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The helical Dirac fermions on the surface of topological insulators host novel relativistic quantum phenomena in solids. Manipulating spins of topological surface state (TSS) represents an essential step towards exploring the theoretically predicted exotic states related to time reversal symmetry (TRS) breaking via magnetism or magnetic field. Understanding Zeeman effect of TSS and determining its g-factor are pivotal for such manipulations in the latter form of TRS breaking. Here, we report those direct experimental observations in Bi2Se3 and Sb2Te2Se by spectroscopic imaging scanning tunneling microscopy. The Zeeman shifting of zero mode Landau level is identified unambiguously by judiciously excluding the extrinsic influences associated with the non-linearity in the TSS band dispersion and the spatially varying potential. The g-factors of TSS in Bi2Se3 and Sb2Te2Se are determined to be 18 and -6, respectively. This remarkable material dependence opens a new route to control the spins in the TSS., Comment: main text: 17 pages, 4 figures; supplementary: 15 pages, 7 figures

We report on the Pt doping effect on surface and electronic structure in Ir$_{\mathrm{1-x}}$Pt$_{\mathrm{x}}$Te$_ {\mathrm{2}}$ by scanning tunneling microscopy (STM) and spectroscopy (STS). The surface prepared by cleavage at 4.2 K shows a triangular lattice of topmost Te atoms. The compounds that undergo structural transition have supermodulation with a fixed wave vector $q = \frac{2\pi}{5a_m}$ (where $a_m$ is the lattice constant in the monoclinic phase) despite the different Pt concentrations. The superconducting compounds show patch structures. The surface of the compound that exhibits neither the superconductivity nor the structural transition shows no superstructure. In all doped samples, the dopant is observed as a dark spot in STM images. The tunneling spectra near the dopant show the change in the local density of state at approximately -200 mV. Such microscopic effects of the dopant give us the keys for establishing a microscopic model of this material., Comment: 6 pages, 3 figures

Massless Dirac electrons in condensed matter have attracted considerable attention. Unlike conventional electrons, Dirac electrons are described in the form of two-component wave functions. In the surface state of topological insulators, these two components are associated with the spin degrees of freedom, hence governing the magnetic properties. Therefore, the observation of the two-component wave function provides a useful clue for exploring the novel spin phenomena. Here we show that the two-component nature is manifested in the Landau levels (LLs) whose degeneracy is lifted by a Coulomb potential. Using spectroscopic-imaging scanning tunneling microscopy, we visualize energy and spatial structures of LLs in a topological insulator Bi2Se3. The observed potential-induced LL splitting and internal structures of Landau orbits are distinct from those in a conventional electron system and are well reproduced by a two-component model Dirac Hamiltonian. Our model further predicts non-trivial energy-dependent spin-magnetization textures in a potential variation. This provides a way to manipulate spins in the topological surface state., Comment: Revised version to appear in Nature Physics. Supplementary information is available at http://www.riken.jp/epmrt/Hanaguri/SI/Bi2Se3_2comp/SI.html

We report on the scanning tunneling spectroscopy experiments on single crystals of IrTe$_{2}$. A structural supermodulation and a local density-of-states (LDOS) modulation with a wave vector of $q$ = 1/5$\times$$2\pi /a_{0}$ ($a_{0}$ is the lattice constant in the $ab$-plane) have been observed at 4.2K where the sample is in the monoclinic phase. %We cannot find an energy gap emerging reproducibly.% on the region where the supermodulation resides. As synchronized with the supermodulation, the LDOS spatially modulates within two energy ranges (below -200 meV and around -100 meV). We further investigated the effect of the local perturbations including the antiphase boundaries and the twin boundaries on the LDOS. These perturbations also modify the LDOS below -200 meV and around -100 meV, even though the lattice distortions induced by these perturbations appear to be different from those by the supermodulation. Our results indicating several microscopic structural effects on the LDOS seem to offer crucial keys for the establishment of the microscopic model describing the parent state., Comment: 5 pages, 4 figures, to be published in Phys. Rev. B

We investigate Dirac fermions on the surface of the topological insulator Bi2Se3 using scanning tunneling spectroscopy. Landau levels (LLs) are observed in the tunneling spectra in a magnetic field. In contrast to LLs of conventional electrons, a field independent LL appears at the Dirac point, which is a hallmark of Dirac fermions. A scaling analysis of LLs based on the Bohr-Sommerfeld quantization condition allowed us to determine the dispersion of the surface band. Near the Fermi energy, fine peaks mixed with LLs appear in the spectra, which may be responsible for the anomalous magneto-fingerprint effect [J. G. Checkelsky et al., Phys. Rev. Lett. 103, 246601 (2009)]., Comment: 4 pages, 4 figures