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Register a new userNonequilibrium spin texture within a thin layer below the surface of current-carrying topological insulator Bi$_2$Se$_3$: A first-principles quantum transport study
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We predict that unpolarized charge current injected into a ballistic thin film of prototypical topological insulator (TI) Bi$_2$Se$_3$ will generate a {it noncollinear spin texture} $mathbf{S}(mathbf{r})$ on its surface. Furthermore, the nonequilibrium spin texture will extend into $simeq 2$ nm thick layer below the TI surfaces due to penetration of evanescent wavefunctions from the metallic surfaces into the bulk of TI. Averaging $mathbf{S}(mathbf{r})$ over few AA{} along the longitudinal direction defined by the current flow reveals large component pointing in the transverse direction. In addition, we find an order of magnitude smaller out-of-plane component when the direction of injected current with respect to Bi and Se atoms probes the largest hexagonal warping of the Dirac-cone dispersion on TI surface. Our analysis is based on an extension of the nonequilibrium Green functions combined with density functional theory (NEGF+DFT) to situations involving noncollinear spins and spin-orbit coupling. We also demonstrate how DFT calculations with properly optimized local orbital basis set can precisely match putatively more accurate calculations with plane-wave basis set for the supercell of Bi$_2$Se$_3$.
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The protected electron states at the boundaries or on the surfaces of topological insulators (TIs) have been the subject of intense theoretical and experimental investigations. Such states are enforced by very strong spin-orbit interaction in solids composed of heavy elements. Here, we study the composite particles -- chiral excitons -- formed by the Coulomb attraction between electrons and holes residing on the surface of an archetypical three-dimensional topological insulator (TI), Bi$_2$Se$_3$. Photoluminescence (PL) emission arising due to recombination of excitons in conventional semiconductors is usually unpolarized because of scattering by phonons and other degrees of freedom during exciton thermalization. On the contrary, we observe almost perfectly polarization-preserving PL emission from chiral excitons. We demonstrate that the chiral excitons can be optically oriented with circularly polarized light in a broad range of excitation energies, even when the latter deviate from the (apparent) optical band gap by hundreds of meVs, and that the orientation remains preserved even at room temperature. Based on the dependences of the PL spectra on the energy and polarization of incident photons, we propose that chiral excitons are made from massive holes and massless (Dirac) electrons, both with chiral spin textures enforced by strong spin-orbit coupling. A theoretical model based on such proposal describes quantitatively the experimental observations. The optical orientation of composite particles, the chiral excitons, emerges as a general result of strong spin-orbit coupling in a 2D electron system. Our findings can potentially expand applications of TIs in photonics and optoelectronics.
The band bending (BB) effect on the surface of the second-generation topological insulators implies a serious challenge to design transport devices. The BB is triggered by the effective electric field generated by charged impurities close to the surface and by the inhomogeneous charge distribution of the occupied surface states. Our self-consistent calculations in the Korringa-Kohn-Rostoker framework showed that in contrast to the bulk bands, the spectrum of the surface states is not bent at the surface. In turn, it is possible to tune the energy level of the Dirac point via the deposited surface dopants. In addition, the electrostatic modifications induced by the charged impurities on the surface induce long range oscillations in the charge density. For dopants located beneath the surface, however, these oscillations become highly suppressed. Our findings are in good agreement with recent experiments, however, our results indicate that the concentration of the surface doping cannot be estimated from the energy shift of the Dirac cone within the scope of the effective continuous model for the protected surface states.
We perform ab-initio calculations on Bi$_mathrm{{Se}}$ antisite defects in the surface of Bi$_2$Se$_3$, finding strong low-energy defect resonances with a spontaneous ferromagnetism, fixed to an out-of-plane orientation due to an exceptional large magnetic anisotropy energy. For antisite defects in the surface layer, we find semi-itinerant ferromagnetism and strong hybridization with the Dirac surface state, generating a finite energy gap. For deeper lying defects, such hybridization is largely absent, the magnetic moments becomes more localized, and no energy gap is present.
We report on microscopic tight-binding modeling of surface states in Bi$_2$Se$_3$ three-dimensional topological insulator, based on a sp$^3$ Slater-Koster Hamiltonian, with parameters calculated from density functional theory. The effect of spin-orbit interaction on the electronic structure of the bulk and of a slab with finite thickness is investigated. In particular, a phenomenological criterion of band inversion is formulated for both bulk and slab, based on the calculated atomic- and orbital-projections of the wavefunctions, associated with valence and conduction band extrema at the center of the Brillouin zone. We carry out a thorough analysis of the calculated bandstructures of slabs with varying thickness, where surface states are identified using a quantitative criterion according to their spatial distribution. The thickness-dependent energy gap, attributed to inter-surface interaction, and the emergence of gapless surface states for slabs above a critical thickness are investigated. We map out the transition to the infinite-thickness limit by calculating explicitly the modifications in the spatial distribution and spin-character of the surface states wavefunction with increasing the slab thickness. Our numerical analysis shows that the system must be approximately forty quintuple-layers thick to exhibit completely decoupled surface states, localized on the opposite surfaces. These results have implications on the effect of external perturbations on the surface states near the Dirac point.
We present a theoretical study on the high-field charge transport on the surface of Bi$_2$Se$_3$ and reproduce all the main features of the recent experimental results, i.e., the incomplete current saturation and the finite residual conductance in the high applied field regime [Costache {it et al.}, Phys. Rev. Lett. {bf 112}, 086601 (2014)]. Due to the hot-electron effect, the conductance decreases and the current shows the tendency of the saturation with the increase of the applied electric field. Moreover, the electric field can excite carriers within the surface bands through interband precession and leads to a higher conductance. As a joint effect of the hot-electron transport and the carrier excitation, the conductance approaches a finite residual value in the high-field regime and the current saturation becomes incomplete. We thus demonstrate that, contrary to the conjecture in the literature, the observed transport phenomena can be understood qualitatively in the framework of surface transport alone. Furthermore, if a constant bulk conductance which is insensitive to the field is introduced, one can obtain a good quantitative agreement between the theoretical results and the experimental data.
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