As a copper-oxide based antiferromagnetic (AF) insulator is doped with charge carriers (“holes”), the long-range-ordered AF state is suppressed, and a superconducting (SC) ground state emerges above a certain doping level. Numerous experiments, such as electron microscpic studies, indicate that cuprates are electronically “inhomogeneous” even in their SC state. Although the origin of these inhomogeneities may well be electronic instabilities such as spin-charge stripes, a general consensus remains elusive. Systematic x-ray diffuse scattering studies of YBa 2 Cu 3 O 6+x (YBCO), Bi 2 Sr 2 CaCu 2 O 8+ d , and (La 1-x Sr x ) 2 CuO 4 (LSCO) have revealed lattice modulations on a “hierarchy” of length scales. In the case of YBCO, as charge carriers are tuned via O-stoichiometry variations, short-range ordered modulations characterized by a wavevector of the form q =(q x , 0, 0) are observed. These modulations correspond to correlated atomic displacements of Ba, Cu, and O atoms, respectively, with correlations extending several unit cells to form “nano-scopic” patches. They form well above room temperature, persist down to the lowest temperatures studied, and, intriguingly, at high doping level appear to be susceptible to Fermi-surface effects. In addition, “bowtie”-shape Huang scattering indicates characteristic coherent strain, signifying an intrinsically inhomogeneous lattice in both YBCO and LSCO from mesocopic to microscopic length scales. The role of lattice distortions in modifying electron-pair potential and exchange interactions has been highlighted recently. It seems that a close interplay between electronic inhomogeneities and lattice modulations on various length scales is inevitable in cuprates as well as oxides, in general.
*Use of the Advanced Photon Source is supported by the U. S. Department of Energy, Office of Science, under Contract No. DE-AC02-06CH11357.