  Engineered lattices in condensed matter physics, such as cold atom optical
lattices or photonic crystals, can have fundamentally different properties from
naturally-occurring electronic crystals. Here, 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 (ARPES). 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.
