Magnetoelectric properties of 500 nm Cr2O3 films

The linear magnetoelectric effect was measured in 500 nm Cr2O3 films grown by rf sputtering on Al2O3 substrates between top and bottom thin film Pt electrodes. Magnetoelectric susceptibility was measured directly by applying an AC electric field and measuring the induced AC magnetic moment using superconducting quantum interference device magnetometry. A linear dependence of the induced AC magnetic moment on the AC electric field amplitude was found. The temperature dependence of the magnetoelectric susceptibility agreed qualitatively and quantitatively with prior measurements of bulk single crystals, but the characteristic temperatures of the film were lower than those of single crystals. It was also possible to reverse the sign of the magnetoelectric susceptibility by reversing the sign of the magnetic field applied during cooling through the N\'eel temperature. A competition between total magnetoelectric and Zeeman energies is proposed to explain the difference between film and bulk Cr2O3 regarding the cooling field dependence of the magnetoelectric effect.Comment: accepted at Physical Review

A Hardy inequality in twisted waveguides

We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes. Namely, it is known that any local bending, no matter how small, generates eigenvalues below the essential spectrum of the Laplacian in the tubes with arbitrary cross-sections rotated along a reference curve in an appropriate way. In the present paper we show that for any other rotation some critical strength of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page

Asymptotic behaviour of the spectrum of a waveguide with distant perturbations

We consider the waveguide modelled by a $n$-dimensional infinite tube. The operator we study is the Dirichlet Laplacian perturbed by two distant perturbations. The perturbations are described by arbitrary abstract operators ''localized'' in a certain sense, and the distance between their ''supports'' tends to infinity. We study the asymptotic behaviour of the discrete spectrum of such system. The main results are a convergence theorem and the asymptotics expansions for the eigenvalues. The asymptotic behaviour of the associated eigenfunctions is described as well. We also provide some particular examples of the distant perturbations. The examples are the potential, second order differential operator, magnetic Schroedinger operator, curved and deformed waveguide, delta interaction, and integral operator

Coherent control of injection currents in high-quality films of Bi2Se3

Films of the topological insulator Bi2Se3 are grown by molecular beam epitaxy with in-situ reflection high-energy electron diffraction. The films are shown to be high-quality by X-ray reflectivity and diffraction and atomic-force microscopy. Quantum interference control of photocurrents is observed by excitation with harmonically related pulses and detected by terahertz radiation. The injection current obeys the expected excitation irradiance dependence, showing linear dependence on the fundamental pulse irradiance and square-root irradiance dependence of the frequency-doubled optical pulses. The injection current also follows a sinusoidal relative-phase dependence between the two excitation pulses. These results confirm the third-order nonlinear optical origins of the coherently controlled injection current. Experiments are compared to a tight-binding band structure to illustrate the possible optical transitions that occur in creating the injection current.Comment: 11 pages, 3 figure, journal articl

On spectrum of a Schroedinger operator with a fast oscillating compactly supported potential

We study the phenomenon of an eigenvalue emerging from essential spectrum of a Schroedinger operator perturbed by a fast oscillating compactly supported potential. We prove the sufficient conditions for the existence and absence of such eigenvalue. If exists, we obtain the leading term of its asymptotics expansion.Comment: The article is originally written in Russian. The translation in English is made by D. Boriso

Bose-Einstein Condensation in Geometrically Deformed Tubes

We show that Bose-Einstein condensate can be created in quasi-one-dimensional systems in a purely geometrical way, namely by bending or other suitable deformation of a tube.Comment: RevTex, 4pages, no figure

Spectrum of the Schr\"odinger operator in a perturbed periodically twisted tube

We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of "slowing down" the twisting in the mean gives rise to a non-empty discrete spectrum.Comment: LaTeX2e, 10 page