Scanning tunneling spectroscopy studies on high-quality Bi2Te3 crystals exhibit perfect correspondence to ARPES data, hence enabling identification of different regimes measured in the local density of states (LDOS). Oscillations of LDOS near a step are analyzed. Within the main part of the surface band oscillations are strongly damped, supporting the hypothesis of topological protection. At higher energies, as the surface band becomes concave, oscillations appear which disperse with a particular wave-vector that may result from an unconventional hexagonal warping term.PACS numbers: 71.18.+y, 71.20.Nr, A new type of three-dimensional (3D) bulk insulating materials with surface Quantum Spin Hall Effect states protected by time reversal symmetry has been recently predicted [1], and soon afterwards observed experimentally in BiSb bulk crystals [2]. Subsequently, Bi 2 Te 3 has been argued to be a similar three-dimensional topological insulator (TI), exhibiting a bulk gap and a single, non-degenerate Dirac fermion band on the surface [3]. Indeed, recent angle resolved photoemission spectroscopy (ARPES) confirmed that prediction [4]. In particular, with appropriate hole-doping, the Fermi level could be tuned to intersect only the surface states, indicating fully gapped bulk states as is expected from a three-dimensional TI. While ARPES could confirm the nature of the band, it is still a challenge to demonstrate unambiguously the topologically "protected" nature of the surface state in Bi 2 Te 3 , or any other 3D TI system.In this paper we present scanning tunneling microscopy (STM) and spectroscopy (STS) studies on high-quality doped Bi 2 Te 3 crystals. First we show that the STS spectra exhibit remarkable correspondence to ARPES data, hence enabling us to identify each region of the local density of states (LDOS) measured. Second, by analyzing the electron-waves (Friedel-oscillations) observed near cleavage steps, we show that within the main part of the surface state band oscillations are strongly damped, a hallmark of the strong supression of backscattering, hence supporting the hypothesis of a protected band. Finally, we show that in the region in which the surface band is warped, pronounced oscillations appear, with a distinct nesting wave-vector. Possible influence of the bulk conduction band on the oscillations is also proposed.For the present study we used Sn and Cd doped single crystals of Bi 2 Te 3 (see Fig. 1a for crystal structure and Fig. 1b,c for ARPES data). Nominal doping levels between 0 and 0.27% for Sn, and up to 1% for Cd were incorporated to compensate n-type doping from vacancy and anti-site defects that are common in the Bi 2 Te 3 system. Actual doping was determined separately using chemical and Hall-effect methods and were shown by ARPES [4] to be in excellent agreement with the relative position of the Dirac point with respect to the Fermi energy. For example, undoped crystals exhibit a Dirac point at ∼ −335 meV, 0.27% Sn doping yielded a Dirac point at ∼ −300 meV, while for a typical ∼ 1% Cd...

The coherent optical manipulation of solids is emerging as a promising way to engineer novel quantum states of matter 1-5 . The strong time-periodic potential of intense laser light can be used to generate hybrid photon-electron states. Interaction of light with Bloch states leads to Floquet-Bloch states, which are essential in realizing new photo-induced quantum phases [6][7][8] . Similarly, dressing of free-electron states near the surface of a solid generates Volkov states, which are used to study nonlinear optics in atoms and semiconductors 9 . The interaction of these two dynamic states with each other remains an open experimental problem. Here we use time-and angle-resolved photoemission spectroscopy (Tr-ARPES) to selectively study the transition between these two states on the surface of the topological insulator Bi 2 Se 3 . We find that the coupling between the two strongly depends on the electron momentum, providing a route to enhance or inhibit it. Moreover, by controlling the light polarization we can negate Volkov states to generate pure Floquet-Bloch states. This work establishes a systematic path for the coherent manipulation of solids via light-matter interaction.The manipulation of solids using ultrafast optical pulses has opened up a new paradigm in condensed matter physics by allowing the study of emergent physical properties that are otherwise inaccessible in equilibrium 1,2,10 . An important example is provided by the Floquet-Bloch states 11 , which emerge in solids owing to a coherent interaction between Bloch states inside the solid and a periodic driving potential. This is a consequence of the Floquet theorem 12 , which states that a Hamiltonian periodic in time with period T has eigenstates that are evenly spaced by the drive energy (2π/T ). Floquet-Bloch states have generated a lot of interest recently both for realizing exotic states of matter such as a Floquet Chern insulator 7 , as well as understanding non-equilibrium periodic thermodynamics 13,14 . Experimental observation of these states requires the measurement of the transient electronic band structure of a crystal as it is perturbed by light. As has recently been demonstrated 15 in the topological insulator Bi 2 Se 3 , time-and angleresolved photoemission spectroscopy (Tr-ARPES) is a key tool that can achieve this. Characteristic signatures of Floquet-Bloch states in the Tr-ARPES spectra include replicas of the original band structure that are separated by the driving photon energy 15 .In addition to Floquet-Bloch states, light can also generate other coherent phenomena in solids [16][17][18] . In particular, it can dress freeelectron states near the surface of a solid (Fig. 1a), as the surface can provide the momentum conservation necessary for a photon to interact with a free electron. This dressing was first observed in time-resolved photoemission experiments 17 and has subsequently been referred to as laser-assisted photoemission (LAPE). LAPE is typically understood [19][20][21] by invoking the Volkov solution, which is an e...

In this Letter we present detailed study of the density of states near defects in Bi2Se3. In particular, we present data on the commonly found triangular defects in this system. While we do not find any measurable quasiparticle scattering interference effects, we do find localized resonances, which can be well fitted by theory [R. R. Biswas and A. V. Balatsky, Phys. Rev. B 81, 233405(R) (2010)] once the potential is taken to be extended to properly account for the observed defects. The data together with the fits confirm that while the local density of states around the Dirac point of the electronic spectrum at the surface is significantly disrupted near the impurity by the creation of low-energy resonance state, the Dirac point is not locally destroyed. We discuss our results in terms of the expected protected surface state of topological insulators.