Spatial characters of metallic surface states of topological insulators

We study the electronic structure of metallic surface states in Bi$_{2}$Se$_{3}$, Bi$_{2}$Te$_{3}$, and Sb$_{2}$Te$_{3}$ using an ab-initio pseudopotential density-functional method. We implemented the spin-orbit interaction into the SIESTA in a form of additional fully non-local projectors. For surface states on (001) surface, we used a supercell containing 10 quintuple layers. We obtained bulk and surface electronic structures of topological insulators Bi$_{2}$Se$_{3}$, Bi$_{2}$Te$_{3}$, and Sb$_{2}$Te$_{3}$, which are close to previous theoretical results and consistent with Dirac-cone band dispersions measured by angle-resolved photoemission spectroscopy. Then, we analyzed the wavefunctions of the metallic surface states near the Fermi level to find out spatial distributions of the surface-state wavefunctions, which turn out to be localized in the surface region with a typical spread of about 2 quintuple layers, and the shapes of the wavefunctions around Bi (or Sb) atoms close to the surface. This work was supported by the NRF of Korea (Grant No. 2009-0081204) and KISTI Supercomputing Center (Project No. KSC-2008-S02-0004).