  We present a simple model that we believe captures the key aspects of the
competition between superconducting and insulating states in twisted bilayer
graphene. Within this model, the superconducting phase is primary, and arises
at generic fillings, but is interrupted by the insulator at commensurate
fillings. Importantly, the insulator forms because of electron-electron
interactions, but the model is agnostic as to the superconducting pairing
mechanism, which need not originate with electron-electron interactions. The
model 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 analyze this model assuming weak wire-puddle and wire-wire couplings.
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 external Zeeman fields.
These features are consistent with experimental observations in magic-angle
twisted bilayer graphenes despite the distinct microscopic details. We further
study the full phase diagram of this model and discover that it contains
several distinct correlated insulating states, which we characterize herein.
