Resonant and magnetic doping control of the topological state of (Bi,Sb)₂(Se,Te)₃

There are two persistent challenges to exploiting the unique properties of topological insulators. The first is to separate the unwanted bulk transport from the topologically protected surface state transport. The second is to control the nature of the topological state, such as a spin Hall insulator, a Chern insulator, and an axion insulator. To reduce scattering between the bulk states and the surface states, band-structure distortion is required to localize the Fermi energy (E_F) in the bulk bandgap. Resonant doping could (1) distort the curvature of the valence band, (2) shift Fermi energy, and (3) increase the density of states. The type and location of the resonant dopants (Sn and Ga) and magnetic dopants (Cr and Mn) control the nature of the bulk and surface states in the (Bi,Sb)₂(Se,Te)₃ system. Employing density functional theory (DFT) and maximally localized Wannier functions (MLWFs), we calculate the effect of resonant and magnetic doping on the bulk and surface states. Our results show that Sn-doping distorts the curvature of the valence band and increases the density of states and effective mass in valence band. Magnetic located in the surface quintuple layers are energetically favorable and yield surface states isolated from the bulk states. Changing the magnetic moments of the top and bottom dopants switches the Chern insulator state into an axion insulator state.