Supersolid phases of a doped valence-bond quantum antiferromagnet: evidence for a coexisting superconducting order parameter

Motivated by numerical evidence of the valence-bond ground state of the two-dimensional Heisenberg pyrochlore lattice, we argue using a t-J model that it evolves under doping into novel phases characterized by superconductivity coexisting with the underlying valence-bond solid order. A fermionic mean-field theory supplemented by exact diagonalization results provide strong arguments in favor of the stability of such supersolid phases. The resemblance with modulated superconducting patterns in high-Tc cuprates as well as possible relevance to frustrated noncuprate superconductors such as spinels and pyrochlores is discussed.