Robust Protection from Backscattering in the Topological Insulator ${\mathrm{Bi}}_{1.5}{\mathrm{Sb}}_{0.5}{\mathrm{Te}}_{1.7}{\mathrm{Se}}_{1.3}$

Robust Protection from Backscattering in the Topological Insulator ${Bi}_{1.5} {Sb}_{0.5} {Te}_{1.7} {Se}_{1.3}$

Sunghun Kim, Shunsuke Yoshizawa, Yukiaki Ishida, Kazuma Eto, Kouji Segawa, Yoichi Ando, Shik Shin, and Fumio Komori

Phys. Rev. Lett. 112, 136802 – Published 1 April 2014

Abstract

Electron scattering in the topological surface state (TSS) of the topological insulator ${Bi}_{1.5} {Sb}_{0.5} {Te}_{1.7} {Se}_{1.3}$ was studied using quasiparticle interference observed by scanning tunneling microscopy. It was found that not only the 180° backscattering but also a wide range of backscattering angles of 100°–180° are effectively prohibited in the TSS. This conclusion was obtained by comparing the observed scattering vectors with the diameters of the constant-energy contours of the TSS, which were measured for both occupied and unoccupied states using time- and angle-resolved photoemission spectroscopy. The robust protection from backscattering in the TSS is good news for applications, but it poses a challenge to the theoretical understanding of the transport in the TSS.

Received 11 October 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.136802

Authors & Affiliations

Sunghun Kim^1,*, Shunsuke Yoshizawa¹, Yukiaki Ishida¹, Kazuma Eto², Kouji Segawa², Yoichi Ando^2,†, Shik Shin¹, and Fumio Komori^1,‡

¹Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
²Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, Japan

^*kimsh@issp.u-tokyo.ac.jp
^†y_ando@sanken.osaka-u.ac.jp
^‡komori@issp.u-tokyo.ac.jp

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Vol. 112, Iss. 13 — 4 April 2014

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Figure 1
(a),(b) STM images of a cleaved surface of ${Bi}_{1.5} {Sb}_{0.5} {Te}_{1.7} {Se}_{1.3}$ . Protrusions are Te or Se atoms at the surface. The density of surface point defects is less than 3%. The sample bias voltage and tunneling current were $- 0.4 V$ and 20 pA in (a) and $- 0.6 V$ and 100 pA in (b). (c) Crystal structure of ${Bi}_{1.5} {Sb}_{0.5} {Te}_{1.7} {Se}_{1.3}$ . (d) Typical differential-conductance curve measured on a cleaved surface at 5 K. The positions of the top of the bulk valence band, the Dirac point, and the bottom of the bulk conduction band are marked by arrows. The latter is known from the result of TrARPES.
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Figure 2
(a),(b) Differential-conductance images of the cleaved surface for $V_{B}$ of (a) 280 mV and (b) 60 mV in the bulk band gap. (c),(d) Corresponding FT amplitude images. (e),(f) Cross sections of the FT amplitude for the images (c) and (d), respectively. The results in the $\bar{Γ がんま} − \bar{K}$ (solid red line) and $\bar{Γ がんま} − \bar{M}$ (dotted blue line) directions are shown. (g) FT amplitude images as functions of $V_{B}$ and the scattering-vector length $q$ in the $\bar{Γ がんま} − \bar{K}$ (left) and $\bar{Γ がんま} − \bar{M}$ (right) directions. Diamond (red) and square (blue) symbols indicate the critical scattering-vector lengths in the two directions.
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Figure 3
(a),(b) Photoemission intensity images of the cleaved surface of ${Bi}_{1.5} {Sb}_{0.5} {Te}_{1.7} {Se}_{1.3}$ plotted along the $\bar{Γ がんま} − \bar{K}$ direction; images (a) and (b) were obtained before ( $- 0.8 ps$ ) and after ( $+ 1.1 ps$ ) filling the unoccupied states with the 1.5 eV pump photons, respectively. Dispersions above the Fermi level became visible by pumping electrons into the unoccupied side. The bottom of the unoccupied bulk conduction band is indicated by an arrow. The inset of (a) shows the surface Brillouin zone, together with the range covered by the TrARPES measurements shown as a short thick line.
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Figure 4
(a) The critical scattering-vector lengths $q_{cx}$ and $q_{cy}$ and the diameter of constant-energy contour of the TSS are plotted for various energies from $E_{D}$ to $E_{D} + 310 meV$ ; $q_{cx}$ and $q_{cy}$ were obtained from Fig. 2, and the diameter of the TSS in the $\bar{Γ がんま} − \bar{K}$ direction was calculated from Fig. 3. (b) Schematic picture of the energy-dependent shape of the upper Dirac cone together with the available scattering vectors at representative energies. (c),(d) Schematic pictures for circular and warped TSS, respectively, to indicate that the critical scattering-vector lengths being 75% of the diameter of TSS corresponds to the maximum scattering angle of 100°; any scattering with a larger angle requires longer scattering vectors and hence is prohibited.
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Physical Review Letters

Robust Protection from Backscattering in the Topological Insulator Bi1.5Sb0.5Te1.7Se1.3

Sunghun Kim, Shunsuke Yoshizawa, Yukiaki Ishida, Kazuma Eto, Kouji Segawa, Yoichi Ando, Shik Shin, and Fumio Komori

Phys. Rev. Lett. 112, 136802 – Published 1 April 2014

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Robust Protection from Backscattering in the Topological Insulator ${Bi}_{1.5} {Sb}_{0.5} {Te}_{1.7} {Se}_{1.3}$