Half-metal and other fractional metal phases in doped AB bilayer graphene

We argue theoretically that, in doped $AB$ bilayer graphene, electron-electron coupling can give rise to the spontaneous formation of fractional metal phases. These states, being generalizations of a more common half-metal, have a Fermi surface that is perfectly polarized not only in terms of a spin-related quantum number, but also in terms of the valley index. The proposed mechanism assumes that the ground state of undoped bilayer graphene is a spin-density-wave insulator, with a finite gap in the single-electron spectrum. Upon doping, the insulator is destroyed and replaced by a fractional metal phase. As doping increases, transitions between various types of fractional metal (half-metal, quarter-metal, etc.) are triggered. Our findings are consistent with recent experiments on doped $AB$ bilayer graphene, in which a cascade of phase transitions between different isospin states was observed.