When a three-dimensional material is constructed by stacking different two-dimensional layers into an ordered structure, new and unique physical properties can emerge. An example is the delafossite PdCoO2, which consists of alternating layers of metallic Pd and Mott-insulating CoO2 sheets. To understand the nature of the electronic coupling between the layers that gives rise to the unique properties of PdCoO2, we revealed its layer-resolved electronic structure combining standing-wave X-ray photoemission spectroscopy and ab initio many-body calculations. Experimentally, we have decomposed the measured VB spectrum into contributions from Pd and CoO2 layers. Computationally, we find that many-body interactions in Pd and CoO2 layers are highly different. Holes in the CoO2 layer interact strongly with charge-transfer excitons in the same layer, whereas holes in the Pd layer couple to plasmons in the Pd layer. Interestingly, we find that holes in states hybridized across both layers couple to both types of excitations (charge-transfer excitons or plasmons), with the intensity of photoemission satellites being proportional to the projection of the state onto a given layer. This establishes satellites as a sensitive probe for inter-layer hybridization. These findings pave the way towards a better understanding of complex many-electron interactions in layered quantum materials.

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.