  One of the most remarkable characteristics of topological materials is that
they have special surface states, which are determined by the topological
properties of their bulk materials. The angle resolved photoemission
spectroscopy (ARPES) is a powerful tool to explore the surface states, which
allows to further investigate the topological phase transitions. However, it is
very difficult to compare the first-principle calculated band structures to the
ARPES results,when the systems are doped or alloyed, because the band
structures are heavily folded.We develop an efficient band unfolding method
based on numerical atomic orbitals (NAOs). We apply this method to study the
surface states of the non-magnetically and magnetically doped topological
insulators Bi$_2$Se$_3$ and the topological crystalline insulators
Pb$_{1-x}$Sn$_{x}$Te.
