Regulation of Te atomic vacancy defects in the intrinsic magnetic topological insulator $$\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}$$ MnBi 6 Te 10

Recently, the newly discovered magnetic topological insulator $$\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}$$ MnBi 6 Te 10 has become a hot research topic in condensed matter physics because of its effects such as quantum anomalous Hall effect, axion insulation effect, and topological magnetoelectric effect. The magnetic topological insulator $$\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}$$ MnBi 6 Te 10 is a potential energy material with superlattice like stacking structure. Based on first-principles calculations, we computed the band structure and density of states of five unequal Te atomic vacancy defects in ferromagnetic $$\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}$$ MnBi 6 Te 10 and found that $$\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}$$ MnBi 6 Te 10 has defects and, like intrinsic $$\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}$$ MnBi 6 Te 10 , the band inversion occurs near the $$\varGamma $$ Γ -high-symmetry point, where the conduction band is mainly contributed by the $$\textit{p}$$ p orbitals of Bi, but the valence band is mainly occupied by the $$\textit{p}$$ p orbitals of Te. But with defective sites, $$\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}$$ MnBi 6 Te 10 changes from having a band gap to having no band gap. This implies that the defect of $$\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}$$ MnBi 6 Te 10 is transformed from the intrinsic topological phase of $$\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}$$ MnBi 6 Te 10 to the metallic phase. By calculating the density of states, we find that the Fermi level crosses the valence band in the $$\hbox {V}_{{Te}}$$ V Te 1 and $$\hbox {V}_{{Te}}$$ V Te 4 defect systems, while it crosses the conduction band in the $$\hbox {V}_{{Te}}$$ V Te 2, $$\hbox {V}_{{Te}}$$ V Te 3 and $$\hbox {V}_{{Te}}$$ V Te 5 systems. The charge density difference calculations show that the Te vacancy defects at different equivalence sites mainly affect some atomic layers in their vicinity and exhibit different charge distribution characteristics for the neighboring atomic layers, respectively, essentially because of the different bonding environments in which the defects are located. Our results of different Te defect states in $$\hbox {MnBi}_{{6}}\hbox {Te}_{{10}}$$ MnBi 6 Te 10 provides valuable theoretical guidance for the experimental synthesis of single-crystal materials and the regulation of defect states in practical applications, and in addition, it has an important impact on the exploration of new quantum materials. Graphic abstract