Two- and three-dimensional incommensurate modulation in optimally-dopedBi2Sr2CaCu2O8+δJournal Articles
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abstract
X-ray scattering measurements on optimally-doped single crystal samples of
the high temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ reveal
the presence of three distinct incommensurate charge modulations, each
involving a roughly fivefold increase in the unit cell dimension along the {\bf
b}-direction. The strongest scattering comes from the well known (H, K$\pm$
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_c$$\sim$20 $\AA$ in the {\bf c} direction, and of $\xi_b$$\sim$ 185 $\AA$
parallel to the incommensurate wavevector. We interpret these features as
arising from three dimensional incommensurate domains and the interfaces
between them, respectively. In addition we investigate the recently discovered
incommensuate modulations which peak up at (1/2, K$\pm$ 0.21, L) and related
wavevectors. 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 nanostructure observed
in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ using STM topography.
