Spontaneous breaking of rotational symmetry in superconductors

We show that homogeneous superconductors with broken spin/isospin symmetry lower their energy via a transition to a novel superconducting state where the Fermi surfaces are deformed to a quasiellipsoidal form at zero total momentum of Cooper pairs. In this state, the gain in the condensation energy of the pairs dominates over the loss in the kinetic energy caused by the lowest order (quadrupole) deformation of Fermi surfaces from the spherically symmetric form. The phase transition from the spherically symmetric state to the superconducting state with broken rotational symmetry is first order.