Modification of topological surface states in novel Mn$_{1-x}$A$_{x}$Bi$_2$Te$_4$/MnBi$_2$Te$_4$ (A = Si, Ge, Sn, Pb) topological systems

The possibility of changing the bandgap value of topological surface states in materials based on the MnBi$_2$Te$_4$ intrinsic antiferromagnetic topological insulator is investigated using ab initio calculations. These materials are produced by the substitution of nonmagnetic chemical elements (A = Si, Ge, Sn, Pb) for magnetic metal atoms (Mn) in the surface (Mn$_{1-x}$A$_{x}$Bi$_2$Te$_4$/MnBi$_2$Te$_4$) septuple layer. The results exhibit a significant modulation of the bandgap in a wide range from 60 meV to 0 meV with an increase in the doping level $x$. Moreover, it is found that the bandgap behavior depends on a dopant. Namely, a monotonic dependence of the bandgap on $x$ is found for Si and Ge, whereas the bandgap minimum at $x = 0.75$ exists for Sn and Pb. The results obtained in this work suggest that the main mechanism of the bandgap modulation in the materials under study is a change in the localization of topological surface states.