When quantum mechanics and Coulomb repulsion are combined in a pristine solid, some of the most fascinating electronic phases in nature can emerge. Interactions between electrons can form correlated insulators, electronic liquids, and in extreme cases even quantum electronic solids. These phases are predicted to exhibit their most striking features in real-space, however, they are also extremely fragile, preventing their visualization with existing experimental tools. In this talk, I will describe our experiments that use a pristine carbon nanotube as a new type of a scanning probe, capable of imaging electrical charge with unprecedented sensitivity and minimal invasiveness. I will show how using this platform we were able to obtain the first images of the quantum crystal of electrons, visualize the collective hydrodynamic flow of interacting electrons in graphene, and unravel the parent state that underlies the physics of strongly-interacting electrons in the recently-discovered system of magic angle twisted bilayer graphene.
