Theory of noncentrosymmetric and other unconventional superconductors

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One of the main 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, with high-temperature cuprates and iron pnictides, strontium ruthenate, heavy-fermion and organic compounds being some of the examples. Superconductors are said to be "unconventional" if their properties cannot be explained by the standard models of superconductivity, in particular, the Bardeen-Cooper-Schrieffer theory. The main objective of this 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 superconductivity in crystals with a complicated, e.g. multiband, electronic structure. Even in conventional superconductors, going beyond the domain of the Bardeen-Cooper-Schrieffer theory often reveals an interesting and rich physics. For instance, understanding the nonequilibrium properties of nonuniform superconducting phases requires new ideas and theoretical techniques. We hope that the results of this research will provide insight into the physics of 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.