Interplay between Mn-acceptor state and Dirac surface states in Mn-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ topological insulator

We investigate the properties of a single substitutional Mn impurity and its associated acceptor state on the (111) surface of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ topological insulator. Combining ab initio calculations with microscopic tight-binding modeling, we identify the effects of inversion symmetry and time-reversal-symmetry breaking on the electronic states in the vicinity of the Dirac point. In agreement with experiments, we find evidence that the Mn ion is in the $+2$ valence state and introduces an acceptor in the bulk band gap. The Mn acceptor has predominantly $p$ character and is localized mainly around the Mn impurity and its nearest-neighbor Se atoms. Its electronic structure and spin-polarization are determined by the hybridization between the Mn $d$ levels and the $p$ levels of surrounding Se atoms, which is strongly affected by electronic correlations at the Mn site. The opening of the gap at the Dirac point depends crucially on the quasiresonant coupling and the strong real-space overlap between the spin-chiral surface states and the midgap spin-polarized Mn-acceptor states.

Figure 1

Band structure of pristine (a),(b) and Mn-doped (c)–(f) ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, calculated with DFT for $U=0$. The inset shows the gap at the Dirac point caused by the TRS breaking. Circles show the contribution of the bottom (a),(d) and top (b),(e) surface states and of the Mn $d$ orbitals (f). The radius of the circles is proportional to the relative weight at a given energy and $k$ point. Arrows in panels (d) and (e) mark the Dirac points of the bottom and top TSS, respectively.

Figure 2

Band structure of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ calculated with the TB model using a $3\times 3\times 6$-QL supercell with (a) a nonmagnetic and (b) a magnetic impurity, substituting a Bi atom in the topmost Bi ML. Band structure for a nonmagnetic impurity at different depth in a $3\times 3\times 5$-QL slab: (c) topmost ML, (d) $5\mathrm{th}$ ML below the surface, and (e) $13\mathrm{th}$ ML, corresponding to the middle of the slab.

Figure 3

Partial $p$-DOS for Se atoms in the top two (a),(d) and bottom two (b),(e) Se MLs; (c),(f) $d$-DOS for the Mn impurity. Left panels are for $U=0$; right panels are for $U=4$ eV. Positive (negative) DOS corresponds to majority (minority) spin. The vertical line marks the position of the Fermi level $\left(E=0\right)$.

Figure 4

(a) (111) ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ surface with a Mn impurity in the second ML. DOS around the Fermi energy for Mn-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ slab for $U=0$ without SOI: (b) total DOS; (c) partial $p$-DOS for the two Se atoms above and below Mn, which are not NN to Mn [indicated by arrows in panel (a)]; (d) partial $p$-DOS for the six NN Se atoms; (e) partial $d$-DOS for the Mn impurity. Note that the total DOS in panel (b) includes contributions from all atoms in the supercell and from the interstitial region.

Figure 5

LDOS of Mn-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ integrated over the energy range $\pm 0.13$ eV around the Fermi level. Positive (negative) energy window correspond to empty- (filled-)state imaging. (a) Empty-state LDOS projected in the $xz$ plane, perpendicular to the (111) surface. LDOS projected on the the (111) surface: (b),(c) at 1 Å above and (d),(e) exactly on the surface. Left (right) panels are for filled (empty) states. Note the logarithmic color scale.