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Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is © the Owner Societies 2018 Supplemental Information ∗ ∗ k Kai-Cheng Zhang, ,† Yong-Feng Li, ,‡,‡ Yong Liu,§ and Yan Zhu College of Mathematics and Physics, Bohai University, Jinzhou 121013, China, School of Science, Inner Mongolia University of Science and Technology, Baotou 014010, China, Key laboratory of Integrated Exploitation of Bayan Obo Multi-Metal Resources, Inner Mongolia University of Science and Technology, Baotou 014010, China, State Key Laboratory of Metastable Materials Science & Technology and College of Science, Yanshan University, Qinhuangdao 066004, China, and Department of Physics, Nanjing University of Aeronautics and Astronautics,Nanjing 210016, China E-mail: [email protected]; [email protected] ∗To whom correspondence should be addressed †College of Mathematics and Physics, Bohai University, Jinzhou 121013, China ‡School of Science, Inner Mongolia University of Science and Technology, Baotou 014010, China ¶Key laboratory of Integrated Exploitation of Bayan Obo Multi-Metal Resources, Inner Mongolia University of Science and Technology, Baotou 014010, China §State Key Laboratory of Metastable Materials Science & Technology and College of Science, Yanshan University, Qinhuangdao 066004, China kDepartment of Physics, Nanjing University of Aeronautics and Astronautics,Nanjing 210016, China 1 1 1 0 0 E nergy (eV) E nergy (eV) -1 -1 Γ Γ Κ K' Γ Γ K K' (a) (b) 1 1 0 0 E nergy (eV) E nergy (eV) -1 -1 Γ KK' Γ Γ K K' Γ (c) (d) 1 1 0 0 E nergy (eV) E nergy (eV) -1 -1 Γ K K' Γ Γ Γ (e)K (f) K' Figure S1: (Color online) Band structures without (left column) and with (right column) spin- orbital coupling for Os-Fe@G (top), Os-Ru@G (middle), and Os-Rh@G (bottom) by GGA+U method. The red and blue curves in the plots of left column represent the majority and minority spin bands respectively. The red and blue circles represent the degenerate dxz=yz states (majority) and dxy=x2−y2 states (minority) respectively. The larger the size of symbol, the heavier of the weight. Large topological band-gap is opened for Os-Fe@G (b) and Os-Rh@G (f) at the Fermi level due to the spin-orbital coupling. For Os-Ru@G, the band-gap is slightly below the Fermi level. 2.

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