The spontaneous self-arrangement of electrons into static and periodically modulated patterns, a phenomenon commonly termed as charge order or charge-density-wave, has recently resurfaced as a prominent, universal ingredient for the physics of copper oxide high-temperature superconductors. Its antagonist coexistence with superconductivity, together with a putative connection to a quantum critical point beyond optimal doping, are symptomatic of a very fundamental role played by this collective electronic state for the physics of cuprates.
Resonant x-ray scattering (RXS) has rapidly become the technique of choice for the study of charge order in momentum space , owing to its ability to directly identify a breaking of translational symmetry in the electronic density. We have used RXS in Bi-, Nd, and Y-based cuprates to detect charge-density-waves even in presence of short-ranged order [2-3], exploring a realm previously accessible only by STM. Using the information available from the full two-dimensional momentum space, we have taken this experimental methodology further to reveal the local (intra-unit-cell) symmetry in the charge distribution [4,5].
To conclude, I will discuss recent results and future perspectives concerning the study of the nanoscale (10-100 nm) texture of electronic orders using coherent soft x-ray scattering in scanning (RXS nanomapping) and imaging (ptychography and holography) mode.
 R. Comin and A. Damascelli, Resonant x-ray scattering studies of charge order in cuprates, Annual Reviews of Condensed Matter Physics (2016).
 R. Comin, et al., Charge Order Driven by Fermi-Arc Instability in Bi2Sr2-xLaxCuO6+d, Science 343, 390 (2014).
 E. da Silva Neto*, R. Comin*, et al., Charge ordering in the electron-doped superconductor Nd2-xCexCuO4, Science 347, 282 (2015).
 R. Comin, et al., Broken translational and rotational symmetry via charge stripe order in underdoped YBa2Cu3O6+y, Science 347, 1335 (2015).
 R. Comin, et al., Symmetry of charge order in cuprates, Nature Materials 14, 796 (2015).