Interactions among electrons and the topology of their energy bands can create novel quantum phases of matter. The discovery of electronic bands with flat energy dispersion in magic-angle twisted bilayer graphene (MATBG) has created a unique opportunity to search for new correlated and topological electronic phases. We have developed new scanning tunneling microscopy (STM) and spectroscopy (STS) techniques to probe the nature of electronic correlations and to detect the novel phases in this two-dimensional systems. Density-tuned STS studies have enabled us to study the properties of MATBG as function of carrier concentration revealing key and new properties of this novel material. These measurements establish that MATBG is a strong correlated system at all partial filling of its flat bands.  The strength of the interactions, which can be measured in our experiments, is found to be larger than the flat bandwidth in the non-interacting limit. We demonstrate that these interactions drive a cascade of transitions at each integer filling of these bands, creating likely the insulating states at low temperatures that are spin or valley polarized. Most recently, we developed a new STS technique to detect topological phases and their associated Chern numbers and used it to show that strong interactions drive the formation of unexpected topological insulating phases in MATBG . These phases, which are stabilized by a weak magnetic field, are rare examples of when topology emerges from interaction between electrons. I will describe these experiments, and other ongoing efforts, that illustrate the power of atomic scale experiments in revealing novel physics of electrons in moiré superlattices.
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