We investigate the properties of a single substitutional Mn impurity and its associated acceptor state on the (111) surface of Bi$_2$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 quasi-resonant coupling and the strong real-space overlap between the spin-chiral surface states and the mid-gap spin-polarized Mn-acceptor states.
Combining density-functional theory calculations and microscopic tight-binding models, we investigate theoretically the electronic and magnetic properties of individual substitutional transition-metal impurities (Mn and Fe) positioned in the vicinity of the (110) surface of GaAs. For the case of the $[rm Mn^{2+}]^0$ plus acceptor-hole (h) complex, the results of a tight-binding model including explicitly the impurity $d$-electrons are in good agreement with approaches that treat the spin of the impurity as an effective classical vector. For the case of Fe, where both the neutral isoelectronic $[rm Fe^{3+}]^0$ and the ionized $[rm Fe^{2+}]^-$ states are relevant to address scanning tunneling microscopy (STM) experiments, the inclusion of $d$-orbitals is essential. We find that the in-gap electronic structure of Fe impurities is significantly modified by surface effects. For the neutral acceptor state $[{rm Fe}^{2+}, h]^0$, the magnetic-anisotropy dependence on the impurity sublayer resembles the case of $[{rm Mn}^{2+}, h]^0$. In contrast, for $[{rm Fe}^{3+}]^{0}$ electronic configuration the magnetic anisotropy behaves differently and it is considerably smaller. For this state we predict that it is possible to manipulate the Fe moment, e.g. by an external magnetic field, with detectable consequences in the local density of states probed by STM.
We investigate the effect of an external magnetic field on the physical properties of the acceptor hole states associated with single Mn acceptors placed near the (110) surface of GaAs. Crosssectional scanning tunneling microscopy images of the acceptor local density of states (LDOS) show that the strongly anisotropic hole wavefunction is not significantly affected by a magnetic field up to 6 T. These experimental results are supported by theoretical calculations based on a tightbinding model of Mn acceptors in GaAs. For Mn acceptors on the (110) surface and the subsurfaces immediately underneath, we find that an applied magnetic field modifies significantly the magnetic anisotropy landscape. However the acceptor hole wavefunction is strongly localized around the Mn and the LDOS is quite independent of the direction of the Mn magnetic moment. On the other hand, for Mn acceptors placed on deeper layers below the surface, the acceptor hole wavefunction is more delocalized and the corresponding LDOS is much more sensitive on the direction of the Mn magnetic moment. However the magnetic anisotropy energy for these magnetic impurities is large (up to 15 meV), and a magnetic field of 10 T can hardly change the landscape and rotate the direction of the Mn magnetic moment away from its easy axis. We predict that substantially larger magnetic fields are required to observe a significant field-dependence of the tunneling current for impurities located several layers below the GaAs surface.
