Robust Surface States and Coherence Phenomena in Magnetically Alloyed ${\mathrm{SmB}}_{6}$

Robust Surface States and Coherence Phenomena in Magnetically Alloyed ${SmB}_{6}$

Lin Miao, Chul-Hee Min, Yishuai Xu, Zengle Huang, Erica C. Kotta, Rourav Basak, M. S. Song, B. Y. Kang, B. K. Cho, K. Kißner, F. Reinert, Turgut Yilmaz, Elio Vescovo, Yi-De Chuang, Weida Wu, Jonathan D. Denlinger, and L. Andrew Wray

Phys. Rev. Lett. 126, 136401 – Published 31 March 2021

Abstract

Samarium hexaboride is a candidate for the topological Kondo insulator state, in which Kondo coherence is predicted to give rise to an insulating gap spanned by topological surface states. Here we investigate the surface and bulk electronic properties of magnetically alloyed ${Sm}_{1 - x} M_{x} B_{6}$ ( $M = Ce$ , Eu), using angle-resolved photoemission spectroscopy and complementary characterization techniques. Remarkably, topologically nontrivial bulk and surface band structures are found to persist in highly modified samples with up to 30% Sm substitution and with an antiferromagnetic ground state in the case of Eu doping. The results are interpreted in terms of a hierarchy of energy scales, in which surface state emergence is linked to the formation of a direct Kondo gap, while low-temperature transport trends depend on the indirect gap.

Received 24 February 2020
Revised 19 January 2021
Accepted 5 March 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.136401

Physics Subject Headings (PhySH)

Antiferromagnetism Kondo effect Topological insulators

Rare-earth alloys

Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Lin Miao¹, Chul-Hee Min², Yishuai Xu³, Zengle Huang⁴, Erica C. Kotta³, Rourav Basak³, M. S. Song⁵, B. Y. Kang⁵, B. K. Cho⁵, K. Kißner², F. Reinert², Turgut Yilmaz⁶, Elio Vescovo⁶, Yi-De Chuang⁴, Weida Wu ⁴, Jonathan D. Denlinger⁷, and L. Andrew Wray ^3,*

¹School of Physics, Southeast University, Nanjing 211189, China
²Experimentelle Physik VII and Würzburg-Dresden Cluster of Excellence ct.qmat, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
³Department of Physics, New York University, New York, New York 10003, USA
⁴Rutgers Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
⁵School of Materials Science and Engineering, Gwangju Institute of Science and Technology (GIST), Gwangju 61005, Korea
⁶National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA
⁷Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

^*Corresponding author. lawray@nyu.edu

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Vol. 126, Iss. 13 — 2 April 2021

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Figure 1
Surface states after 30% Ce doping. (a) The Fermi surface of ${Sm}_{0.7} {Ce}_{0.3} B_{6}$ , with dashed lines tracing ovoid surface state electron pockets. (b) A low-energy ARPES cut along the $\bar{X} − \bar{Γ} − \bar{X}$ momentum axis (cut 1). (c) Surface (blue) and bulk (black) bands are traced on momentum distribution curves from (b), with an energy step of 6 meV. (d) A band structure diagram showing (blue) a topological surface state and (black) hybridization-gapped bulk bands along the $\bar{M} − \bar{X} − \bar{M}$ axis. The lower half of the surface Dirac cone is expected to be a weaker bulk-degenerate resonance state. (e) The two dimensionality of the surface state is visible in $k_{z}$ dependence of the cut 2 Fermi surface. (f),(g) An ARPES cut along the $\bar{M} − \bar{X} − \bar{M}$ direction. The energy step in (g) is 5 meV. All measurements were performed at $T = 20 K$ .
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Figure 2
Surface state emergence after 20% Eu doping. (a) The Fermi surface of ${Sm}_{0.8} {Eu}_{0.2} B_{6}$ . (b) A low-energy ARPES cut taken along the high-symmetry $\bar{X} − \bar{Γ} − \bar{X}$ direction [traced in (a)] is shown as a function of temperature and annotated with the momentum-axis center of mass of Fermi level features. Raw data underlying the $T = 10$ (c) and 180 K (d) images are traced with surface (blue) and bulk (black) bands. The Fermi level is indicated with a thicker line, and the energy step is 6 meV. (e) Raw data curves within 50 meV of the Fermi level are shown for selected temperatures, with an energy step of 7 meV.
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Figure 3
Resistivity and susceptibility of magnetically doped alloys. (a) Magnetic susceptibility of Ce-alloyed ${SmB}_{6}$ . Data for pristine ${CeB}_{6}$ and ${SmB}_{6}$ are extracted from Refs. [55, 56]. (b) Magnetic susceptibility of Eu-alloyed ${SmB}_{6}$ . Drop arrows mark the magnetic transition at 10% and 20% Eu doping levels. (c) Resistivity of Ce-alloyed ${SmB}_{6}$ . A black drop arrow marks the onset of the $T < 10 K$ surface conductivity plateau for ${SmB}_{6}$ , which happens to coincide with bulk-derived resistivity kinks in the alloyed samples. Data for pristine ${CeB}_{6}$ and ${SmB}_{6}$ are extracted from Refs. [57, 58], and an inset compares the resistivity trends for ${CeB}_{6}$ and ${Sm}_{0.7} {Ce}_{0.3} B_{6}$ . (d) Resistivity of Eu-alloyed ${SmB}_{6}$ , with data for pristine ${EuB}_{6}$ extracted from Ref. [59]. Red and blue arrows indicate magnetic transitions, as in (b).
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Figure 4
Coherence, hybridization, and surface state emergence. (a) The $4 f$ band feature width at half maximum in alloys is evaluated from a Voigt fit and compared with pristine ${SmB}_{6}$ as a function of temperature. A shaded region indicates the threshold below which surface states become visible to ARPES. (b) A schematic showing surface states spanning the Fermi level (FL) hybridization gap. Bulk states with zero $z$ -axis momentum are drawn as solid lines, and the $k_{z}$ -projected bulk state continuum is shown with light yellow shading. (c) Diagrams show the temperature-resolved evolution of TKI bulk band structure intersecting the $X$ point. Middle: as coherence increases with the lowering of temperature, topologically inverted direct hybridization gaps open at band crossing points. Right: as temperature decreases further, the presence or absence of an indirect gap within the Kondo band structure defines the trend of resistivity. The topologically inverted parity symmetries are indicated by “ $+$ ” ( $d$ orbital) and “ $-$ ” ( $f$ orbital) signs.
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Physical Review Letters

Robust Surface States and Coherence Phenomena in Magnetically Alloyed SmB6

Lin Miao, Chul-Hee Min, Yishuai Xu, Zengle Huang, Erica C. Kotta, Rourav Basak, M. S. Song, B. Y. Kang, B. K. Cho, K. Kißner, F. Reinert, Turgut Yilmaz, Elio Vescovo, Yi-De Chuang, Weida Wu, Jonathan D. Denlinger, and L. Andrew Wray

Phys. Rev. Lett. 126, 136401 – Published 31 March 2021

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Robust Surface States and Coherence Phenomena in Magnetically Alloyed ${SmB}_{6}$