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Abstract: The current understanding of the superconductor-insulator transition isdiscussed level by level in a cyclic spiral-like manner. At the first level,physical phenomena and processes are discussed which, while of no formalrelevance to the topic of transitions, are important for their implementationand observation; these include superconductivity in low electron densitymaterials, transport and magnetoresistance in superconducting island films andin highly resistive granular materials with superconducting grains, and theBerezinskii-Kosterlitz-Thouless transition. The second level discusses andsummarizes results from various microscopic approaches to the problem, whetherbased on the Bardeen-Cooper-Schrieffer theory the disorder-induced reductionin the superconducting transition temperature; the key role of Coulomb blockadein high-resistance granular superconductors; superconducting fluctuations in astrong magnetic field or on the theory of the Bose-Einstein condensation. Aspecial discussion is given to phenomenological scaling theories. Experimentalinvestigations, primarily transport measurements, make the contents of thethird level and are for convenience classified by the type of material usedultrathin films, variable composition materials, high-temperaturesuperconductors, superconductor-poor metal transitions. As a separate topic,data on nonlinear phenomena near the superconductor-insulator transition arepresented. At the final, summarizing, level the basic aspects of the problemare enumerated again to identify where further research is needed and how thisresearch can be carried out. Some relatively new results, potentially of keyimportance in resolving the remaining problems, are also discussed.



Author: V.F. Gantmakher, V.T. Dolgopolov

Source: https://arxiv.org/







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