Phase Diagram of Kane-Mele Hubbard model at small doping

Topological insulators have received a lot of attention in the last decade due to a multitude of prospects, including quantum computing. Kane-Mele (KM) model is one of the first models of a time-reversal invariant topological insulator. Although the topological properties of the KM model have been studied extensively, the effects of interaction are still less explored. In this work, we study the effect of Hubbard interaction at small doping around half-filling. We use the Density matrix renormalization group method to characterize different phases of 6- and 8-leg cylinders. We identify superconducting and spin density wave states at different doping and interaction. Our result shows a rich phase diagram of the Kane-Mele Hubbard model at small doping.