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We advert to the fact that presence of valence fluctuations (VFs) insemiconductors with in-gap impurity bands unconditionally leads to dynamicalchanges (fluctuations) of energies of localized impurity states. We providearguments that in the impurity subnetwork consisting of centers having energylevels fluctuating around the Fermi energy there exist favorable conditions forhops from occupied states to empty states of less energy. Consequently, wepropose original valence-fluctuation induced hopping mechanism as a newpossibility to explain unusual metallic-like conduction of SmB$_6$ and otherKondo insulators experimentally observed at lowest temperatures. Interestingly,the proposed mechanism infers enhanced metallic-like surface conductivity ofSmB$_6$, what resembles a characteristic property of topological insulator, andis in agreement with experimental observations attempting to prove theexistence of topologically protected surface state in SmB$_6$.

SmB$_6$: Topological insulator or semiconductor with valence-fluctuation induced hopping transport?