Coulomb screening and thermodynamic measurements in magic-angle twisted trilayer graphene

We report Coulomb screening measurements on magic-angle twisted trilayer graphene (tTLG). Utilizing a double-layer structure, we directly control the strength of Coulomb correlation between charge carriers in tTLG using proximity screening from the adjacent  Bernal bilayer graphene (BLG), which is separated from tTLG by a 2 nm thick insulating barrier. By studying the influence of Coulomb screening on the stability of the superconducting phase, we argue that Coulomb repulsion competes against the underlying mechanism of Cooper pairing. This behavior is observed both at B=0 and in the presence of a large in-plane magnetic field that violates the Pauli-limit. Furthermore, we characterize the isospin properties of the moiré flat band in magic-angle tTLG using a combination of transport and thermodynamic measurements. We show that the correlated insulator at half moiré filling is spin polarized, which likely results from the extraordinarily large  spin stiffness in tTLG. At the same time, a spin polarized insulator state is potentially consistent with a spin triplet superconducting order parameter.  Our findings provide constraints for understanding the nature of the unique superconducting phase in magic-angle twisted trilayer graphene.