  Materials with non-trivial topology in their electronic structures enforce
the existence of helical Dirac fermionic surface states. We discovered emergent
topological phases in the stacked structures of topological insulator and band
insulator layers where the surface Dirac fermions interact to each other with
particular helicity ordering. Using first-principles calculations and a model
Lagrangian, we explicitly demonstrated that such helicity ordering occurs in
real materials of ternary chalcogen compounds and determines their topological
insulating phase. Our results reveal the rich collective nature of interacting
surface Dirac fermions, and pave the way for utilizing topological phases for
technological devices such as non-volatile memories.
