  The rare-earth ditellurides are known to form two-dimensional square lattice
where the strong Fermi surface nesting leads to structural modulation. In
contrast to charge density waves, the supercell modulation is accompanied by
the formation of the periodic Te vacancy network, where the Te deficiency
affects the nesting vector (i.e. the supercell size) via tuning the chemical
potential. In this work, first principles electronic structure calculations for
the $\sqrt{5}\times\sqrt{5}$ supercell, that commonly appears in this family of
tellurides, unveil interesting electronic, transport, and migration properties
of the Te defect lattice in DyTe$_{1.8}$. The reconstruction of the
Te-deficient square lattice, consisting of a single Te-dimer and a pair
Te-trimers per unit cell, gives rise to an out-of-plane polarization, whose
direction depends on the position of the dimer. This results in various
close-in-energy parallel and antiparallel polarization configurations of
successive Te layers depending on the dimer positions. We predict that the
orientation of the Te dimers, and hence the corresponding structural motifs,
can be reversibly switched between two in-plane perpendicular directions under
tensile epitaxial strain via a piezoelectric substrate, resulting in a colossal
conductivity switching. Furthermore, the Te-dimer orientations result in
asymmetric Fermi surface which can be confirmed by quantum oscillations
measurements. Finally, we present numerical results for the migration paths and
energy landscape through various divacancy configurations in the presence or
absence of epitaxial strain.
