Abstract: We studied the effect of sample geometry on the evolution of the superconducting state in nanoscale Nb circular and square loops by transport measurements. A multistage resistive transition with temperature is found for both samples, which is related to the effect of contact leads made from the same superconducting material. The H-T phase diagrams close to Tc0 show clear periodic oscillations on top of a parabolic background, i.e., Little-Parks effect. However, the amplitude of the oscillations decreases faster in the circular loop compared to the one in the square sample. Numerical simulations are conducted within the nonlinear Ginzburg-Landau theory to show the effect of sample geometry on the nucleation of superconductivity in superconducting loop structures.

Abstract: Electron continement and its effect on the superconducting-to-normal phase transition driven by a magentic field and/or a current is studied in nanowires. Our investigation is based on a self-consistent numerical solution of the Bogoliubov-de Gennes equations. We find that in a parallel magneitc field and/or in the presence of a supercurrent the transition from the superconducting to the normal phase occurs as a cascade of discontinuous jumps in the superconducting order parameter for diameters D < 10 divided by 15 nm at T = 0. The critical magentic field exhibits quantum-size oscillations with pronounced resonant enhancements as a function of the wire radius.

Abstract: We apply density-functional theory to study the adsorption of water clusters on the surface of a graphene sheet and find i) graphene is highly hydrophobic and ii) adsorbed water has very little effect on the electronic structure of graphene. A single water cluster on graphene has a very small average dipole moment which is in contrast with an ice layer that exhibits a strong dipole moment.

Abstract: We study single- and two-electron parabolic quantum dots in the presence of linear Dresselhaus and Rashba spin-orbit interactions. Contributions of both types of spin-orbit coupling are investigated in the context of the spin polarization of the system at high magnetic fields. We demonstrate that for negative Landé factors the effect of the Dresselhaus coupling is suppressed at high magnetic field, which for structures without inversion asymmetry leads to a completely spin-polarized system and a strict antisymmetry of the wave functions with respect to the interchange of spatial-electron coordinates. For negative Landé factor the Rashba coupling is preserved at high field and consequently the spin polarization of the systems as well as the spatial antisymmetry of the two-electron wave function remain approximate.

Abstract: Antagonistic symmetries of superconducting polygons and their induced multivortex states in a homogeneous magnetic field may lead to the appearance of antivortices in the vicinity of the superconducting/normal-state boundary (where mesoscopic confinement is particularly strong). Resulting vortex-antivortex (V-Av) molecules match the sample symmetry but are extremely sensitive to defects and fluctuations and remain undetected experimentally. Here we show that V-Av states can reappear deep in the superconducting state due to an array of perforations in a polygonal setting, surrounding a central hole. Such states are no longer caused by the symmetry of the sample but rather by pinning itself, which prevents the vortex-antivortex annihilation. As a result, even micron size, clearly spaced V-Av molecules can be stabilized in large mesoscopic samples.

Abstract: We investigate localized electron and hole states in parabolic quantum dots of biased graphene bilayers in the presence of a perpendicular magnetic field. These quantum dots can be created by means of nanostructured gates or by position-dependent doping, which can create a gap in the otherwise gapless dispersion of a graphene bilayer. Numerical results show the energy levels of confined electrons and holes as a function of the dot parameters and the magnetic field. Remarkable crossings of energy levels are found.

Abstract: The properties of a two-dimensional electron are investigated in the presence of a circular step magnetic-field profile. Both electrons with parabolic dispersion as well as Dirac electrons with linear dispersion are studied. We found that in such a magnetic quantum dot no electrons can be confined. Nevertheless close to the Landau levels quasibound states can exist with a rather long lifetime.

Abstract: The tunneling coupling in three vertically stacked (In,Ga)As/GaAs quantum rings is investigated. With increasing inter-ring separation (d), we find that the nonuniform strain results into a crossing of the lowest-energy electron states. Strain is also responsible for an increase in the ground electron energy above the level in the single quantum ring. The ground hole energy level exhibits decrease when d decreases, which is typical for antibonding states in an unstrained structure. These effects lead to a local maximum in the dependence of the ground-state exciton energy on d. Our theoretical results compare well with recent photoluminescence measurements but deviate considerably from the calculations for flat bands in quantum-ring molecules. We conclude that the nonuniform character of the strain distribution gives rise to a peculiar exciton hybridization in self-assembled quantum-ring molecules.

Abstract: We study the properties of a capacitive 13.56 MHz discharge with a mixture of Ar/C₂H₂ taking into account the plasmochemistry and growth of heavy hydrocarbons. A hybrid model was developed to combine the kinetic description for electron motion and the fluid approach for negative and positive ion transports and plasmochemical processes. A significant change in plasma parameters related to injection of 5.8% portion of acetylene in argon was observed and analyzed. We found that the electronegativity of the mixture is about 30%. The densities of negatively and positively charged heavy hydrocarbons are sufficiently large to be precursors for the formation of nanoparticles in the discharge volume.

Abstract: We investigate theoretically the ballistic transport in a two-dimensional electron gas, which is rolled up as a tube and is micro-structured into a Hall bar. A uniform magnetic field applied to such a curved surface results in a non-uniform perpendicular magnetic field. The bend resistances become asymmetric with respect to the orientation of the magnetic field due to the varying magnetic field along the junction. The resistance asymmetry is strongly affected by corrugation due to the varying mobility along different crystallographic directions. We compare our results with a recent transport measurement.

Abstract: We study the electron wave packet moving through a bent channel. We demonstrate that the packet transmission probability becomes an asymmetric function of the magnetic field when the electron packet is capacitively coupled to a metal plate. The coupling occurs through a nonlinear potential which translates a different kinetics of the transport for opposite magnetic-field orientations into a different potential felt by the scattered electron.

Abstract: The effect of a metallic gate on the bound states of a shallow donor located near the gate is studied. We calculate the energy spectrum as a function of the distance between the metallic gate and the donor and find an anti-crossing behavior in the energy levels for certain distances. We show how a transverse electric field can tune the average position of the electron with respect to the metallic gate and the impurity.

Abstract: We study vortex configurations in mesoscopic superconducting squares. Our theoretical approach is based on the analytical solution of the London equation using the Green's function method. The potential energy landscape found is then used in Langevin-type molecular-dynamics simulations to obtain stable vortex configurations. We show that the filling rules for vortices in squares with increasing applied magnetic field can be formulated, although in a different manner than in disks, in terms of the formation of vortex 'shells'. We discuss metastable states and the stability of the vortex configurations found with respect to variations of the material parameters and deformations of the shape of the sample.

Abstract: Using three-dimensional (3D) numerical discretization of the GinzburgLandau (GL) equations, we investigate the superconducting state of a sphere with a piercing hole in the presence of a magnetic field. In the case of samples with central perforation, in axially applied homogeneous magnetic field, we realized unconventional vortex states of broken symmetry due to complex, 3D competing interactions, which depend on the GL parameter ê. For certain sizes of the sample, non-hysteretic multi-vortex entry and exit is predicted with the non-existence of some vorticities as stable states. In a tilted magnetic field, we studied the gradual transformation of 3D flux patterns into 1D vortex chains, where vortices align along the perforation, and the evolvement of the multi-vortex entry as well. We analyze the flux-guiding ability of the hole in a tilted field, which leads to fractional flux response in magnetization M(H) curves.

Abstract: We study theoretically the simultaneous effect of regular and random pinning potentials on the vortex lattice structure at filling factor of 1. This structure is determined by a competition between the square symmetry of regular pinning array, by the intervortex interaction favoring a triangular symmetry, and by the randomness trying to depin vortices from their regular positions. Both analytical and molecular-dynamics approaches are used. We construct a phase diagram of the system in the plane of regular and random pinning strengths and determine typical vortex lattice defects appearing in the system due to the disorder. We find that the total disordering of the vortex lattice can occur either in one step or in two steps. For instance, in the limit of weak pinning, a square lattice of pinned vortices is destroyed in two steps. First, elastic chains of depinned vortices appear in the film; but the vortex lattice as a whole remains still pinned by the underlying square array of regular pinning sites. These chains are composed into fractal-like structures. In a second step, domains of totally depinned vortices are generated and the vortex lattice depins from regular array.