Functional renormalization approach to multiband systems and application the doped Kitaev-Heisenberg model

Synopsis

Correlated fermions give rise to some of the most intriguing phenomena in condensed matter physics-archive such as metal insulator transitions or unconventional superconductivity resulting from a complex interplay and competition of different energy scales. The functional renormalization group (fRG) in combination with Fermi surface patching is a well-established method for studying Fermi liquid instabilities of correlated fermion systems. So far, the fRG has successfully exploited models without sizable spin-orbit coupling (SOC), e.g., models for cuprates, pnictides, and hexagonal lattices such as graphene. More recently, however, the non-trivial physics-archive resulting from strong spin-orbit coupling (SOC) has become a major field of research due to its essential role for topological phases. In my talk, I present a further development of the functional RG method to approach multiband systems with spin-orbit coupling. Explicitly, I show how it can be applied to study the quantum many-body instabilities of the doped Kitaev-Heisenberg Hamiltonian on the honeycomb lattice as a minimal model for a doped spin-orbit Mott insulator. This spin-1/2 model is believed to describe the magnetic properties of the layered transition-metal oxide Na2IrO3. We find superconducting triplet p-wave instabilities driven by ferromagnetic exchange and various singlet pairing phases. Beyond quarter filling, the p-wave pairing gives rise to a topological state with protected Majorana edge-modes. For antiferromagnetic Kitaev and ferromagnetic Heisenberg exchange we obtain bond-order instabilities at van Hove filling supported by nesting and density-of-states enhancement, yielding dimerization patterns of the electronic degrees of freedom on the honeycomb lattice.