Strain-induced ferroelectricity in simple rocksalt binary oxides

The alkaline earth binary oxides adopt a simple rocksalt structure and form an important family of compounds because of their large presence in the earth's mantle and their potential use in microelectronic devices. In comparison to the class of multifunctional ferroelectric perovskite oxides, however, their practical applications remain limited and the emergence of ferroelectricity and related functional properties in simple binary oxides seems so unlikely that it was never previously considered. Here, we show using first-principles density functional calculations that ferroelectricity can be easily induced in simple alkaline earth binary oxides such as barium oxide (BaO) using appropriate epitaxial strains. Going beyond the fundamental discovery, we show that the functional properties (polarization, dielectric constant and piezoelectric response) of such strained binary oxides are comparable in magnitude to those of typical ferroelectric perovskite oxides, so making them of direct interest for applications. Finally, we show that magnetic binary oxides such as EuO, with the same rocksalt structure, behave similarly to the alkaline earth oxides, suggesting a route to new multiferroics combining ferroelectric and magnetic properties

Trace anomaly of the conformal gauge field

The proposed by Bastianelli and van Nieuwenhuizen new method of calculations of trace anomalies is applied in the conformal gauge field case. The result is then reproduced by the heat equation method. An error in previous calculation is corrected. It is pointed out that the introducing gauge symmetries into a given system by a field-enlarging transformation can result in unexpected quantum effects even for trivial configurations.Comment: 9 pages, LaTeX file, BI-TP 93/3

Noncooperative algorithms in self-assembly

We show the first non-trivial positive algorithmic results (i.e. programs whose output is larger than their size), in a model of self-assembly that has so far resisted many attempts of formal analysis or programming: the planar non-cooperative variant of Winfree's abstract Tile Assembly Model. This model has been the center of several open problems and conjectures in the last fifteen years, and the first fully general results on its computational power were only proven recently (SODA 2014). These results, as well as ours, exemplify the intricate connections between computation and geometry that can occur in self-assembly. In this model, tiles can stick to an existing assembly as soon as one of their sides matches the existing assembly. This feature contrasts with the general cooperative model, where it can be required that tiles match on \emph{several} of their sides in order to bind. In order to describe our algorithms, we also introduce a generalization of regular expressions called Baggins expressions. Finally, we compare this model to other automata-theoretic models.Comment: A few bug fixes and typo correction

The importance of the electronic contribution to linear magnetoelectricity

We demonstrate that the electronic contribution to the linear magnetoelectric response, usually omitted in first-principles studies, can be comparable in magnitude to that mediated by lattice distortions, even for materials in which responses are strong. Using a self-consistent Zeeman response to an applied magnetic field for noncollinear electron spins, we show how electric polarization emerges in linear magnetoelectrics through both electronic- and lattice-mediated components -- in analogy with the high- and low-frequency dielectric response to an electric field. The approach we use is conceptually and computationally simple, and can be applied to study both linear and non-linear responses to magnetic fields.Comment: 5 pages, 3 figure