| Recent scanning tunneling microscopy on two different cuprate families has revealed unidirectional bond-centered modulation in local electronic density of states. Motivated by this result we investigate the emergence of spontaneous modulations in the d-wave superconducting resonating valence bond phase using the t-J model at x=1/8 doping. Half-filled charge domains separated by four lattice spacings are found to form along one of the crystal axes leading to modulated superconductivity with out-of-phase d-wave order parameters in neighboring domains. Both renormalized mean-field theory and variational Monte Carlo calculations yield that the energies of modulated and uniform phases are very close to each other. Moreover, we have also found closely related stripe phase originating from the staggered flux phase, a candidate for the pseudogap normal phase of lightly doped cuprates. |
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