Is $\mathrm{SmB_6}$ a topological Kondo insulator?
In plain words
$\mathrm{SmB_6}$ 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 $\mathrm{SmB_6}$ 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.
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