Profiling spin and orbital texture of a topological insulator in full momentum space

Letter

Profiling spin and orbital texture of a topological insulator in full momentum space

H. Bentmann, H. Maaß, J. Braun, C. Seibel, K. A. Kokh, O. E. Tereshchenko, S. Schreyeck, K. Brunner, L. W. Molenkamp, K. Miyamoto, M. Arita, K. Shimada, T. Okuda, J. Kirschner, C. Tusche, H. Ebert, J. Minár, and F. Reinert

Phys. Rev. B 103, L161107 – Published 15 April 2021

Abstract

We investigate the coupled spin and orbital textures of the topological surface state in ${Bi}_{2}$ (Te, ${Se)}_{3}$ (0001) across full momentum space using spin- and angle-resolved photoelectron spectroscopy and relativistic one-step photoemission theory. For an approximately isotropic Fermi surface in ${Bi}_{2} {Te}_{2} Se$ , the measured intensity and spin momentum distributions, obtained with linearly polarized light, qualitatively reflect the orbital composition and the orbital-projected in-plane spin polarization, respectively. In ${Bi}_{2} {Te}_{3}$ , the in-plane lattice potential induces a hexagonal anisotropy of the Fermi surface, which manifests in an out-of-plane photoelectron spin polarization with a strong dependence on light polarization, excitation energy, and crystallographic direction.

Received 19 November 2020
Accepted 1 April 2021

DOI:https://doi.org/10.1103/PhysRevB.103.L161107

Physics Subject Headings (PhySH)

Spin-orbit coupling Surface states Topological insulators Topological materials

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

H. Bentmann ^1,*, H. Maaß¹, J. Braun², C. Seibel¹, K. A. Kokh^3,4,5, O. E. Tereshchenko^3,6, S. Schreyeck⁷, K. Brunner⁷, L. W. Molenkamp⁷, K. Miyamoto⁸, M. Arita⁸, K. Shimada ⁸, T. Okuda⁸, J. Kirschner⁹, C. Tusche^9,10,11, H. Ebert², J. Minár¹², and F. Reinert¹

¹Experimentelle Physik VII and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany, European Union
²Department Chemie, Physikalische Chemie, Universität München, Butenandtstrasse 5-13, D-81377 München, Germany, European Union
³Novosibirsk State University, 636090 Novosibirsk, Russia
⁴Institute of Geology and Mineralogy, SB RAS, 630090 Novosibirsk, Russia
⁵Kemerovo State University, 650000 Kemerovo, Russia
⁶Institute of Semiconductor Physics, 636090 Novosibirsk, Russia
⁷Institute for Topological Insulators and Physikalisches Institut, Experimentelle Physik III, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany, European Union
⁸Hiroshima Synchrotron Radiation Center, Hiroshima University, Kagamiyama 2-313, Higashi-Hiroshima 739-0046, Japan
⁹Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany, European Union
¹⁰Forschungszentrum Jülich, Peter Grünberg Institut (PGI-6), D-52425 Jülich, Germany, European Union
¹¹Fakultät für Physik, Universität Duisburg-Essen, D-47057 Duisburg, Germany, European Union
¹²New Technologies-Research Center, University of West Bohemia, Univerzitni 8, 306 14 Pilsen, Czech Republic, European Union

^*Corresponding author: hendrik.bentmann@physik.uni- wuerzburg.de

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Issue

Vol. 103, Iss. 16 — 15 April 2021

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Images

Figure 1
(a) Sketch of the experimental geometry. (b) Schematic of a topological surface state with helical spin texture. (c) Color code for the measured spin-resolved momentum distributions in (f) and (g). Momentum distributions of the (d), (e) photoelectron intensity and (f), (g) photoelectron spin polarization measured with $s$ - and $p$ -polarized light ( $h ν =$ 6 eV) for the topological surface state in ${Bi}_{2} {Te}_{2} Se$ (0001). (h), (i) Relativistic one-step photoemission calculations corresponding to the experimental results in (f) and (g). The spin-quantization axis in experiment and theory is along $y$ . All measurements were carried out at a temperature of $\sim 130$ K.
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Figure 2
Azimuthal-angle $ϕ_{k}$ dependence of the photoemission intensity/spin polarization measured in (a), (b) $s$ -polarized geometry and (c), (d) $p$ -polarized geometry. $ϕ_{k}$ is the azimuthal angle along a constant energy contour [cf. Figs. 1–1] and $ϕ_{k} = 0$ corresponds to the positive $k_{x}$ axis. For a given $ϕ_{k}$ , the (a), (c) maximal intensity and (b), (d) spin polarization were extracted from the corresponding data sets in Figs. 1–1. Black lines correspond to fits to the data (see text for details). The data were obtained at $h ν =$ 6 eV at a temperature of $\sim 130$ K.
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Figure 3
(a) ARPES data set of the Fermi surface in ${Bi}_{2} {Te}_{3}$ (0001) ( $h ν = 23$ eV). The outer, snowflake-shaped feature arises from the topological surface state. The arrow indicates the azimuthal rotation of the sample performed to obtain the data in (b). (b) Spin-resolved energy distribution curves (EDCs) measured along different crystalline directions, as summarized in (c). The EDCs were taken at an emission angle of $3^{\circ}$ corresponding to approximately $k_{| |} = 0.12$ Å $^{- 1}$ at the Fermi level. The spin-quantization axis is along $z$ . The EDCs were measured at wave vectors in the plane of light incidence, while the crystalline orientation was varied by azimuthal sample rotation. (d) Spin-resolved EDCs for an orientation along $\bar{Γ} \bar{K}$ measured at different $h ν$ for $p$ polarization and for circularly left and right polarized light. (e) Photon-energy dependence of the measured $S_{z}$ for $p$ -polarized light. All measurements were carried out at a temperature of $\sim 70$ K.
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Figure 4
One-step photoemission calculations for ${Bi}_{2} {Te}_{3}$ (0001) of the angle-resolved photoelectron spin polarization $S_{z}$ along $\bar{Γ} \bar{K}$ for $p$ -polarized light with (a) $h ν = 24$ eV and (b) $h ν = 38$ eV. The wave vector $k_{| |}$ lies in the plane of light incidence.
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