  I present a theory of topological heavy-fermion semiconductors based on the
large-N symplectic representation for the electron spin. The theory is exact in
the limit when the number of spin flavors N=2k is infinite. I find that both
weak and strong topological insulating phases exist for k<3. Furthermore, for
k>2 the weak topological insulating state fully suppressed while only strong
topological and trivial insulator states survive. In addition, using the
mean-field theory results, I consider the tunneling into topologically trivial
and non-trivial phases of a generic heavy-fermion insulators by calculating the
differential tunneling conductance. The implications of the presented results
for the existing heavy-fermion semiconductors are discussed.

Strongly Correlated Electrons;Materials Science