  Heavy fermion systems contain not only strong electron correlations, which
promote a rich set of quantum phases, but also a large spin-orbit coupling,
which tends to endow the electronic states a topological character. Kondo
insulators are understood in terms of a lattice of local moments coupled to
conduction electrons in a half-filled band, i.e., with a dense population of
about one electron per unit cell. Here, we propose that a new class of Kondo
insulator arises when the conduction-electron band is nearly empty ( or,
equivalently, full ) . We demonstrated the effect through a honeycomb Anderson
lattice model. In the empty carrier limit, spin-orbit coupling produces a gap
in the hybridized heavy fermion band, thereby generating a topological Kondo
insulator. This state can be understood in terms of a nearby phase in the
overall phase diagram, a Dirac-Kondo semimetal whose quasiparticle excitations
exhibit a non-trivial Berry phase. Our results point to the dilute carrier
limit of the heavy-fermion systems as a new setting to study strongly
correlated insulating and topological states.
