Chiral SDW and d + id superconductivity in the magic-angle twisted bilayer-graphene

We model the newly synthesized magic-angle twisted bilayer-graphene superconductor with two px,y-like Wannier orbitals on the superstructure honeycomb lattice, where the hopping integrals are constructed via the Slater-Koster formulism by symmetry analysis. The characteristics exhibited in this simple model are well consistent with both the rigorous calculations and experimental observations. Van-Hove singularity and Fermi-surface nesting are found in the doping levels relevant to the correlated insulator and unconventional superconductivity revealed experimentally, base on which we identify the two phases as weak-coupling FS instabilities. Then, with repulsive Hubbard interactions turning on, we performed random-phase-approximation (RPA) based calculations to identify the electron instabilities. As a result, we find chiral d + id topological superconductivity bordering the correlated insulating state near half-filling, identified as noncoplanar chiral spin-density wave (SDW) ordered state, featuring quantum anomalous Hall effect. The phase-diagram obtained in our approach is qualitatively consistent with experiments.


Reference: Cheng-Cheng Liu, Li-Da Zhang, Wei-Qiang Chen, and Fan Yang, arXiv:1804.10009 (2018). (Accepted by PRL)