  We discuss the evolution of topological states and their orbital textures in
the mixed valence compounds SmB6 and YbB6 within the framework of the
generalized gradient approximation plus onsite Coulomb interaction (GGA+U)
scheme for a wide range of values of U. In SmB6, the topological Kondo
insulator (TKI) gap is found to be insensitive to the value of U, but in sharp
contrast, Kondo physics in isostructural YbB6 displays a surprising sensitivity
to U. In particular, as U is increased in YbB6, the correlated TKI state in the
weak-coupling regime transforms into a d-p-type topological insulator phase
with a band inversion between Yb-5d and B-2p orbitals in the intermediate
coupling range, without closing the insulating energy gap throughout this
process. Our theoretical predictions related to the TKI and non-TKI phases in
SmB6 and YbB6 are in substantial accord with recent angle-resolved
photoemission spectroscopy (ARPES) experiments.
