Surfaces and interfaces of topological insulators from relativistic many-body calculations

We introduce the $GW$ and QS$GW$ methods where the spin-orbit coupling is incorporated directly into the self-energy. This is critical to obtain reliable results for topological insulators (TIs) [1]. Within the all-electron FLAPW formalism, we show calculations for Bi [2] and TIs of the Bi$_2$Se$_3$ family [3]. Comparison to photoemission spectroscopies [4,5] shows that the many-body bulk and surface electronic structures agree much better to experiments than the ones from density functional theory (DFT). For example, we show that Bi$_2$Se$_3$ is a direct gap semiconductor [5], in contrast to predictions by DFT. For the description of surfaces of TIs as well as interfaces between TIs and between a TI and a trivial material, we use a basis of Wannier functions to construct slab Hamiltonians. This approach allows us to study very large systems with a high accuracy. [1] Aguilera \textit{et al.}, Phys. Rev. B \textbf{88}, 165136 (2013). [2] Aguilera \textit{et al.}, Phys. Rev. B \textbf{91}, 125129 (2015). [3] Aguilera \textit{et al.}, Phys. Rev. B \textbf{88}, 045206 (2013). [4] Michiardi \textit{et al.}, Phys. Rev. B \textbf{90}, 075105 (2014). [5] Nechaev \textit{et al.}, Phys. Rev. B \textbf{87}, 121111(R) (2013). Correspondence: i.aguilera@fz-juelich.de