  We investigate the competition between the spin-orbit interaction of
itinerant electrons and their Kondo coupling with local moments densely
distributed on the honeycomb lattice. We find that the model at half-filling
displays a quantum phase transition between topological and Kondo insulators at
a nonzero Kondo coupling. In the Kondo-screened case, tuning the electron
concentration can lead to a new topological insulator phase. The results
suggest that the heavy-fermion phase diagram contains a new regime with a
competition among topological, Kondo-coherent and magnetic states, and that the
regime may be especially relevant to Kondo lattice systems with $5d$-conduction
electrons. Finally, we discuss the implications of our results in the context
of the recent experiments on SmB$_6$ implicating the surface states of a
topological insulator, as well as the existing experiments on the phase
transitions in SmB$_6$ under pressure and in CeNiSn under chemical pressure.

Strongly Correlated Electrons