Correlations and valley phenomena in strained graphene superlattices

In this work, we explore two platforms where strained graphene superlattices were observed: spontaneously buckled graphene, and suspended graphene on engineered substrates. In the former, emerging flat bands have been recently shown to realize correlated states analogous to those observed in twisted graphene multilayers. We show that electronic correlations leads to a competition between antiferromagnetic and charge density wave instabilities. Moreover, the charge density wave state 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. To study the effects of strain in suspended graphene superlattices, we perform molecular dynamics simulations. The computed strain field is used to obtain an effective Hamiltonian and the resulting pseudo magnetic field. We use this platform to investigate the presence of defects such as of wrinkles in the electronic structure. Under the quantum Hall regime, we show the existence of valley-polarized chiral edge states. Our results put forward strained graphene superlattices as tunable platforms to investigate valley topology.