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Topological insulators represent a paradigm shift in surface physics. Themost extensively studied Bi$_2$Se$_3$-type topological insulators exhibitlayered structures, wherein neighboring layers are weakly bonded by van derWaals interactions. Using first principles density-functional theorycalculations, we investigate the impact of the stacking sequence on theenergetics and band structure properties of three polymorphs of Bi$_2$Se$_3$,Bi$_2$Te$_3$, and Sb$_2$Te$_3$. Considering their ultrathin films up to 6 nm asa function of its layer thickness, the overall dispersion of the band structureis found to be insensitive to the stacking sequence, while the band gap ishighly sensitive, which may also affect the critical thickness for the onset ofthe topologically nontrivial phase. Our calculations are consistent with bothexperimental and theoretical results, where available. We further investigatetribological layer slippage, where we find a relatively low energy barrierbetween two of the considered structures. Both the stacking-dependent band gapand low slippage energy barriers, suggest that polymorphic stackingmodification may offer an alternative route for controlling the properties ofthis new state of matter.

Stacking-dependent energetics and electronic structure of ultrathin polymorphic V$_2$VI$_3$ topological insulator nanofilms