Oscillatory crossover from two-dimensional to three-dimensional topological insulators

Abstract

We investigate the crossover regime from three-dimensional topological insulators ${\text{Bi}}_{2}{\text{Te}}_{3}$ and ${\text{Bi}}_{2}{\text{Se}}_{3}$ 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 nontrivial two-dimensional behavior.