Topological interface states in the natural heterostructure (PbSe) 5 ( Bi 2 Se 3 ) 6 with Bi Pb defects

We study theoretically the electronic band structure of (${\mathrm{PbSe})}_{5}$(${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$)${}_{6}$, which consists of an ordinary insulator PbSe and a topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$. The first-principles calculations show that this material has a gapped Dirac-cone energy dispersion inside the bulk, which originates from the topological states of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ layers encapsulated by PbSe layers. Furthermore, we calculate the band structures of (${\mathrm{Bi}}_{x}{\mathrm{Pb}}_{1\ensuremath{-}x}\mathrm{Se}$)${}_{5}$(${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$)${}_{6}$ with ${\mathrm{Bi}}_{\mathrm{Pb}}$ antisite defects included in the PbSe layers. The result shows that a high density of ${\mathrm{Bi}}_{\mathrm{Pb}}$ defects can exist in real materials, consistent with the experimentally estimated $x$ of more than 30%. The ${\mathrm{Bi}}_{\mathrm{Pb}}$ defects strongly modify the band alignment between ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ and PbSe layers, while the topological interface states of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ are kept as a gapped Dirac-cone-like dispersion.