Structural aspects of materials with static stripe order

A growing number of cuprate superconductors show evidence of an intrinsic spatial electronic inhomogeneity on a nanometer length scale. Corresponding observations were made with a variety of probes sensitive to the sample's surface or bulk as well as to its average or local structure. Charge and spin stripe correlations constitute one class of inhomogeneity initially derived from neutron scattering data on La-based cuprates. By now magnetic excitation spectra with very similar dispersions were observed in several systems, suggesting that incommensurate spin fluctuations are a universal property of the cuprates. In contrast, it proves much harder to obtain a unified picture for the charge stripe correlations as observed with scattering and tunneling techniques. This article reviews the evidence of charge stripe correlations and their interactions with the crystal lattice in the La-based compounds, which are presently the only cuprates with confirmed static spin and charge stripe order. Particular emphasis is put on the relationship between stripe order and average and local structure properties, isotope effects, phonon anomalies, and doping dependencies. A second important topic concerns new insights obtained in studies of stripes under extreme conditions such as high magnetic fields and high pressure. Furthermore, the tilting of stripes in orthorhombic lattices will be discussed, as well as the possibility of diagonal charge stripes below the metal insulator transition, and alternative models for the stripe phase.