Ab initio study of 2DEG at the surface of topological insulator Bi$_2$Te$_3$

By means of ab initio DFT-calculation we analyze the mechanism that drives the formation and evolution of the 2D electron gas (2DEG) states at the surface of Bi$_2$Te$_3$ topological insulator (TI). As it has been proved earlier it is due to an expansion of the van der Waals (vdW) spacing produced by intercalation of adsorbates. We will show that the effect of this expansion, in this particular surface, leads to several intriguing phenomena. On one hand we observe a different dispersion of the Dirac cone with respect to the ideal surface and the formation of Parabolic Bands (PB) below the conduction band and $M$-shaped bands in the valence band, the latters have been observed recently in photoemission experiments. On the other hand the expansion of the vdW-gaps changes the symmetry of the orbitals forming the Dirac cone and therefore producing modifications in the local spin texture. The localization of these new 2DEG-states and the relocalization of the Dirac cone will be studied as well.