Explicit computation of Drinfeld associator in the case of the fundamental representation of gl(N)

We solve the regularized Knizhnik-Zamolodchikov equation and find an explicit expression for the Drinfeld associator. We restrict to the case of the fundamental representation of $gl(N)$. Several tests of the results are presented. It can be explicitly seen that components of this solution for the associator coincide with certain components of WZW conformal block for primary fields. We introduce the symmetrized version of the Drinfeld associator by dropping the odd terms. The symmetrized associator gives the same knot invariants, but has a simpler structure and is fully characterized by one symmetric function which we call the Drinfeld prepotential.Comment: 14 pages, 2 figures; several flaws indicated by referees correcte

Non-perturbative results for the spectrum of surface-disordered waveguides

We calculated the spectrum of normal scalar waves in a planar waveguide with absolutely soft randomly rough boundaries beyond the perturbation theories in the roughness heights and slopes, basing on the exact boundary scattering potential. The spectrum is proved to be a nearly real non-analytic function of the dispersion $\zeta^2$ of the roughness heights (with square-root singularity) as $\zeta^2 \to 0$. The opposite case of large boundary defects is summarized.Comment: REVTEX 3, OSA style, 9 pages, no figures. Submitted to Optics Letter

On stoichiometry and intermixing at the spinel/perovskite interface in CoFe2O4/BaTiO3 thin films

The performance of complex oxide heterostructures depends primarily on the interfacial coupling of the two component structures. This interface character inherently varies with the synthesis method and conditions used since even small composition variations can alter the electronic, ferroelectric, or magnetic functional properties of the system. The focus of this article is placed on the interface character of a pulsed laser deposited CoFe2O4/BaTiO3 thin film. Using a range of state-of-the-art transmission electron microscopy methodologies, the roles of substrate morphology, interface stoichiometry, and cation intermixing are determined on the atomic level. The results reveal a surprisingly uneven BaTiO3 substrate surface formed after the film deposition and Fe atom incorporation in the top few monolayers inside the unit cell of the BaTiO3 crystal. Towards the CoFe2O4 side, a disordered region extending several nanometers from the interface was revealed and both Ba and Ti from the substrate were found to diffuse into the spinel layer. The analysis also shows that within this somehow incompatible composite interface, a different phase is formed corresponding to the compound Ba2Fe3Ti5O15, which belongs to the ilmenite crystal structure of FeTiO3 type. The results suggest a chemical activity between these two oxides, which could lead to the synthesis of complex engineered interfaces

In situ transmission electron microscopy of resistive switching in thin silicon oxide layers

Silicon oxide-based resistive switching devices show great potential for applications in nonvolatile random access memories. We expose a device to voltages above hard breakdown and show that hard oxide breakdown results in mixing of the SiOx layer and the TiN lower contact layers. We switch a similar device at sub-breakdown fields in situ in the transmission electron microscope (TEM) using a movable probe and study the diffusion mechanism that leads to resistance switching. By recording bright-field (BF) TEM movies while switching the device, we observe the creation of a filament that is correlated with a change in conductivity of the SiOx layer. We also examine a device prepared on a microfabricated chip and show that variations in electrostatic potential in the SiOx layer can be recorded using off-axis electron holography as the sample is switched in situ in the TEM. Taken together, the visualization of compositional changes in ex situ stressed samples and the simultaneous observation of BF TEM contrast variations, a conductivity increase, and a potential drop across the dielectric layer in in situ switched devices allow us to conclude that nucleation of the electroforming—switching process starts at the interface between the SiOx layer and the lower contact

Structural, chemical and magnetic properties of secondary phases in Co-doped ZnO

We have utilized a comprehensive set of experimental techniques such as transmission electron microscopy (TEM) and synchrotron-based x-ray absorption spectroscopy (XAS) and the respective x-ray linear dichroism and x-ray magnetic circular dichroism to characterize the correlation of structural, chemical and magnetic properties of Co-doped ZnO samples. It can be established on a quantitative basis that the superparamagnetic (SPM) behavior observed by integral superconducting quantum interference device magnetometry is not an intrinsic property of the material but stems from precipitations of metallic Co. Their presence is revealed by TEM as well as XAS. Annealing procedures for these SPM samples were also studied, and the observed changes in the magnetic properties found to be due to a chemical reduction or oxidation of the metallic Co species

Alignment of electron optical beam shaping elements using a convolutional neural network

A convolutional neural network is used to align an orbital angular momentum sorter in a transmission electron microscope. The method is demonstrated using simulations and experiments. As a result of its accuracy and speed, it offers the possibility of real-time tuning of other electron optical devices and electron beam shaping configurations