Crystalline order in superfluid He3 films

We predict an inhomogeneous phase of superfluid He3 films in which translational symmetry is spontaneously broken in the plane of the film. This phase is energetically favored over a range of film thicknesses, Dc2(T)<D<Dc1(T), separating distinct homogeneous superfluid phases. The instability at the critical film thickness, Dc2 9ξ(T), is a single-mode instability generating striped phase order in the film. Numerical calculations of the order parameter and free energy indicate a second-order instability to a periodic lattice of degenerate B-like phases separated by domain walls at Dc1 13ξ(T).