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Termination-dependent Surface In-gap States in a Mixed-valent Topological Insulator: SmB$_6$

We have investigated the surface states of a potential mixed-valent topological insulator SmB$_6$ based on the first principles density functional theory slab band structure analysis. We have found that metallic surface states are formed in the bulk band gap region, providing evidence for the topological insulating nature of SmB$_6$. The obtained surface in-gap states are quite different from those in existing reports in that they are formed differently depending on the Sm or B$_6$ surface termination, and are composed of mainly Sm $4f$ state indicating the essentiality of including $f$ electrons in describing the surface states. We have obtained the spin chiral structures of the Fermi surfaces, which are also in accordance with the topological insulating nature of SmB$_6$.