Interaction Effects and Non-Integer Pseudo-Landau Levels in Engineered Periodically Strained Graphene

Strain superlattices (SL) in 2D materials like graphene provide an ideal test bed for generating flat bands and exploring the effects of strong correlations. Here we report STM/STS measurements on an engineered SL generated by placing graphene on a periodic array of silica nanospheres. A pseudomagnetic field as high as 55 T is observed along with the formation of pseudo-Landau levels (pLLs), not only at the expected integer values but also at fractional values. In regions where the Fermi energy intersects the zeroth pLL, we observe that this pLL splits. Using tight binding calculations, we show that our system supports formation of quasi-flat bands. We are also able to simulate the strain induced pLL splitting and show how on-site interaction may create fractional pLLs. Thus, we have demonstrated a customizable, reproducible, and scalable graphene strain superlattice system that can host a range of different correlation driven states.