As a consequence, we observe a 4f-5d band inversion at the X point, resulting in a nontrivial topology, and the ensuing topological indices 1;(000) allows us to classify SmO as a 3D strongly topological semi-metal.
To provide additional confirmation of the topological non-triviality in SmO and to explicitly identify the protected surface states, we have calculated the Bloch spectral density (ABl(k)) of the 12 topmost surface layers of a semi-infinite solid with  and  surfaces (Fig. 6). Consistent with the topological indices, we obtain an odd number of Dirac-cones. For both the surfaces, a single Dirac-cone at Γ, which becomes a surface resonance due to the semi-metallic nature of SmO, is observed, along with two cones each at M and X for the  and  surfaces, respectively.
Having established the nontrivial topology in SmO for the experimental bulk lattice parameter, we considered the scenario of growing thin films of SmO. In general, the lattice parameter of the substrate plays a decisive role in determining the lattice parameter of a thin film. Then, the relevant question to answer is the robustness of the topological semi-metal state as a function of lattice parameter variation. To this end, we have investigated the topological indices for various lattice parameters (Fig. 7). Treating the strong 4f correlations on a mean-field level, the topological semi-metal state is quite robust and remains so, up to 5.38 Å , a 9% increase in lattice parameter. On an experimental level, this result is very promising, since it provides a large range of lattice constants of the substrate onto which SmO thin films can be grown and reveal topological non-triviality. During the evaluation of the topological indices, we became aware of another interesting feature, a nontrivial topology due to s-f band inversion at Γ for 11% and larger lattice constants (≥ 5.5 Å). Albeit no gap will be opened at Γ due to the degenerate quartet in cubic symmetry, thin films of SmO will acquire a tetragonal symmetry induced by strain which lifts the degeneracy and a gap opens, creating a topological insulator.
Thus, our calculations show that the topological nontrivial ground-state of SmO is stable for a large range of Sm-O distances, including both positive and negative strain. The Sm-f band filling is thus tunable by strain, which opens up the possibility to create correlated topological nontrivial bands at different filling. SmO is therefore an ideal candidate for further investigations in bulk and thin-film form.
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