Two- and three-dimensional incommensurate modulation in optimally-doped Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}}

X-ray scattering measurements on optimally doped single crystal samples of the high-temperature superconductor Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} reveal the presence of three distinct incommensurate charge modulations, each involving a roughly fivefold increase in the unit cell dimension along the b direction. The strongest scattering comes from the well known (H, K{+-}0.21, L) modulation and its harmonics. However, we also observe broad diffraction which peak up at the L values complementary to those which characterize the known modulated structure. These diffraction features correspond to correlation lengths of roughly a unit cell dimension, {xi}{sub c}{approx}20 A in the c direction, and of {xi}{sub b}{approx}185 A parallel to the incommensurate wave vector. We interpret these features as arising from three-dimensional incommensurate domains and the interfaces between them, respectively. In addition we investigate the recently discovered incommensurate modulations which peak up at (1/2, K{+-}0.21, L) and related wave vectors. Here we explicitly study the L dependence of this scattering and see that these charge modulations are two dimensional in nature with weak correlations on the scale of a bilayer thickness, and that they correspond to short-range, isotropic correlation lengths within the basal plane. We relate these new incommensurate modulations to the electronic nanostructuremore » observed in Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} using STM topography.« less