Interacting domain-wall network model in twisted bilayer graphene

The interacting domain-wall network systems, which are naturally realized in the twisted bilayer graphene (TBLG) at sub-degree twist angles, are discussed in this talk. Motivated by the superconductor-insulator transition in the TBLG at the magic angle, a simplified model that is composed of a collection of crossed one-dimensional quantum wires whose intersections form a superlattice. At each superlattice point, we place a locally superconducting puddle which can exchange Cooper pairs with the quantum wires. We show that for a range of repulsive intrawire interactions, the system is superconducting at `generic' incommensurate fillings, with the superconductivity being `interrupted' by an insulating phase at commensurate fillings. We further show that the gapped insulating states at commensurate fillings give way to gapless states upon application of Zeeman fields. These features are consistent with experimental observations in magic-angle TBLG despite the distinct microscopic details. We also discuss novel phases driven by the interplay of small velocity and network structure.

Ref: PhysRevB100 115128 (2019)