Role of van der Waals interactions in topological insulators: bulk, surface and interfaces

It is well-known that van der Waals interactions (vdW) play an important role on structural properties of the prototypical 3D topological insulators Bi₂Se₃ and Bi₂Te₃. However, systematic investigations of different implementations of vdW interactions using density functional theory are lacking. We have performed a comprehensive comparison using both semi-empirical (DFT+D2, DFT+D3, Tkatchenko-Scheffler) and first principles (Langreth-Lundqvist DF, SCAN-rVV10) vdW methods in bulk and surface calculations for these materials, treating structural and electronic properties on equal footing. We find that semi-empirical methods, especially D2 produce structural parameters, electronic dispersion, and the Dirac velocity of the surface state close to the experimental values, while other methods exhibit serious problems when applied to Bi₂Se₃ and Bi₂Te₃. We attribute these differences to the importance of the long range r^-6 tail of the vdW interaction, and we discuss its relevance for the properties of topological interfaces.