Superconductivity in granular metals

The thesis by Igor Beloborodov explores several intriguing aspects of superconductivity in granulated materials, driven by recent experimental findings from leading global laboratories. The complex nature of granulated conductors and superconductors necessitates the development of new theoretical methods, which may reveal novel effects that align with experimental observations. The work addresses multiple problems in detail. The first section focuses on calculating the resistivity in a granulated superconductor when a strong magnetic field disrupts the superconducting gap. It demonstrates that as the magnetic field decreases, resistivity initially increases before eventually dropping to zero, explaining recent experimental observations. The second section examines the density of states in a single superconducting grain affected by magnetic impurities, presenting original calculations that explicitly determine the density of states. The third part, though unfinished, indicates that the phenomenon of "quantum dissipation," widely discussed over the past two decades, may differ significantly from conventional understandings. The thesis employs modern theoretical physics techniques, including diagrammatic expansions and random matrix theory, while also discussing experimental contexts. This work serves as a valuable resource for researchers interested in the physics of mesoscopic and granulated conductors and superconductors.