removal of crystal water. Enantioselective carbon-carbon bond formation at the enantiotopic crystal face of aldehydes was established using diisopropylzinc vapor. In addition, asymmetric autocatalysis triggered by chiral compounds arising from H, C and O isotope substitution has been achieved.     

Hot tearing susceptibility of MgZn4.5YxZr0.5 alloys and mechanism

The hot tearing susceptibility of MgZn_(4.5)Y_xZr_(0.5)(x = 0.5, 1, 2, 4, 6) alloys was evaluated using ClyneDavies' theoretical model and a constrained rod casting(CRC) apparatus equipped with a load cell and data acquisition system. The results obtained from these two approaches were in good agreement, illustrating that the hot tearing susceptibility of the investigated alloys is in the order of MgZn_(4.5)Y_xZr_(0.5) MgZn_(4.5)Y_xZr_(0.5) MgZn_(4.5)Y_xZr_(0.5) MgZn_(4.5)Y_xZr_(0.5) MgZn_(4.5)Y_xZr_(0.5). The microstructure and morphology of hot tearing regions were observed by means of X-ray diffraction and scanning electron microscopy. The function curves on variation of contraction force and temperature versus time were recorded by a computer during solidification of the MgZn_(4.5)Y_xZr_(0.5) alloys in a "T" type mold after A/D(Analog to digital) conversion. Results show that both the amount and morphology of the second phases have a great relationship with the hot tearing susceptibility. But the former plays a more important role on that of MgZn_(4.5)Y_xZr_(0.5) alloys. The role of low-melting point eutectic phases on the hot tearing susceptibility of MgZn_(4.5)Y_xZr_(0.5) alloys changes gradually with different Y contents. When Y ≤ 1wt.%, it is mainly a damaging effect on intergranular bonding force; when Y 1wt.%, it is mainly an intergranular feeding effect on formed separated dendrites.     

Role of thermodynamic miscibility gaps in phase selection in sol-gel synthesis of yttrium silicates

Yttrium monosilicate and disilicate are important materials for environmental barrier coatings. The two silicates were synthesized by sol-gel route and their phase selection upon calcination and thermal exposure was studied. First products of crystallization were the monosilicate and yttria. Amorphous silica precipitated out at 1300 °C as apatite phase. During prolonged high temperature treatment, up to 100 h at 1400 °C, the apatite disappeared and the disilicate appeared, only to disappear itself as the system approached equilibrium. Thermodynamic calculations performed using Thermo-Calc software show the presence of a metastable miscibility gaps in the amorphous (liquid) phase field. As a consequence, phase separation in the amorphous phase prior to crystallization is responsible for the formation of yttria-rich and silica-rich phases during crystallization. Multiple phase formation during both, yttrium monosilicate and disilicate synthesis is consistent with the presence of the amorphous phase miscibility gaps around the silicate compositions.     

Expanding the Toolbox of R-Selective Amine Transaminases by Identification and Characterization of New Members

Amine transaminases (ATAs) are used to synthesize enantiomerically pure amines, which are building blocks for pharmaceuticals and agrochemicals. R-selective ATAs belong to the fold type IV PLP-dependent enzymes, and different sequence-, structure- and substrate scope-based features have been identified in the past decade. However, our knowledge is still restricted due to the limited number of characterized (R)-ATAs, with additional bias towards fungal origin. We aimed to expand the toolbox of (R)-ATAs and contribute to the understanding of this enzyme subfamily. We identified and characterized four new (R)-ATAs. The ATA from Exophiala sideris contains a motif characteristic for d -ATAs, which was previously believed to be a disqualifying factor for (R)-ATA activity. The crystal structure of the ATA from Shinella is the first from a Gram-negative bacterium. The ATAs from Pseudonocardia acaciae and Tetrasphaera japonica are the first characterized (R)-ATAs with a shortened/missing N-terminal helix. The active-site charges vary significantly between the new and known ATAs, correlating with their diverging substrate scope.     

Stationary and Progressive Phenotypes Caused by the p.G90D Mutation in Rhodopsin Gene

Mutations in rhodopsin gene (RHO) are a frequent cause of retinitis pigmentosa (RP) and less often, congenital stationary night blindness (CSNB). Mutation p.G90D has previously been associated with CSNB based on the examination of one family. This study screened 60 patients. Out of these 60 patients, 32 were affected and a full characterization was conducted in 15 patients. We described the clinical characteristics of these 15 patients (12 male, median age 42 years, range 8–71) from three families including visual field (Campus Goldmann), fundus autofluorescence (FAF), optical coherence tomography (OCT) and electrophysiology. Phenotypes were classified into four categories: CSNB (N = 3, 20%) sector RP (N = 3, 20%), pericentral RP (N = 1, 6.7%) and classic RP (N = 8, 53.3% (8/15)). The phenotypes were not associated with family, sex or age (Kruskal–Wallis, p > 0.05), however, cystoid macular edema (CME) was observed only in one family. Among the subjects reporting nyctalopia, 69% (22/32) were male. The clinical characteristics of the largest p.G90D cohort so far showed a large frequency of progressive retinal degeneration with 53.3% developing RP, contrary to the previous report.