Surface and Edge States in Topological Semi-metals

We study the topologically non-trivial semi-metals by means of the 6-band Kane model. Existence of surface states is explicitly demonstrated by calculating the LDOS on the material surface. In the strain free condition, surface states are divided into two parts in the energy spectrum, one part is in the direct gap, the other part including the crossing point of surface state Dirac cone is submerged in the valence band. We also show how uni-axial strain induces an insulating band gap and raises the crossing point from the valence band into the band gap, making the system a true topological insulator. We predict existence of helical edge states and spin Hall effect in the thin film topological semi-metals, which could be tested with future experiment. Disorder is found to significantly enhance the spin Hall effect in the valence band of the thin films

Non-magnetic impurities and in-gap bound states in topological insulators

In-gap bound states induced by non-magnetic impurities in various dimensional topological insulators are investigated based on a modified Dirac model that considers quadratic corrections to the mass term. Their existence and features greatly rely on the potential form of the impurity as well as the dimensionality of the topological insulator. It is analytically proven that the impurity potential modeled by the delta function can induce the bound states in one dimension (1D), but not in two and three. For a single non-magnetic impurity with a general isotropic potential, formal solutions are obtained and further numerical calculations are performed. In particular, the in-gap bound states induced by a non-magnetic impurity with isotropic Gaussian potentials in two-dimensional (2D) and three-dimensional (3D) topological insulators are numerically investigated. Information on how many in-gap bound states can be trapped by a non-magnetic Gaussian impurity is presented for the parameters from a series of topologically non-trivial materials. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.published_or_final_versio

Vacancy-induced bound states in topological insulators

We present an exact solution of a modified Dirac equation for topological insulator in the presence of a hole or vacancy to demonstrate that vacancies can induce bound states in the band gap of topological insulators. They arise due to the Z 2 classification of time-reversal invariant insulators. Coexistence of the in-gap bound states and the edge or surface states in topological insulators suggests that imperfections may affect transport properties of topological insulators via additional bound states near the system boundary. © 2011 American Physical Society.published_or_final_versio

Massive Dirac fermions and spin physics in an ultrathin film of topological insulator

We study transport and optical properties of the surface states which lie in the bulk energy gap of a thin-film topological insulator. When the film thickness is comparable with the surface state decay length into the bulk, the tunneling between the top and bottom surfaces opens an energy gap and form two degenerate massive Dirac hyperbolas. Spin dependent physics emerges in the surface bands which are vastly different from the bulk behavior. These include the surface spin Hall effects, spin dependent orbital magnetic moment, and spin dependent optical transition selection rule which allows optical spin injection. We show a topological quantum phase transition where the Chern number of the surface bands changes when varying the thickness of the thin film.Comment: 7 pages, 5 figure

How many supermassive black hole binaries are detectable through tracking relative motions by sub/millimeter VLBI

The sub/millimeter wavelengths (86-690 GHz) very long baseline interferometry (VLBI) will provide $\sim5-40\ \mu$as angular resolution, $\sim10$ mJy baseline sensitivity, and $\sim 1\ \mu$as/yr proper motion precision, which can directly detect supermassive black hole binary (SMBHB) systems by imaging the two visible sources and tracking their relative motions. Such a way exhibits an advantage compared to indirect detect methods of observing periodic signals in motion and light curves, which are difficult to confirm from competing models. Moreover, tracking relative motion at sub/millimeter wavelengths is more reliable, as there is a negligible offset between the emission region and the black hole center. In this way, it is unnecessary to correct the black hole location by a prior of jet morphology as it would be required at longer wavelengths. We extend the formalism developed in D'Orazio & Loeb (2018) to link the observations with the orbital evolution of SMBHBs from the $\lesssim$10 kpc dynamical friction stages to the $\lesssim 0.01$ pc gravitational radiation stages, and estimate the detectable numbers of SMBHBs. By assuming 5\% of AGNs holding SMBHBs, we find that the number of detectable SMBHBs with redshift $z\le 0.5$ and mass $M\leq 10^{11}M_\odot$ is about 20. Such detection relies heavily on proper motion precision and sensitivity. Furthermore, we propose that the simultaneous multi-frequency technique plays a key role in meeting the observational requirements

Effective continuous model for surface states and thin films of three dimensional topological insulators

Two-dimensional effective continuous models are derived for the surface states and thin films of the three-dimensional topological insulator (3DTI). Starting from an effective model for 3DTI based on the first principles calculation [Zhang \emph{et al}, Nat. Phys. 5, 438 (2009)], we present solutions for both the surface states in a semi-infinite boundary condition and in the thin film with finite thickness. An effective continuous model was derived for surface states and the thin film 3DTI. The coupling between opposite topological surfaces and structure inversion asymmetry (SIA) give rise to gapped Dirac hyperbolas with Rashba-like splittings in energy spectrum. Besides, the SIA leads to asymmetric distributions of wavefunctions along the film growth direction, making some branches in the energy spectra much harder than others to be probed by light. These features agree well with the recent angle-resolved photoemission spectra of Bi$_{2}$Se $_{3}$ films grown on SiC substrate [Zhang et al, arXiv: 0911.3706]. More importantly, we use the effective model to fit the experimental data and determine the model parameters. The result indicates that the thin film Bi$_{2}$Se$_{3}$ lies in quantum spin Hall region based on the calculation of the Chern number and the $Z_{2}$ invariant. In addition, strong SIA always intends to destroy the quantum spin Hall state.Comment: 12 pages, 7 figures, references are update

Spin-orbit scattering in quantum diffusion of massive Dirac fermions

Effect of spin-orbit scattering on quantum diffusive transport of two-dimensional massive Dirac fermions is studied by the diagrammatic technique. The quantum diffusion of massive Dirac fermions can be viewed as a singlet Cooperon in the massless limit and a triplet Cooperon in the large-mass limit. The spin-orbit scattering behaves like random magnetic fields only to the triplet Cooperon, and suppresses the weak localization of Dirac fermions in the large-mass regime. This behavior suggests an experiment to detect the weak localization of bulk subbands in topological insulator thin films, in which a narrowing of the cusp of the negative magnetoconductivity is expected after doping heavy-element impurities. Finally, a detailed comparison between the conventional two-dimensional electrons and Dirac fermions is presented for impurities of orthogonal, symplectic, and unitary symmetries.Comment: 5 pages, 3 figures, 2 tables. To be submitted, comments are welcom