Crystalline order in superfluid 3He films

We predict an inhomogeneous phase of superfluid He-3 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, D-c2(T)< D < D-c1(T), separating distinct homogeneous superfluid phases. The instability at the critical film thickness, D-c2 approximate to 9 xi(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 D-c1 approximate to 13 xi(T).