Visualizing the Quantum Phases of Magic Angle Graphene

Twisted bilayer graphene near the magic angle exhibits a remarkable array of quantum phases, whose nature and origin are still poorly understood. In this talk I will describe our nanotube-based scanning single-electron-transistor (SET) experiments that explore and visualize some of these phases. Nanotube SET is an extremely sensitive electrometer, capable of probing a variety of thermodynamic properties of electrons on the nanoscale. By measuring the electronic compressibility¹, we reveal a cascade of spin/valley symmetry-breaking phase transitions. This cascade appears at temperatures well above the onset of the superconducting and correlated insulating phases, demonstrating that it forms the parent state out of which these phases emerge. Measurements of the electronic entropy² reveal that magic angle graphene exhibits a curious analog of the Pomeranchuk effect in ³He. In ³He, counterintuitively, the liquid can solidify upon heating, owing to a large spin entropy of the solid. Here we measure a similar giant magnetic entropy (~1kB per moiré site) near a filling of one electron per moiré site. This entropy drives a Pomeranchuk-like transition from a rather convention metal to a correlated state with nearly-free magnetic moments. However, while in ³He it is easy to understand why the spins of localized atoms in the solid are practically free, it is very surprising to observe nearly-free moments in a metallic, compressible state, making the nature of this newly observed correlated state highly puzzling.

1. Zondiner, U. et al., Nature 582, 203–208 (2020).

2. Rozen, A. et al., Nature 592, 214-14 (2021).