We have investigated the band structure and the band symmetry of mixed-valence insulator SmB$_{ 6}$ systematically within the density functional theory (DFT). We have analyzed the symmetries and characters of Sm $4f$ and $5d$ bands near the Fermi level ($E_F$) in terms of the non-relativistic real cubic bases as well as the relativistic complex bases incorporating the spin-orbit coupling and the cubic crystal field. Further, we have found that the semi-core band located at $\sim 15$ eV below $E_F$ has the mixed parity and thereby affects the parity eigenvalues of the special ${ \bf k}$-points considerably. We have discussed the possible surface states and topological class of SmB$_{ 6}$, based on the bulk parity tables.
Categories: cond-mat.str-el