Is SmB6 a topological Kondo insulator
In plain words
SmB6 conducts on its surface while its interior insulates at low temperature; theory predicts these surface states are topological, meaning protected by symmetry and band structure, but this is not settled.
Precise statement
Determine whether the conducting surfaces of SmB6 are protected by the time-reversal Z2 invariant from $f-d$ band inversion at the $X$ points, with an odd number of Dirac cones, or are trivial polar-surface states. An answer is spin-resolved ARPES and transport (weak antilocalization, thickness independence) on several crystal faces, consistent with a Z2 index computed from the bulk bands.
What would settle it
Spin-resolved ARPES locating Dirac points on at least two surface orientations plus transport showing surface conduction independent of surface termination.
Status in the literature
Surface conduction below about 4 K is established by transport; ARPES evidence on spin texture and Dirac points remains disputed.