Role of surface termination in realizing well-isolated topological surface states within the bulk band gap in TlBiSe$_2$ and TlBiTe$_2$

摘要

Electronic structures associated with the flat (polar) Se/Te- orTl-terminated surfaces of TlBiSe$_2$ and TlBiTe$_2$ are predicted to harbor notonly Dirac cone states, but also trivial dangling bond states near the Fermienergy. However, the latter, trivial states have never been observed inphotoemission measurements. In order to address this discrepancy, we havecarried out {\it ab-initio} calculations for various surfaces of TlBiSe$_2$ andTlBiTe$_2$. A rough nonpolar surface with an equal number of Se/Te and Tl atomsin the surface atomic layer is found to destroy the trivial dangling bondstates, leaving only the Dirac cone states in the bulk energy gap. Theresulting energy dispersions of the Dirac states are in good accord with thecorresponding experimental dispersions in TlBiSe$_2$ as well as TlBiTe$_2$. Wealso show that in the case of flat, Se terminated, high-index (221) and (112)surfaces of TlBiSe$_2$, the trivial surface states shift energetically belowthe Dirac node and become well-separated from the Dirac cone states.