Interplay of Superconductivity and Localization

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A central research area in condensed matter physics is theoretical prediction, classification, and description as well as experimental investigation of different phases of matter. The project is devoted to the theoretical study of phase transitions between superconducting, metallic, and insulating states in two-dimensional disordered interacting systems. The fundamental theoretical problem addressed in the proposal is that of the interplay of superconductivity, disorder, and electronic correlations. The major direction of the project is related to low-dimensional disordered superconducting structures. One of the central questions within this direction is the nature of the Superconductor-Insulator Transition in disordered systems, its degree of universality, and character of transport in its vicinity. The Superconductor-Insulator Transition (SIT) belongs to a broad class of disorder-induced quantum phase transitions which includes Anderson metal-insulator transition and quantum Hall transition. Localization-delocalization quantum phase transitions form an actively developing field of condensed matter physics. Electron-electron interaction effects at the transitions represent one of central research directions. Critical properties in the corresponding quantum critical regimes are governed by interplay of disorder- and interaction-controlled quantum-coherent effects. The project is intended to develop a coherent picture of disordered superconductors involving all the key ingredients: superconducting correlation, disorder-induced multifractality, and electron-electron interactions in various channels. The emphasis will be put on superconducting properties of thin films demonstrating the supeconductor -insulator transition and novel materials for high temperature superconductivity. The main expected result is the phase diagram describing different states of strongly correlated low-dimensional systems. The objectives of the project are expected to be particularly relevant for searching high-temperature superconductivity in novel materials. Methodologically, it is planned to generalize the interacting sigma-model with the interaction in the Cooper channel to include additional correlation mechanisms and unconventional symmetries.The Work Plan consists of the three inter-related Tasks:1. To develop a comprehensive theory of the SIT in thin films.2. To investigate the finite-T superconducting transition in disordered films, going beyond the mean-field description.3. To identify possibilities of disorder-induced enhancement of superconductivity in novel materials and nanosystems.