Abstract: We present a Ginzburg-Landau theory for a two-band superconductor with emphasis on MgB2. We propose experiments which lead to identification of the possible scenarios: whether both sigma- and pi-bands superconduct or sigma-alone. According to the second scenario a microscopic theory of superconducting MgB2 is proposed based on the strongly interacting or-electrons and non-correlated pi-electrons of boron ions. The kinematic and Coulomb interactions of sigma-electrons provide the superconducting state with an anisotropic gap of s(*)-wave symmetry. The critical temperature T-c has a non-monotonic dependence on the distance r between the centers of gravity of sigma- and pi-bands. The position of MgB2 on a bell-shaped curve T-c (r) is identified in the overdoped region. The derived superconducting density of electronic states is in agreement with available experimental and theoretical data. It is argued that the effects of pressure are crucial to identify the microscopic origin of superconductivity in MgB2. Possibilities for increase of T, are discussed.

Abstract: We present full ab initio calculations of the phonon band structure of thin Si nanowires oriented along the [110] direction. Using these phonon dispersion relations we investigate the structural stability of these wires. We found that all studied wires were stable also when doped with either B or P, if the unit cell was taken sufficiently large along the wire axis. The evolution of the phonon dispersion relations and of the sound velocities with respect to the wire diameters is discussed. Softening is observed for acoustic modes and hardening for optical phonon modes with increasing wire diameters.

Abstract: A system of classical charged particles interacting through a dipole repulsive potential, which are confined in a two-dimensional hardwall trap, is studied. The cluster consists of 16 particles, together with 4 defect particles. The technique of Brownian dynamics is used to simulate experimental binary colloidal systems [1]. The melting properties and the reentrant behavior of the system, which was studied before for clusters of identical particles [2], are studied for the binary mixture. The defect particles, which have a smaller charge than the other particles, stabilize the cluster, melt at a higher value of the coupling parameter F as compared to the other particles and have a strong influence on the melting properties of the other particles.

Abstract: We show that a superconducting quantum nanowire undergoes a new type of BCS-BEC crossover each time when an electron subband approaches the Fermi surface. In this case the longitudinal Cooper-pair size drops by two-three orders of magnitude down to a few nanometers. This unconventional BCS-BEC crossover is driven by quantum-size effects rather than by tuning the fermion-fermion interaction.

Abstract: Recent technological advances resulted in high-quality superconducting metallic nanofilms and nanowires. The physical properties of such nanostructures are governed by the size-quantization of the transverse electron spectrum. This has a substantial impact on the basic superconducting characteristics, e.g., the order parameter, the critical temperature and the critical magnetic field. In the present paper we give an overview of our theoretical results on this subject. Based on a numerical self-consistent solution of the Bogoliubov-de Gennes equations, we investigate how the superconducting properties are modified in the quantum-size regime.

Abstract: Certain crystals, consisting of molecules with unusually large spin, exhibit macroscopically observable signatures of quantum tunneling, when a slowly varying external magnetic field is applied parallel to the easy axis of the crystal. Recently it has been observed that jumps in the magnetization are sometimes accompanied by the emission of infrared radiation. We discuss the connection of the tunneling with the electromagnetic transition, and we address the questions: to what extent can the radiation be considered as a collective, superradiant emission, and what is the role played by the cavity in the experiments? Our conclusion is that among the reported experimental coditions the radiation is not superradidance, but rather a maserlike effect.

Abstract: We studied the optical Aharonov-Bohm effect for an exciton in a semiconductor quantum ring. A perpendicular electric field applied to a quantum ring with large height, is able to tune the exciton ground state energy such that it exhibits a weak observable Aharonov-Bohm oscillations. This Aharonov-Bohm effect is tunable in strength and period.

Abstract: Experimentally, multivortex states and giant vortex states in mesoscopic superconductors can be distinguished directly by using the multiple-small-tunnel-junctions, and indirectly by studying the temperature dependence of the expulsion fields. These experimental results are compared with the theoretical prediction from the nonlinear Ginzburg- Landau theory.