A quantum twisting microscope (QTM) enables energy- and momentum-resolved measurements of quantum phases through tunneling spectroscopy in twistable van der Waals heterostructures. Here, we improve its resolution and extend its range to higher energies and twist angles by integrating hexagonal boron nitride as a tunneling dielectric. This advance reveals previously inaccessible dispersion features in tunneling between two monolayer graphene sheets, consistent with a logarithmic correction to the linear Dirac spectrum arising from electron-electron interactions, with a fine-structure constant alpha approximate to 0.32 +/- 0.01. Remarkably, these extremely subtle corrections are resolved even at room temperature. Our results highlight the exceptional sensitivity of the QTM, where interferometric interlayer tunneling amplifies small band-structure modifications. They further show that strong electron-electron interactions persist in symmetric, nonordered graphene states and demonstrate the QTM's capability to probe spectral functions and excitations of correlated ground states across twisted and untwisted two-dimensional systems.

The discovery of magic angle twisted bilayer graphene (MATBG), in which two sheets of monolayer graphene are precisely stacked at a specific angle, has opened up a plethora of grand new opportunities in the field of topology, superconductivity, strange metal, and other strongly correlated effects. This review will focus on the various forms of quantum phases in MATBG revealed through quantum transport measurements. The goal is to highlight the uniqueness and current understanding of the various phases, especially how electronic interaction plays a role in them, as well as open questions in regard to the phase diagram.