Density functional theory, combined with the larger body of work that was built upon it to form the present scope of ab initio methods, has had a fundamental impact on the quantitative modeling of electronic structure in quantum materials. While under many circumstances it needs to be refined to picture the role of electronic interactions correctly, ab initio methods are always an invaluable starting point. In particular, it allows to map out the whole single-particle parameter space depen- dence on modifications such as pressure, temperature, external fields, chemical substitution, doping, substrate conditions, and others. In order to study unconventional superconductivity in such a band structure model, however, the set of methods available at present often necessitate an extensive processing and effective modeling (downfolding) before they become applicable. With the randomphase approximation (RPA) method, for example, it is numerically hard to study multiple bands im- plied by the number of atoms per unit cell, different orbitals, and spin-orbit coupling, in particular for three-dimensional systems. These limitations likewise apply to multi-orbital functional renormaliza- tion group (FRG), where, even in its most elementary form, the N-point discretization of the given Fermi surfaces implies a set of N 3 coupled integro-differential equations. As one intends to pursue a thorough optimization of system parameters to define the optimal electronic host for a given super- conducting state of choice, however, an even tighter bottleneck appears, as the same RPA or FRG analysis would have to be repeated many times.
In our SFB 1170 project research agenda, we wish to combine density functional theory ab initio methods with a weak coupling analysis of superconductivity rooted in the pioneering work of Kohn and Luttinger. This has recently been revived for certain two-dimensional systems. As one performs a perturbative instability analysis in the Cooper channel, the only input needed are the Fermi surfaces including the momentum-resolved eigenstates of the relevant bands, which is precisely what ab initio methods can provide. As such, we intend to develop an open-source software package which will be designed to be compatible with common DFT software and can thus be used as a standardized post-processing application for ab initio data. This will not render more elaborate methods for su- perconductivity obsolete, but rather provide an invaluable starting point to single out the interesting parameter regimes for unconventional superconductivity in two and three spatial dimensions, includ- ing those scenarios in which spin-orbit coupling plays a vital role. We intend to apply this technology to shed light on topologically non-trivial superconductivity in spin-orbit coupled bulk materials of in- terest for the SFB 1170, such as iridates, ruthenates, and non-centrosymmetric semimetals, where unconventional superconductivity with mixed spin-singlet/spin-triplet order parameters is likely to be expected.