Unidirectional d-wave superconducting domains in the two-dimensional t-J model

Motivated by the recently observed pattern of unidirectional domains in high-T(c) superconductors [Y. Kohsaka , Science 315, 1380 (2007)], 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 reveal that the energies of modulated and uniform phases are very close to each other.