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Influence of point defects on the electronic and topological properties of monolayer WTe$_2$

In some topological insulators, such as graphene and WTe$_2$, band inversion originates from chemical bonding and space group symmetry, in contrast to materials such as Bi$_2$Se$_3$, where the band inversion derives from relativistic effects in the atoms. In the former, band inversion is susceptible to changes of the chemical environment, e.g. by defects, while the latter are less affected by defects due to the larger energy scale associated with atomic relativistic effects. Motivated by recent experiments, we study the effect of Te-vacancies and Te-adatoms on the electronic properties of WTe$_2$. We find that the Te-vacancies have a formation energy of $2.21$ eV, while the formation energy of the Te-adatoms is much lower with $0.72$ eV. The vacancies strongly influence the band structure and we present evidence that band inversion is already reversed at the nominal composition of WTe$_{1.97}$. In contrast, we show that the adatoms do not change the electronic structure in the vicinity of the Fermi level and thus the topological properties. Our findings indicate that Te-adatoms should be present in thin films that are grown in a Te-rich environment, and we suggest that they have been observed in scanning tunneling microscopy experiments.