  We propose a new state of matter in which the pairing interactions carve out
a gap within the interior of a large Fermi ball, while the exterior surface
remains gapless. This defines a system which contains both a superfluid and a
normal Fermi liquid simultaneously, with both gapped and gapless quasiparticle
excitations. This state can be realized at weak coupling. We predict that a
cold mixture of two species of fermionic atoms with different mass will exhibit
this state. For electrons in appropriate solids, it would define a material
that is simultaneously superconducting and metallic.
