Superconductivity is the astonishing physical phenomenon of a material conducting electrical current without any resistance, i.e. without any ohmic losses. Ever since its discovery more than one 100 years ago, superconductivity has fascinated scientists, who have attempted to develop suitable theories. To increase the understanding of novel forms of superconductivity, we develop theoretical methods and selfconsistent calculations.
The theory of Bardeen, Cooper and Schrieffer provides a basic description of conventional superconductivity mediated by quantized lattice vibrations. However, new and unusual forms of superconductivity have been discovered, which require new conceptual understanding. Among these are high-temperature superconductivity in copper-oxides and other unconventional forms that may appear in two-dimensional materials, heterostructures, and topological materials, as well as quasi-1D materials (Bechgaard and Fabre salts, chromium pnictide). Coupling of 1D systems with strong intrinsic unconventional pairing to clean metallic substrates may further result in micron-length superconducting devices working at high temperatures. To investigate these unconventional superconductors we use low-energy effective models, develop the anisotropic multiband Eliashberg framework for computing high-temperature superconductivity, and employ and extend the numerical density matrix renormalization group to parallel supercomputers (both stand-alone and in conjunction with mean-field methods). Other areas of interest are odd-frequency pairing and strong-coupling superconductivity.