Ab initio investigation of impurity-induced in-gap states in ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$

We investigate in-gap states emerging when a single $3d$ transition metal impurity is embedded in topological insulators (${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$). We use a combined approach relying on first-principles calculations and an Anderson impurity model. By computing the local density of states of Cr, Mn, Fe, and Co embedded not only in surfaces of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ but also in their bulk phases, we demonstrate that in-gap states originate from the hybridization of the electronic states of the impurity with bulk bands and not with the topological surface states as is usually assumed. This finding is analyzed using a simplified Anderson impurity model. These observations are in contradiction with the prevailing models used to investigate the magnetic doping of topological insulators [R. R. Biswas et al., Phys. Rev. B 81, 233405 (2010)], which attribute the origin of the in-gap states to the hybridization with the topological surface states.

Figure 1

Atomic structure. (a) Crystal structure of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ characterized by a primitive unit cell containing five inequivalent atoms (two Bi, two Te2, and one Te1). The rhombohedral primitive vectors $\{{\vec{v}}_1,{\vec{v}}_2,{\vec{v}}_3\}$ are also shown. For the slab, six quintuple layers are used. The cut to create the surface is indicated on the figure. The position of the impurity in the real space calculations is indicated by a red arrow. (b) Top view of the crystal structure showing the ABC stacking of the different layers. (c) Side view of the quintuple layer showing the stacking of the layers along the $z$ direction.

Figure 2

First-principles simulated spin-resolved LDOS for $3d$ impurities (Cr, Mn, Fe, and Co) embedded in (a) the (111) surface of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, (b) the (111) surface of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, (c) the bulk of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, and (d) in the bulk of a ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ bulk. The majority-spin channel is represented in full lines, while the minority-spin channel is given in dashed lines. The energies are given with respect to ${\varepsilon }_{\text{F}}$ and the bulk band gap is highlighted in light blue.

Figure 3

(a) Modeled $d_{xy}$ contribution to the majority LDOS of Cr, Mn, Fe, and Co embedded in ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ bulk within the Anderson model. (b) The straight lines represent $\varepsilon -{\varepsilon }_i^{\uparrow }$, where ${\varepsilon }_i^{\uparrow }$ is the energy level of the majority $d_{xy}$ orbital. The real and imaginary parts of the bulk (surface) hybridization function are depicted in magenta (brown). The Dirac point is located at ${\varepsilon }_{\text{D}}=-0.2$ eV. The used model parameters are given in Table 2.