Theory of insulating phase and superconductivity in twisted bilayer graphene*

A correlated insulating phase and superconductivity have been recently observed in twisted bilayer graphene (tBG). We study theoretically these two phases in both the weak and strong coupling limit. In the weak coupling limit, using the random phase approximation, we find various possible combinations of density wave phases and pairing symmetries [1]. In the strong coupling limit, the insulating phase is anti-ferromagnetically (AFM) ordered, like in monolayer graphene [2]. However, we find there is no local magnetic moment in this AFM phase due to the special form of Wannier functions. Using the spin-fermion model, we find attractive electron-electron interaction mediated by the critical AFM fluctuations. This attractive interaction leads to chiral d+id superconductivity. Using a finite size tight-binding model, we show explicitly the existence of edge Majorana modes.

[1] E Laksono et al., Solid State Communications 282, 38-44 (2018)
[2] HK Tang et al., Science 361 (6402), 570-574 (2018)