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Register a new userProbing the wavefunction of the surface states in Bi$_2$Se$_3$ topological insulator: a realistic tight-binding approach
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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.
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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.
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.
The influence of individual impurities of Fe on the electronic properties of topological insulator Bi$_2$Se$_3$ is studied by Scanning Tunneling Microscopy. The microscope tip is used in order to remotely charge/discharge Fe impurities. The charging process is shown to depend on the impurity location in the crystallographic unit cell, on the presence of other Fe impurities in the close vicinity, as well as on the overall doping level of the crystal. We present a qualitative explanation of the observed phenomena in terms of tip-induced local band bending. Our observations evidence that the specific impurity neighborhood and the position of the Fermi energy with respect to the Dirac point and bulk bands have both to be taken into account when considering the electron scattering on the disorder in topological insulators.
Scanning tunneling microscopy and spectroscopy have been used to investigate the femtosecond dynamics of Dirac fermions in the topological insulator Bi$_2$Se$_3$ ultrathin films. At two-dimensional limit, bulk electrons becomes quantized and the quantization can be controlled by film thickness at single quintuple layer level. By studying the spatial decay of standing waves (quasiparticle interference patterns) off steps, we measure directly the energy and film thickness dependence of phase relaxation length $l_{phi}$ and inelastic scattering lifetime $tau$ of topological surface-state electrons. We find that $tau$ exhibits a remarkable $(E-E_F)^{-2}$ energy dependence and increases with film thickness. We show that the features revealed are typical for electron-electron scattering between surface and bulk states.
Topological insulators are bulk insulators with exotic surface states, protected under time-reversal symmetry, that hold promise in observing many exciting condensed-matter phenomena. In this report, we show that by having a topological insulator (Bi$_2$Se$_3$) in proximity to a magnetic insulator (EuS), a metal-to-insulator transition in the surface state, attributed to opening of an exchange gap, can be observed whose properties are tunable using bottom gate voltage and external magnetic field. Our study provides evidence of gate-controlled enhanced interface magnetism with the signature of half-integer quantum Hall effect when the Fermi level is tuned into the exchange gap. These results pave the way for using magnetic proximity effect in developing topological electronic devices.
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