  Using the t--J model (which can also include Coulomb repulsion) and the
``plain vanilla'' renormalized mean-field theory of Zhang et al. (1988),
stability of inhomogeneous 4a x 4a superstructures as those observed in
cuprates superconductors around hole doping 1/8 is investigated. We find a
non-uniform 4a x 4a bond order wave involving simultaneously small (~ 10^-2 t)
inhomogeneous staggered plaquette currents as well as a small charge density
modulation similar to pair density wave order. On the other hand, no supersolid
phase involving a decoupling in the superconducting particle-particle channel
is found.
