  Square net tellurides host an array of electronic ground states and commonly
exhibit charge-density-wave ordering. Here we report the epitaxy of
DyTe$_{2-\delta}$ on atomically flat MgO (001) using molecular beam epitaxy.
The films are single phase and highly oriented as evidenced by transmission
electron microscopy and X-ray diffraction measurements. Epitaxial strain is
evident in films and is relieved as the thickness increases up to a value of
approximately 20 unit cells. Diffraction features associated with a supercell
in the films are resolved which is coupled with Te-deficiency. First principles
calculations attribute the formation of this defect lattice to nesting
conditions in the Fermi surface, which produce a periodic occupancy of the
conducting Te square-net, and opens a band gap at the chemical potential. This
work establishes the groundwork for exploring the role of strain in tuning
electronic and structural phases of epitaxial square-net tellurides and related
compounds.
