Observation of a nodal chain with Dirac surface states in $\mathrm{Ti}{\mathrm{B}}_{2}$

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Observation of a nodal chain with Dirac surface states in $Ti B_{2}$

C.-J. Yi, B. Q. Lv, Q. S. Wu, B.-B. Fu, X. Gao, M. Yang, X.-L. Peng, M. Li, Y.-B. Huang, P. Richard, M. Shi, G. Li, Oleg V. Yazyev, Y.-G. Shi, T. Qian, and H. Ding

Phys. Rev. B 97, 201107(R) – Published 11 May 2018

Abstract

Topological nodal-line semimetals (TNLSMs) are characterized by symmetry-protected band crossings extending along one-dimensional lines in momentum space. The nodal lines exhibit a variety of possible configurations, such as nodal ring, nodal link, nodal chain, and nodal knot. Here, using angle-resolved photoemission spectroscopy, we observe nodal rings on the orthogonal $k_{z} = 0$ and $k_{x} = 0$ planes of the Brillouin zone in $Ti B_{2}$ . The nodal rings connect with each other on the intersecting line Γ-K of the orthogonal planes forming a remarkable nodal-chain structure. Furthermore, we observe surface states (SSs) on the (001) cleaved surface, which are consistent with the calculated SSs considering the contribution from both Ti and B terminations. The calculated SSs have novel Dirac-cone-like band structures, which are distinct from the usual drumhead SSs with a single flatband proposed in other TNLSMs.

Received 21 February 2018

DOI:https://doi.org/10.1103/PhysRevB.97.201107

Physics Subject Headings (PhySH)

First-principles calculations Surface states Topological materials Topological phases of matter

Node-line semimetals

Angle-resolved photoemission spectroscopy Density functional theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

C.-J. Yi^1,2, B. Q. Lv^1,2, Q. S. Wu^3,4, B.-B. Fu^1,2, X. Gao^1,2, M. Yang^1,2, X.-L. Peng^1,2, M. Li⁵, Y.-B. Huang⁵, P. Richard^1,2,7, M. Shi⁶, G. Li¹, Oleg V. Yazyev^3,4, Y.-G. Shi^1,*, T. Qian^1,2,7,†, and H. Ding^1,2,7,‡

¹Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²University of Chinese Academy of Sciences, Beijing 100049, China
³Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
⁴National Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
⁵Shanghai Synchrotron Radiation Facility, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201204, China
⁶Paul Scherrer Institute, Swiss Light Source, CH-5232 Villigen PSI, Switzerland
⁷Collaborative Innovation Center of Quantum Matter, Beijing, China

^*Corresponding author: ygshi@iphy.ac.cn
^†Corresponding author: tqian@iphy.ac.cn
^‡Corresponding author: dingh@iphy.ac.cn

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Vol. 97, Iss. 20 — 15 May 2018

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Figure 1
(a) Schematics of four topological configurations formed by nodal lines: (i) nodal ring, (ii) nodal link, (iii) nodal chain, and (iv) nodal knot. (b) Crystal structure of $Ti B_{2}$ . (c) Three-dimensional (3D) bulk Brillouin zone (BZ) and projected (001) surface BZ of $Ti B_{2}$ . $k_{x}$ , $k_{y}$ , and $k_{z}$ are along the Γ-M, Γ-K, and Γ-A directions, respectively. (d) Momentum locations of the four classes of nodal lines in the BZ of $Ti B_{2}$ . (e) Calculated band structures of $Ti B_{2}$ along several high-symmetry lines without SOC. (f) X-ray-diffraction data measured on the (001) plane of a $Ti B_{2}$ single crystal. (g) Core-level photoemission spectrum showing the characteristic Ti $3 p$ and B $1 s$ peaks. The inset shows a typical single crystal of $Ti B_{2}$ .
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Figure 2
(a) and (b) Experimental FSs on the Γ-M-L-A ( $k_{y} = 0$ ) and Γ-K-H-A ( $k_{x} = 0$ ) planes, respectively. (c) and (d) Corresponding calculated FSs. (e) and (f) ARPES intensity plots showing experimental band dispersions along Γ-M and Γ-K, respectively. (g) Same as (f) but measured in the second BZ. (h)–(j) Corresponding curvature intensity plots. For comparison, the calculated bands are superposed on top of the experimental data.
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Figure 3
(a) and (b) Experimental and calculated FSs, respectively, on the $k_{z} = 0$ plane. (c) and (d) Experimental and calculated FSs, respectively, on the $k_{z} = π$ plane. (e) and (f) ARPES and curvature intensity plots, respectively, showing band dispersions along Γ-K-M, indicated as C3 in (a). (g) and (h) ARPES and curvature intensity plots, respectively, showing band dispersions along K-M-K, indicated as C4 in (a). For comparison, the calculated bands are superposed on top of the experimental data in (f) and (h). (i) A 3D plot of the combined experimental FSs on the $k_{z} = 0$ and $k_{x} = 0$ planes. (j) Calculated 3D FSs in the BZ.
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Figure 4
(a) ARPES intensity plot at $E_{F}$ measured on a freshly cleaved (001) surface. (b) and (c) Calculated SS FSs for a (001) slab system with the B and Ti terminations, respectively. (d) Combination of the results in (b) and (c). (e) Curvature intensity plot showing band dispersions along the high-symmetry path $\bar{Γ} − \bar{M} − \bar{K} − \bar{Γ}$ . (f) and (g) Calculated SS bands for a (001) slab system with the B and Ti terminations, respectively. (h) Combination of the results in (f) and (g). (i) Band dispersions extracted from the experimental data in (e). Red and blue symbols represent the SS bands of the Ti and B terminations, respectively. (j) Same as (h) but with the energy range same as in (i) for direct comparison. (k) and (l) Schematics of the four- and two-band nodal rings with Dirac and drumhead SSs, respectively.
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Physical Review B

covering condensed matter and materials physics

Observation of a nodal chain with Dirac surface states in $Ti B_{2}$

C.-J. Yi, B. Q. Lv, Q. S. Wu, B.-B. Fu, X. Gao, M. Yang, X.-L. Peng, M. Li, Y.-B. Huang, P. Richard, M. Shi, G. Li, Oleg V. Yazyev, Y.-G. Shi, T. Qian, and H. Ding

Phys. Rev. B 97, 201107(R) – Published 11 May 2018

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Physical Review B

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Observation of a nodal chain with Dirac surface states in TiB2

C.-J. Yi, B. Q. Lv, Q. S. Wu, B.-B. Fu, X. Gao, M. Yang, X.-L. Peng, M. Li, Y.-B. Huang, P. Richard, M. Shi, G. Li, Oleg V. Yazyev, Y.-G. Shi, T. Qian, and H. Ding

Phys. Rev. B 97, 201107(R) – Published 11 May 2018

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Observation of a nodal chain with Dirac surface states in $Ti B_{2}$