Pairing instability in a nematic Fermi liquid

Strong interaction between fermions may lead to a novel quantum ground state where the rotational symmetry is spontaneously broken while the translational symmetry is still preserved. Such a 'nematic' Fermi liquid has a spontaneously deformed Fermi surface and supports a gapless Goldstone mode associated with the broken rotational symmetry. We consider a nematic Fermi liquid of fermions carrying two internal quantum numbers that, for example, may represent the layer degree of freedom of a bilayer system. It is found that the effective interaction mediated by a collective mode gives rise to a pairing instability of the underlying fermions under certain conditions, leading to the conclusion that the nematic order could be useful for superconductivity.