  A major remaining challenge in the superconducting cuprates is the
unambiguous differentiation of the composition and electronic structure of the
CuO$_2$ layers and those of the intermediate layers. The large c axis for these
materials permits employing soft x-ray (930.3 eV) standing wave (SW) excitation
in photoemission that yields atomic layer-by-atomic layer depth resolution of
these properties. Applying SW photoemission to
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ yields the depth distribution of atomic
composition and the layer-resolved densities of states. We detect significant
Ca presence in the SrO layers and oxygen bonding to three different cations.
The layer-resolved valence electronic structure is found to be strongly
influenced by the supermodulation structure--as determined by comparison to DFT
calculations, by Ca-Sr intermixing, and by the Cu 3d-3d Coulomb interaction,
further clarifying the complex interactions in this prototypical cuprate.
Measurements of this type for other quasi-two-dimensional materials with
large-c represent a promising future direction.
