Superconducting charge-ordered states in cuprates

Motivated by recent neutron scattering and scanning tunneling microscopy (STM) experiments on cuprate superconductors, we discuss charge-ordered states, in particular with two-dimensional charge modulation patterns, coexisting with superconductivity. We extend previous studies of a large-$N$ mean-field formulation of the $t-J$ model. In addition to bond-centered superconducting stripe states at low doping, we find checkerboard-modulated superconducting states which are favorable in an intermediate doping interval. We also analyze the energy dependence of the Fourier component of the local density of states at the ordering wave vector for several possible modulation patterns, and compare with STM results.