Supermoiré low-energy effective theory of twisted trilayer graphene

Twisted trilayer graphene features a supermoir\'e pattern on top of two moir\'e patterns between adjacent layers. Here, the authors have devised a supermoir\'e effective model for the staircase twisted trilayer graphene, manifesting a gauge field originating from non-Abelian Berry connection acting as a pseudo magnetic field, and a space-dependent anisotropic velocity for the low-energy Dirac electrons. The supermoir\'e low-energy band structures and profiles of density of states can therefore be accessed by solving the effective model numerically.