Weak-coupling theory of half-metals and other fractional metallic phases in biased doped Bernal bilayer graphene

Abstract: The paper presents a theoretical study of many-body electronic phases in doped and electrically biased Bernal-stacked (AB) bilayer graphene. We develop a variational mean-field theory with no fitted parameters. For the electron-electron interaction, we employ a parameter-free random-phase approximation to model the short-range screened Coulomb repulsion. The remaining long-range Coulomb potential energy is dictated by the geometry of the sample, behaving as a parallel-plate capacitor. We formulate the theory directly in terms of the experimentally controlled displacement field $\frak D$ rather than the interaction-renormalized interlayer potential difference. It makes our theory better suited for direct comparison with experiment. The resulting phase diagram is quite rich. It hosts several fractional-metal states connected by first- and second-order transitions. At higher bias and doping, three distinct fractional metallic states emerge. We classify these phases by the number of doped sectors and the symmetry of the order parameters. Our results - obtained without any parameter fitting - reproduce key qualitative and quantitative features of recent experiments. This includes the energy scale associated with the loss of fractional metallic order. At lower bias and doping, the model stabilizes a broad spectrum of fractional-metal phases with more exotic symmetry-breaking patterns. This suggests that further experimental exploration of the latter regime is warranted.