$4f$ Crystal Field Ground State of the Strongly Correlated Topological Insulator $SmB_{6}$

We investigated the crystal-electric field ground state of the $4f$ manifold in the strongly correlated topological insulator $SmB_{6}$using core-level nonresonant inelastic x-ray scattering. The directional dependence of the scattering function that arises from higher multipole transitions establishes unambiguously that the $Γ8$ quartet state of the Sm $f^5 J=5/2$ configuration governs the ground-state symmetry and, hence, the topological properties of $SmB_{6}$. Our findings contradict the results of density functional calculations reported so far