Bilayer graphene can become a fractional metal

In a metal, electron interactions can cause a perfect spin polarization of the Fermi surface. For such a phase, only half of the noninteracting Fermi surface is available, and thus this state is commonly referred to as a ``half metal.'' Here we argue that in multiband 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'' phase. Its Fermi surface (Fermi contour) is simultaneously polarized relative to spin-related and valley-related operators. The resultant state is nematic and possesses peculiar transport properties: the electric current carries both valley-related and spin-related quanta. In addition, since the two polarizations can be controlled independently of each other, the quarter metal is a promising candidate for spintronics and valleytronics applications. Other types of Fermi-surface fractionalization are also discussed.