Topological surface states on the nonpolar (110) and (111) surfaces of ${\mathrm{SmB}}_{6}$

Topological surface states on the nonpolar (110) and (111) surfaces of ${SmB}_{6}$

Dong-Choon Ryu, Chang-Jong Kang, Junwon Kim, Kyoo Kim, G. Kotliar, J.-S. Kang, J. D. Denlinger, and B. I. Min

Phys. Rev. B 103, 125101 – Published 1 March 2021

Abstract

In order to clarify the controversial issue of the topological nature in a mixed-valent Kondo system, ${SmB}_{6}$ , we have explored the surface states on the nonpolar (110) surface of ${SmB}_{6}$ , employing both angle-resolved photoemission spectroscopy (ARPES) experiment and ab initio density-functional theory (DFT) band calculations. Based on ARPES spectroscopic fingerprints and the DFT surface band structures, we ascribe the observed spectral weights at $\bar{X}$ and $\bar{Y}$ on the (110) surface Brillouin zone to topological surface states (TSSs) of “topological insulator (TI)” nature and of “topological crystalline insulator (TCI)” nature, respectively. With varying the chemical potential, the double Dirac cones of the TCI nature exhibit a Lifshitz transition of Fermi surfaces with intriguing spin textures. We have also examined the TSSs on the nearly nonpolar (111) surface of ${SmB}_{6}$ in connection with a recently reported ARPES result and proposed a way to probe the Dirac points that are buried in the bulk-projected bands.

Received 29 November 2020
Accepted 16 February 2021

DOI:https://doi.org/10.1103/PhysRevB.103.125101

Physics Subject Headings (PhySH)

Symmetry protected topological states Topological insulators

Kondo insulators Topological materials

First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Dong-Choon Ryu^1,*, Chang-Jong Kang^2,*, Junwon Kim^1,*, Kyoo Kim ^1,3,†, G. Kotliar^2,4, J.-S. Kang⁵, J. D. Denlinger^6,‡, and B. I. Min ^1,§

¹Department of Physics, Pohang University of Science and Technology, Pohang 37673, Korea
²Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
³MPPHC_CPM, Pohang University of Science and Technology, Pohang 37673, Korea
⁴Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
⁵Department of Physics, The Catholic University of Korea, Bucheon 14662, Korea
⁶Advanced Light Source, Lawrence Berkeley Laboratory, Berkeley, California 94720, USA

^*These authors contributed equally to this work.
^†Present address: Korea Atomic Energy Research Institute (KAERI), 111 Daedeok-daero, Daejeon 34057, Korea.
^‡Corresponding author: JDDenlinger@lbl.gov
^§Corresponding author: bimin@postech.ac.kr

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Vol. 103, Iss. 12 — 15 March 2021

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Figure 1
(a) Nonpolar (110) surface of ${SmB}_{6}$ . (b) bulk and (001), (110), and (111) surface BZs of ${SmB}_{6}$ . There are three mirror symmetry lines on the (110) surface: $\bar{Γ} − \bar{X}, \bar{Γ} − \bar{Y}$ , and $\bar{X} − \bar{S}$ . (c) LEED data of the prepared (110) surface of ${SmB}_{6}$ . (d),(e) ARPES data for the (110) surface of ${SmB}_{6}$ obtained at 15 K using LV polarization. (d) Wide-energy-range dispersion images through $\bar{S} − \bar{Y} − \bar{S}$ measured at $h ν = 70 eV$ . (e) Near- $E_{F}$ energy dispersion images through $\bar{S} − \bar{X} − \bar{S}$ measured at 66 eV and $\bar{S} − \bar{Y} − \bar{S}$ measured at 40 eV, respectively. Fermi-edge intensity line profiles (MDC at $E_{F}$ in red) highlight the $E_{F}$ -crossing in-gap states. Red-dotted and yellow-broken arrows denote the energy positions of $E_{F}$ and $- 50$ meV, respectively, at which angle-dependent CE maps were measured (see Fig. 3 below). (f) Photon-dependent map ( $h ν = 30 - 120 eV$ ) at the (110) surface BZ boundary ( $k_{y} = 0.54 Å^{- 1}$ ) with $E_{F}$ and $- 50$ meV energy slices, showing 2D vertical $\bar{Y}$ states and 3D bulk states around $X$ and $M$ , respectively. Dotted arcs correspond to the angle map energy, shown in Fig. 3.
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Figure 2
(a),(b) Band structures for the (110) surface of ${SmB}_{6}$ with the surface potential $V_{s} = 0$ , and (c),(d) those with $V_{s} = 0.02 eV$ . The double Dirac-cone surface states near $\bar{Y}$ in (a) and (c) are magnified in (b) and (d). Dirac point along $\bar{Γ} − \bar{Y}$ and the gap opening along $\bar{Y} − \bar{S}$ are clearly visible in (d). Opposite mirror eigenvalues ( $+ i$ and $- i$ ) protect the band crossing along $\bar{Γ} − \bar{Y}$ . (e)–(h) Constant-energy (CE) surfaces centered at $\bar{Y}$ as a function of energy cut ( $E_{c}$ ) denoted by white arrow for the (110) surface with $V_{s} = 0.02 eV$ , which exhibits a Lifshitz transition of FS's. Spin texture for each CE surface reveals either the Dresselhaus type [(e)–(g)] or the Rashba type (h), depending on $E_{c}$ . When compared with experimental results, the DFT energy values in (a)–(h) should be rescaled by a factor of 1/10, which is estimated by the quasiparticle weight at $E_{F}$ from the DMFT self-energy of the $4 f$ electrons [20].
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Figure 3
(a) Angle-dependent ( $k_{x} − k_{y}$ ) CE maps for the (110) surface of ${SmB}_{6}$ obtained at 66 eV with energy slices at $E_{F}$ (red dotted) and $- 50$ meV (yellow broken), using both LH and LV polarization, respectively. Broken lines $# 1$ and $# 2$ correspond to EDC image cuts in Fig. 1. (b) Theoretical FS with spin helicity (left) and CE map at $- 0.5 eV$ (right). For the comparison between theory and experiment, one needs to take into account the scale factor of 1/10 in the DFT $4 f$ -band width due to the band renormalization effect [20]. Namely, the DFT energy $- 0.5 eV$ in (b) would correspond to the ARPES energy $- 50$ meV in (a).
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Figure 4
(a) Band structure and (b) FS for the (111) surface of ${SmB}_{6}$ with $B_{6}$ termination. (c)–(e) (111) surface band structures for different surface potential $V_{s}$ .
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Physical Review B

covering condensed matter and materials physics

Topological surface states on the nonpolar (110) and (111) surfaces of ${SmB}_{6}$

Dong-Choon Ryu, Chang-Jong Kang, Junwon Kim, Kyoo Kim, G. Kotliar, J.-S. Kang, J. D. Denlinger, and B. I. Min

Phys. Rev. B 103, 125101 – Published 1 March 2021

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Physical Review B

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Topological surface states on the nonpolar (110) and (111) surfaces of SmB6

Dong-Choon Ryu, Chang-Jong Kang, Junwon Kim, Kyoo Kim, G. Kotliar, J.-S. Kang, J. D. Denlinger, and B. I. Min

Phys. Rev. B 103, 125101 – Published 1 March 2021

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Topological surface states on the nonpolar (110) and (111) surfaces of ${SmB}_{6}$