  Flat bands emerging in buckled monolayer graphene superlattices have been
recently shown to realize correlated states analogous to those observed in
twisted graphene multilayers. Here, we demonstrate the emergence of valley
topology driven by competing electronic correlations in buckled graphene
superlattices. We show, both by means of atomistic models and a low-energy
description, that the existence of long-range electronic correlations leads to
a competition between antiferromagnetic and charge density wave instabilities,
that can be controlled by means of screening engineering. Interestingly, we
find that the emergent charge density wave has a topologically non-trivial
electronic structure, leading to a coexistent quantum valley Hall insulating
state. In a similar fashion, the antiferromagnetic phase realizes a
spin-polarized quantum valley-Hall insulating state. Our results put forward
buckled graphene superlattices as a new platform to realize interaction-induced
topological matter.
