Electric field induced anomalous Hall effects and nematic phases in carrier doped rhombohedral trilayer graphene*

The enhanced density of states near charge neutrality due to the flattening of the bands in ABC trilayers makes this type of multilayer graphene systems prone to form correlated ordered phases in sufficiently clean devices. We show by means of mean field Hartree-Fock calculations with long-range Coulomb interactions that the energetically favored ground state for ABC trilayer graphene turns from the layer antiferromagetic (LAF) phase to the valley polarized anomalous Hall (AH) phase upon a small carrier doping and application of a perpendicular electric field. The uneven filling of the three electron or hole pockets near the band edges upon carrier doping makes the system prone to form nematic phases with broken rotational symmetry due to momentum space condensation, an exchange driven mechanism that tends to lower the energies of electronic states that are closer together in momentum space. Our result suggests the possibility of switching electrically on and off the trigonal 120^o rotational symmetry of the carrier doped ground states.