Frustrated Cooper pairing and f -wave supersolidity in cold-atom optical lattices

Geometric frustration in quantum magnetism refers to the fact that magnetic interactions on different bonds cannot be simultaneously minimized. The usual Cooper pairing systems favor uniform spatial distributions of pairing phases among different lattice sites without frustration. In contrast, we propose ``frustrated Cooper pairing'' in non-bipartite lattices which leads to supersolid states of Cooper pairs. Not only the amplitudes of the pairing order parameter but also its signs vary from site to site. This exotic pairing state naturally occurs in the $p$-orbital bands in optical lattices with ultracold spinless fermions. In the triangular lattice, it exhibits an unconventional supersolid state with the $f$-wave symmetry.