Nematic and Partially Polarized Phases in Rhombohedral Graphene with Varying Number of Layers: An Extensive Hartree-Fock Study.

Rhombohedral (ABC-stacked) graphene systems with different number of layers feature an abundance of correlated phases and superconducting states in experimental measurements with different doping and displacement fields. Some of the superconducting pockets can emerge from - or close to - one of the correlated states. Therefore, studying the phase diagram of these phases for varying number of layers can be useful to interpret the experimental observations. To achieve this, systematic Hartree-Fock calculations have been performed in the presence of long-range Coulomb interactions. By varying the external displacement field and carrier density, a cascade of metallic partially-isospin-polarized phases that spontaneously break spin and/or valley (flavor) symmetries is found. In addition, these states can present nematicity, stabilized by electron-electron interactions, exhibiting rich internal complexity. Polarized states are more stable for electron doping, and they are found for systems with up to 20 layers. Moreover, the tunability of the phase diagram via substrate screening and spin-orbit coupling proximity effects is studied. The results offer new insights into the role of correlations and symmetry breaking in graphitic systems, which will motivate future experimental and theoretical works.