Chemical Potential Characterization of Symmetry-Breaking Phases in a Rhombohedral Trilayer Graphene

Rhombohedral trilayer graphene has recently emerged asa naturalflat-band platform for studying interaction-driven symmetry-breakingphases. The displacement field (D) can further flattenthe band to enhance the density of states, thereby controlling theelectronic correlation that tips the energy balance between spin andvalley degrees of freedom. To characterize the energy competition,chemical potential measurement a direct thermodynamic probeof Fermi surfaces is highly demanding to be conducted undera constant D. In this work, we characterize D-dependent isospin flavor polarization, where electronicstates with isospin degeneracies of one and two can be identified.We also developed a method to measure the chemical potential at afixed D, allowing for the extraction of energy variationduring phase transitions. Furthermore, symmetry breaking could alsobe invoked in Landau levels, manifesting as quantum Hall ferromagnetism.Our work opens more opportunities for the thermodynamic characterizationof displacement-field tuned van der Waals heterostructures.