Fermi surface instabilities of spin-orbit-coupled metals*

The pursuit of novel phases in correlated electron systems, such as possibly topological instances of unconventional superconductivity, must consider multiple energy scales including interaction strength, electronic band width, and, in particular, spin-orbit coupling (SOC). While density functional theory and related ab initio techniques can provide a detailed description of a materials electronic structure that can carefully account for the effects of SOC, it is necessary to additionally refine quantum many body techniques to study Fermi surface instabilities in the presence of SOC. Starting from a picture of itinerant electrons, we study the effect of electronic correlations on the Fermi surface via renormalization group techniques. Combining ab initio electronic structures with perturbative and functional renormalization group calculations, we develop the toolbox to analyse a plethora of symmetry breaking phases arising from the interplay of SOC, fermi surface topology, and electronic correlations.