  We investigate the crossover regime from three dimensional topological
insulators $Bi_2Te_3$ and $Bi_2Se_3$ to two dimensional topological insulators
with quantum spin Hall effect when the layer thickness is reduced. Using both
analytical models and first-principles calculations, we find that the crossover
occurs in an oscillatory fashion as a function of the layer thickness,
alternating between topologically trivial and non-trivial two dimensional
behavior.
