A central research area in condensed matter physics is the description and classification of different phases of matter. Our research is devoted to the theoretical study of phase transitions between superconducting metallic, and insulating states in one- and two-dimensional disordered interacting systems. We address the fundamental theoretical problem of the interplay of superconductivity, disorder, and electronic correlations. Our long-term goal is a development of a comprehensive picture of disordered correlated critical states, both near and far from equilibrium. The main expected result is the phase diagram describing different states of strongly correlated low-dimensional systems.
The first major direction of our research is related to low-dimensional disordered superconducting structures. A particular emphasis will be put on the superconductor-insulator transitionin superconducting films, quantum wires, and Josephson-junction arrays. Further, we will study Majorana excitations in topological superconductors as well as effects of noise and decoherence. One of the central questions within this direction is the nature of the superconductor-insulator transition in low-dimensional disordered systems, its degree of universality, and character of transport in its vicinity. Further, the proposal addresses a complex of problems whose solution appears to be particularly important for exploring the possibilities of enhancing superconductor transition temperature in novel materials and nanostructures. A coherent picture of disordered superconductors involving all the key ingredients -- superconducting correlation, disorder-induced multifractality, and electron-electron interactions in various channels – will be developed.
The second closely related major direction of the project is the study of metal-insulator transitions focusing on the interplay of interaction (including interaction-induced critical fluctuations) with disorder-induced localization and multifractality. Furthermore, we will explore localization in the absence of static disorder due to dynamical fluctuations at high-temperatures. The systems to be explored include: disordered spin chains, quantum wires, quantum Hall systems, semiconductor two-dimensional systems (also with magnetic impurities), graphene, surface and edge states of topological insulators.
Our research consists of three interrelated Topics: