Oscillatory crossover from two dimensional to three dimensional topological insulators

Chao-Xing Liu, HaiJun Zhang, Binghai Yan, Xiao-Liang Qi, Thomas Frauenheim, Xi Dai, Zhong Fang, Shou-Cheng Zhang

Published 2009-08-25, updated 2009-09-16Version 2

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.