Superconductivity in granular metals

The thesis of Igor Beloborodov is devoted to study of several interesting aspects of superconductivity in granulated materials. The theoretical investigation presented here is motivated by recent experiments performed in leading laboratories in the world. Although there are many peculiar features of the systems that make them interesting to experimentalists and material scientists, theory of granulated conductors and superconductors is quite complicated and not less interesting. It demands development of new methods and one can expect new effects that can be directly compared with existing experiments.

Several different problems are considered in detail in the present thesis. The first part of the work is devoted to calculation of the resistivity in a granulated superconductor in the situation when the superconducting gap is destroyed by a strong magnetic field. It contains a nice demonstration that when decreasing the magnetic field the resistivity first grows and only later drops to zero. This can explain an experiment carried out recently where such an effect was observed. In the second part the author considers the density of states in a single superconducting grain in the presence of magnetic impurities. Although, some qualitative considerations existed in the literature the method of calculations and the calculations themselves are completely original and the density of states is found explicitly. The third part contains a work that has not been finished yet. However, these preliminary results already show that a phenomenon of the so called "quantum dissipation" which is under intensive discussion in the last two decades, may be quite different from the usually excepted picture.

The results obtained in the thesis are performed using modern methods of theoretical physics including diagrammatic expansions, random matrix theory, functional integrations, etc. At the same time, a discussion of experiments is also presented. Reading of the thesis can be of a great help for researches who want to learn what is going in the physics of mesoscopic and granulated conductors and superconductors.