Surface coupling in Bi₂Se₃ ultrathin films by screened Coulomb interaction

Single-particle band theory has been very successful in describing the band structure of topological insulators. However, with decreasing thickness of topological insulator thin films, single-particle band theory is insufficient to explain their band structures and transport properties due to the existence of top and bottom surface-state coupling. Here, we reconstruct this coupling with an equivalently screened Coulomb interaction in Bi₂Se₃ ultrathin films. The thickness-dependent position of the Dirac point and the magnitude of the mass gap are discussed in terms of the Hartree approximation and the self-consistent gap equation. We find that for thicknesses below 6 quintuple layers, the magnitude of the mass gap is in good agreement with the experimental results. Our work provides a more accurate means of describing and predicting the behaviour of quasi-particles in ultrathin topological insulator films and stacked topological systems.