Probing entropy and magnetization in graphene heterostructures

We developed a technique to determine entropy and magnetization by measuring chemical potential in van der Waals heterostructures. In twisted bilayer graphene with near 1.1 degree rotate angle, large entropy – on the order of unity per unit cell in unit of Boltzmann constant – is discovered around filling factor +-1. The entropy is suppressed by in-plane magnetic field, suggesting a weakly coupled isospin-ordered phase with strong fluctuations at higher temperatures, while the corresponding low temperature ground state is isospin unpolarized. This is in contrast with the typical scenario that ordered phase are favored at lower temperature, and is an analogue to the Pomerachuk effect discovered in 3He. We also applied this technique to  non-Moiré type graphene systems, such as Bernal stack bilayer graphene.