Evolution of the confined states in graphene nanobubbles

In this study, we use a full tight-binding model to explore the behavior of graphene nanobubbles between the interface of twisted bilayer graphene (TBG-1.05^∘), uncovering the simultaneous existence of confined states and pseudo-Landau level (pLL) states under minor strain conditions. We find that the energy separation of the confined states aligns with a linear N rule, while pLL states follow a typical √N rule. As the height of the bubble and the local strain escalate, the low-energy segment of the local density of states transforms from confined states to pLL states. Our findings establish that the effect of a perpendicular magnetic field can effectively distinguish between confined and pLLs. Our results offer a crucial stepping stone towards the strain-engineering of electronic states in graphene-based nanostructures.