  It is known that electron interactions can cause a perfect spin polarization
of the Fermi surface of a metal. In such a situation only half of the
non-interacting Fermi surface is available, and thus this phase is commonly
referred to as a 'half-metal'. Here we argue that, in multi-band electronic
systems with nesting, further 'fractionalization' of the Fermi surface is
possible. Taking the AA bilayer graphene as a convenient test case, we
demonstrate that, under suitable conditions imposed on the electron
interactions, doped AA bilayer graphene can host a 'quarter-metal' state. In
such a state, only one quarter of the non-interacting Fermi surface (Fermi
contour) reaches the Fermi energy. At higher doping level, other 'fractional'
metals can emerge. We briefly analyze the transport properties of these
proposed phases.
