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A major remaining challenge in the superconducting cuprates is theunambiguous differentiation of the composition and electronic structure of theCuO$_2$ layers and those of the intermediate layers. The large c axis for thesematerials permits employing soft x-ray (930.3 eV) standing wave (SW) excitationin photoemission that yields atomic layer-by-atomic layer depth resolution ofthese properties. Applying SW photoemission toBi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ yields the depth distribution of atomiccomposition and the layer-resolved densities of states. We detect significantCa presence in the SrO layers and oxygen bonding to three different cations.The layer-resolved valence electronic structure is found to be stronglyinfluenced by the supermodulation structure--as determined by comparison to DFTcalculations, 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 withlarge-c represent a promising future direction.

physical review. b./physical review. b

Atomic-layer-resolved composition and electronic structure of the  cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ from soft x-ray standing-wave  photoemission