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

Abstract

We model the newly synthesized magic-angle twisted bilayer-graphene superconductor with two $p_{x,y}$-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 experiment observations. A van Hove singularity and Fermi-surface (FS) 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.

First submitted to PRL in April 26th, accepted in October 22nd. Here we for the first time proposed that the pairing mechanism in this system is "exchanging density-wave fluctuation". We also for the first time related the emergence of the "correlated insulator" and SC in this material to the presence of the van-Hove singularity and the FS-nesting within the flat band