Entropic evidence for a Pomeranchuk effect in Magic Angle graphene

In the 1950's, Pomeranchuk predicted that, counterintuitively, liquid 3He may solidify upon heating, due to a high excess spin entropy in the solid phase. Here, using both local and global electronic entropy and compressibility measurements, we show that an analogous effect occurs in magic angle twisted bilayer graphene. Near a filling of one electron per moiré unit cell, we observe a dramatic increase in the electronic entropy to about 1kB per unit cell. This large excess entropy is quenched by an in-plane magnetic field, pointing to its magnetic origin. A sharp jump in the compressibility as a function of the electron density, associated with a reset of the Fermi level back to near the Dirac point, marks a clear boundary between two phases. We map this jump as a function of electron density, temperature, and magnetic field. This reveals a phase diagram that is consistent with a Pomeranchuk-like temperature- and field-driven transition from a rather conventional metal to a correlated state with nearly-free magnetic moments. The correlated state features an unusual dichotomy between properties associated with itinerant electrons, such as the absence of a thermodynamic gap, metallicity, and a Dirac-like compressibility, and properties usually associated with localized moments, such as a large entropy and its disappearance with magnetic field. Moreover, the energy scales characterizing these two sets of properties are vastly different: whereas the compressibility jump onsets at T∼30K, the bandwidth of magnetic excitations is ∼3K or smaller. This dichotomy and the large separation of energy scales have key implications for the physics of correlated states in twisted bilayer graphene.