Vortex phases in mesoscopic cylinders with suppressed surface superconductivity

Vortex structures in mesoscopic cylinder placed in external magnetic field are studied under the general de Gennes boundary condition for the order parameter corresponding to the suppression of surface superconductivity. The Ginzburg-Landau equations are solved based on trial functions for the order parameter for vortex-free, single-vortex, multivortex, and giant vortex phases. The equilibrium vortex diagrams in the plane of external field and cylinder radius and magnetization curves are calculated at different values of de Gennes "extrapolation length" characterizing the boundary condition for the order parameter. The comparison of the obtained variational results with some available exact solutions shows good accuracy of our approach.Comment: RevTex, 11 pages, 10 figure

In Memoriam Leonid V. Keldysh

Leonid Keldysh -- one of the most influential theoretical physicists of the 20th century -- passed away in November 2016. Keldysh is best known for the diagrammatic formulation of real-time (nonequilibrium) Green functions theory and for the theory of strong field ionization of atoms. Both theories profoundly changed large areas of theoretical physics and stimulated important experiments. Both these discoveries emerged almost simultaneously -- like Einstein, also Keldysh had his \textit{annus mirabilis} -- the year 1964. But the list of his theoretical developments is much broader and is briefly reviewed here