Abstract: Gold nanoparticles are studied extensively due to their unique optical and catalytical properties. Their exact shape determines the properties and thereby the possible applications. Electron tomography is therefore often used to examine the three-dimensional (3D) shape of nanoparticles. However, since the acquisition of the experimental tilt series and the 3D reconstructions are very time consuming, it is difficult to obtain statistical results concerning the 3D shape of nanoparticles. Here, we propose a new approach for electron tomography that is based on artificial neural networks. The use of a new reconstruction approach enables us to reduce the number of projection images with a factor of 5 or more. The decrease in acquisition time of the tilt series and use of an efficient reconstruction algorithm allows us to examine a large amount of nanoparticles in order to retrieve statistical results concerning the 3D shape.

Abstract: We study electron tunneling through a planar magnetic and electric barrier on the surface of a three-dimensional topological insulator. For the double barrier structures, we find (i) a directional-dependent tunneling which is sensitive to the magnetic field configuration and the electric gate voltage, (ii) a spin rotation controlled by the magnetic field and the gate voltage, (iii) many Fabry-Pérot resonances in the transmission determined by the distance between the two barriers, and (iv) the electrostatic potential can enhance the difference in the transmission between the two magnetization configurations, and consequently lead to a giant magnetoresistance. Points (i), (iii), and (iv) are alike with that in graphene stemming from the same linear-dispersion relations.

Abstract: We examine the propagation of the recently discovered electron vortex beams in a longitudinal magnetic field. We consider both the Aharonov-Bohm configuration with a single flux line and the Landau case of a uniform magnetic field. While stationary Aharonov-Bohm modes represent Bessel beams with flux- and vortex-dependent probability distributions, stationary Landau states manifest themselves as nondiffracting Laguerre-Gaussian beams. Furthermore, the Landau-state beams possess field- and vortex-dependent phases: (i) the Zeeman phase from coupling the quantized angular momentum to the magnetic field and (ii) the Gouy phase, known from optical Laguerre-Gaussian beams. Remarkably, together these phases determine the structure of Landau energy levels. This unified Zeeman-Landau-Gouy phase manifests itself in a nontrivial evolution of images formed by various superpositions of modes. We demonstrate that, depending on the chosen superposition, the image can rotate in a magnetic field with either (i) Larmor, (ii) cyclotron (double-Larmor), or (iii) zero frequency. At the same time, its centroid always follows the classical cyclotron trajectory, in agreement with the Ehrenfest theorem. Interestingly, the nonrotating superpositions reproduce stable multivortex configurations that appear in rotating superfluids. Our results open an avenue for the direct electron-microscopy observation of fundamental properties of free quantum-electron states in magnetic fields.

Abstract: The occurrence and origin of diffuse intensity contours in electron micrographs of AgBr crystals are investigated. The observations are interpreted in terms of a model, which attributes diffuse scattering to the presence of predominant atom or vacancy clusters of a particular polyhedral type. It is shown that irrespective of the crystal morphology, interstitial Ag ions order in AgBr material in clusters of finite size along 001 type planes. A different geometry of the diffuse intensity locus observed for triangular and hexagonal tabular grains is explained in terms of the different twin plane morphology of these grains.

Abstract: A parabolic quantum dot (QD) as realized by biasing nanostructured gates on bilayer graphene is investigated in the presence of electron-electron interaction. The energy spectrum and the phase diagram reveal unexpected transitions as a function of a magnetic field. For example, in contrast to semiconductor QDs, we find a valley transition rather than only the usual singlet-triplet transition in the ground state of the interacting system. The origin of these features can be traced to the valley degree of freedom in bilayer graphene. These transitions have important consequences for cyclotron resonance experiments.

Abstract: Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an additional conjecture, fulfilled in solvable limits, we suggest a simple expression of the ground state energy for an equally-spaced energy-level model, which is applicable along the whole crossover from the superconducting state to the pairing fluctuation regime. Solving Richardson equations numerically, we demonstrate a good accuracy of our expression.

Abstract: The fluorination of La2CuO4 can lead to different oxyfluoride compounds depending on the TF2 temperature of the fluorine gas treatment. When 150-degrees-C T(F2) less-than-or-equal-to 200-degrees-c less-than-or-equal-to 200-degrees-C a superconducting material is obtained. Previous neutron diffraction experiments as well as the EXAFS measurements at the La L(III) edge indicate that extra anions lie in an interstitial site between the two (LaO) layers. Electron diffraction patterns clearly show the existence of an incommensurate modulation due to the presence of shear planes. A second phase is also pointed out which can be obtained as a major component when the fluorination temperature is raised to 230-degrees-C. This phase which is not a superconductor crystallizes with the monoclinic symmetry.

Abstract: The fine structure of the Dirac energy spectrum in graphene induced by electron-optical phonon coupling is investigated in the portion of the spectrum near the phonon emission threshold. The derived new dispersion equation in the immediate neighborhood below the threshold corresponds to an electron-phonon bound state. We find that the singular vertex corrections beyond perturbation theory strongly increase the electron-phonon binding energy scale. The predicted enhancement of the effective electron-phonon coupling can be measured using angle-resolved spectroscopy.

Abstract: Small numbers N < 5 of two-dimensional Coulomb-interacting electrons trapped in a parabolic potential placed in a perpendicular magnetic field are investigated. The reduced wave function of this system, which is obtained by fixing the positions of N-1 electrons, exhibits strong correlations between the electrons and the zeros. These zeros axe often called vortices. An exact-diagonalization scheme is used to obtain the wave functions and the results are compared with results obtained from the recently proposed rotating electron molecule (REM) theory. We find that the vortices gather around the fixed electrons and repel each other, which is to a much lesser extend so for the REM results.