Landau quantization and the thickness limit of topological insulator thin films of Sb$_{2}$Te$_{3}$

We report the experimental observation of Landau quantization of molecular beam epitaxy grown Sb$_{2}$Te$_{3}$ thin films by a low-temperature scanning tunneling microscope. Different from all the reported systems, the Landau quantization in Sb$_{2}$Te$_{3}$ topological insulator is not sensitive to the intrinsic substitutional defects in the films. As a result, a nearly perfect linear energy dispersion of surface states as 2D massless Dirac fermion system is observed. We demonstrate that 4 quintuple layers are the thickness limit for Sb$_{2}$Te$_{3}$ thin film being a 3D topological insulator.