Quantum Liquid Crystal Phases in Fermionic Superfluids with Pairing between Fermion Species of Unequal Densities

Superfluidity in fermionic systems originates from pairing of fermions, and Bose condensation of these so-called Cooper pairs. The Cooper pairs are usually made of fermions of different species; for example in superconductors they are pairs of electrons with opposite spins. Thus the most favorable situation for pairing and superfluidity is when the two species of fermions that form pairs have the same density. This paper studies the possible superfluid states when the two pairing species have different densities, and show that the resultant states have remarkable similarities to the phases of liquid crystals. This enables us to provide a unified description of the possible pairing phases, and understand the phase transitions among them.