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Samarium hexaboride (SmB$_6$), a representative Kondo insulator, has beencharacterized recently as a likely topological insulator. It is also a materialwith strong electron correlations, evident by the temperature dependence of itsbandgap and the existence of a nearly flat collective mode whose energy lieswithin the bandgap. Similar strong correlations can affect or even destabilizethe two-dimensional metallic state of topological origin at the crystalboundary. Here we construct the minimal lattice model of the correlatedboundary of topological Kondo insulators, and make phenomenological predictionsfor its possible ground states. Depending on the microscopic properties of theinterface between the topological Kondo material and a conventional insulator,the boundary metal can exhibit a varied degree of hybridization between the $d$and $f$ orbitals of the rare earth element, yielding a rich two-dimensionalheavy fermion phenomenology. A pronounced participation of the $f$ orbitals isexpected to create a heavy fermion Dirac metal, possibly unstable to a spindensity wave, electron localization or even superconductivity. The oppositelimit of "localized magnetic moments" helped by the partial Kondo screening onthe crystal boundary can bring about a non-Fermi liquid of $d$ electrons thatexhibits two-dimensional quantum electrodynamics, or other unconventionalstates. In addition, ultra-thin films made from topological Kondo insulatorscould open the possibility of creating exotic incompressible quantum liquidswith non-Abelian fractional excitations, whose dynamics shaped by the strongRashba spin-orbit coupling resembles that of fractional quantum Hall systems.

Two-dimensional heavy fermions on the strongly correlated boundaries of Kondo topological insulators