Two and Three Dimensional Incommensurate Modulation in Optimally-Doped Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$

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$$\sim$20 $\mathring{A}$ in the {\bf c} direction, and of ${\xi }_b$$\sim$ 185 $\mathring{A}$ 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.

8 pages, 8 figures

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• Anomalous density fluctuations in a strange metal
• Absence of time reversal symmetry breaking in La_{2-x}Sr_{x}CuO_{4}
• Spatially correlated incommensurate lattice modulations in an atomically thin high-temperature Bi_{2.1}Sr_{1.9}CaCu_{2.0}O_{8+δ} superconductors
• Materials preparation, single crystal growth, and the phase diagram of the cuprate high temperature superconductor La1.6-xNd0.4SrxCuO4
• High resolution X-ray scattering studies of structural phase transitions in underdoped La${}_{2-x}$Ba${}_x$CuO${}_4$
• Diffuse Scattering from Correlated Electron Systems
• Quantitative characterization of the nanoscale local lattice strain induced by Sr dopants in La${}_{1.92}$Sr${}_{0.08}$CuO${}_4$
• Periodic Atomic Displacements and Visualization of the Electron-Lattice Interaction in the Cuprate
• The k-space Origins of Scattering in Bi2Sr2CaCu2O8+x