Engineered lattices in condensed matter physics, such as cold-atom optical lattices or photonic crystals, can have properties that are fundamentally different from those of naturally occurring electronic crystals. We report a novel type of artificial quantum matter lattice. Our lattice is a multilayer heterostructure built from alternating thin films of topological and trivial insulators. Each interface within the heterostructure hosts a set of topologically protected interface states, and by making the layers sufficiently thin, we demonstrate for the first time a hybridization of interface states across layers. In this way, our heterostructure forms an emergent atomic chain, where the interfaces act as lattice sites and the interface states act as atomic orbitals, as seen from our measurements by angle-resolved photoemission spectroscopy. By changing the composition of the heterostructure, we can directly control hopping between lattice sites. We realize a topological and a trivial phase in our superlattice band structure. We argue that the superlattice may be characterized in a significant way by a one-dimensional topological invariant, closely related to the invariant of the Su-Schrieffer-Heeger model. Our topological insulator heterostructure demonstrates a novel experimental platform where we can engineer band structures by directly controlling how electrons hop between lattice sites.

A major remaining challenge in the superconducting cuprates is the unambiguous differentiation of the composition and electronic structure of the CuO2 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-layer depth resolution of these properties. Applying SW photoemission to Bi2Sr2CaCu2O8+δ 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 atomic supermodulation structure, as determined by comparison to density functional theory calculations, by Ca-Sr intermixing, and by correlation effects associated with 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.