  We analyze the impact of strong correlations on the surface states of a
three-dimensional topological Kondo insulator. An important observation is that
correlations are strongly increased at the surface, which leads to an
energetical confinement of the surface $f$-electrons into a narrow window
around the Fermi energy at low enough temperature. This correlation effect in
combination with the nontrivial topology has two remarkable consequences: (i)
coexistence of light and heavy surface states at low temperatures. While heavy
surface states are formed directly in the surface layer, light surface states
are formed in the next-nearest surface layer. Furthermore, (ii) with increasing
the temperature, the heavy surface states become incoherent and only light
surface states can be observed. The coexistence of light and heavy surface
states is thereby a remarkable characteristic of the combination of strong
correlations and nontrivial topology. We believe that these results are
applicable to the candidate topological Kondo insulator SmB6.
