Thermodynamic study of magic-angle graphene using scanning SET.

I will present local measurements of electronic compressibility, entropy, and magnetization in magic-angle graphene, taken by a scanning single-electron transistor (SET).
These measurements show that as carriers are added, the system undergoes a cascade of sharp phase transitions, which appear as strong asymmetric jumps of the electronic compressibility near integer fillings of the moiré lattice. Furthermore, At a filling of one electron per moiré site, the phase transition exhibits a Pomeranchuk-like effect, in which the less compressible phase is the more entropic one.
I will then suggest an interpretation of this cascade of phase transitions in terms of an unusual sequence of band population driven by exchange interaction. As carriers are added to the system, the four electronic ‘flavors,’ which correspond to the spin and valley degrees of freedom, are not filled equally. Rather, they are populated such that at each transition, a single spin/valley flavor takes all the carriers from its partially filled peers, ‘resetting’ them to the vicinity of the charge neutrality point. As a result, the Dirac-like character observed near charge neutrality reappears after each integer filling.