Despite three decades studying superconductivity in cuprate-based materials, we are still left with an incomplete understanding of how their superconducting state at unexpectedly high temperatures emerges from a “soup” of multiple broken-symmetry phases (i.e. ordered states). Although states of broken translational symmetry (i.e. charge order) were known to exist in some cuprates, only recently have we realized [1,2] that charge order could be the missing piece of the high-Tc puzzle. To understand how charge order fits in the puzzle, we require a suite of new measurements to specifically address: What does the charge order ‘look’ like? Is the charge order, like superconductivity, ubiquitous to all cuprates or just a material-specific accident? Is it helpful or harmful to superconductivity? Which electronic orbitals form the ordered patterns? Is it related to the mysterious pseudogap phase? Do the electron spins participate in the charge order phenomenon?
In this talk, I will discuss how we pushed the limits of scanning tunneling microscopy and spectroscopy (STM/S) and resonant (inelastic) x-ray scattering (R(I)XS) to address some of these questions [2-5]. In particular, I will focus on how STS can be used to ‘take pictures’ of charge order patterns with atomic resolution in solids and how soft RXS has emerged as an extremely sensitive technique to detect charge order in quantum materials.
 G. Ghiringhelli, et al. Science 337, 821 (2012).
 E. H. da Silva Neto, et al. Science 343, 393 (2014).
 E. H. da Silva Neto, et al. Science 347, 282 (2015).
 E. H. da Silva Neto, et al. Science Advances 2 (8), e1600782 (2016).
 E. H. da Silva Neto, et al. PRB, Rapid Comm. 98, 161114(R) (2018).