Theory of noncentrosymmetric and other unconventional superconductors

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One of the major driving forces of modern technology is the research into new materials. Superconductors, which are the materials that can conduct electricity without any energy losses, are of particular importance. The majority of superconducting materials at the focus of current research belong to the class of unconventional superconductors. High-temperature cuprates and iron pnictides, strontium ruthenate, heavy-fermion and organic compounds are just some of the examples. Superconductors are said to be "unconventional" if their properties cannot be explained by the standard microscopic theories of superconductivity, in particular, the Bardeen-Cooper-Schrieffer model.***The main objective of the research proposal is to better understand, both microscopically and phenomenologically, such interesting novel materials as superconductors without inversion symmetry and other "topological superconductors", and also ferromagnetic superconductors. Even in conventional superconductors, going beyond the domain of the Bardeen-Cooper-Schrieffer theory often reveals rich physics, for instance, the dramatic effects of fluctuations in nonuniform superconducting phases, whose understanding requires new ideas and theoretical techniques.****We hope that the results of this research will provide insight into the physics of other complex superconducting and superfluid systems. The broader impact resulting from the proposed activity will be training of a new generation of highly qualified personnel through an exposure to a wide range of ideas and methods of contemporary condensed matter physics. **