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: Responses of mesoscopic superconducting rings and disks to perpendicular magnetic fields are studied by using the multiple-small-tunnel-junction method, in which transport properties of several small tunnel junctions attached to the sample are measured simultaneously. This allows us for a direct experimental observation of the paramagnetic supercurrent, which is closely related to the paramagnetic Meissner effect. The results are compared with numerical results based on the nonlinear Ginzburg-Landau theory.

Abstract: The rate of water flow through hydrophobic nanocapillaries is greatly enhanced as compared to that expected from macroscopic hydrodynamics. This phenomenon is usually described in terms of a relatively large slip length, which is in turn defined by such microscopic properties as the friction between water and capillary surfaces and the viscosity of water. We show that the viscosity of water and, therefore, its flow rate are profoundly affected by the layered structure of confined water if the capillary size becomes less than 2 nm. To this end, we study the structure and dynamics of water confined between two parallel graphene layers using equilibrium molecular dynamics simulations. We find that the shear viscosity is not only greatly enhanced for subnanometer capillaries, but also exhibits large oscillations that originate from commensurability between the capillary size and the size of water molecules. Such oscillating behavior of viscosity and, consequently, the slip length should be taken into account in designing and studying graphene-based and similar membranes for desalination and filtration.