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SmB$_6$, known to be a Kondo insulator, has received intense scrutiny inrecent years due to its paradoxical experimental signatures: while somequantities show an insulating behavior, others point to a metallic state. Thishas led to the conjecture that SmB$_6$ hosts nontrivial excitations within itsbulk gap, and has spawned several theories to that effect. In principle, thereexists an alternative possibility: the system is a metal but unusually withboth metal- and insulator-like properties. Inspired by this possibility, Iconsider a minimal model of a Kondo insulator---a flat band hybridized with aparabolic band---that is slightly electron doped, i.e., the chemical potentialis in the conduction band but close to the band edge. By calculating the dcconductivity, ac conductivity, specific heat, and quantum oscillations at thephenomenological level, I show that these quantities exhibit unusual behaviorsthat are, surprisingly, qualitatively consistent with those observedexperimentally in SmB$_6$. The rapid change of band curvature around thechemical potential arising from the strong particle-hole asymmetry and thenarrow gap in the model, a feature not usually encountered in the textbookcases of metals or insulators, is at the heart of the unusual behaviors.

Anomalies in a slightly doped insulator with strong particle-hole asymmetry and narrow gap---the case for SmB$_6$?