Topological insulators (TIs) are materials that are insulating in the bulk but have zero band-gap surface states with linear dispersion and are protected by time-reversal symmetry. These unique characteristics could pave the way for many promising applications that include spintronic devices and quantum computations. It is important to understand and theoretically describe TIs as accurately as possible to predict properties. Quantum mechanical approaches, specifically first-principles density-functional-theory (DFT)-based methods, have been used extensively to model electronic properties of TIs. Here we provide a comprehensive assessment of a variety of DFT formalisms and how these capture the electronic structure of TIs. We concentrate on ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ as examples of prototypical TI materials. We find that the generalized gradient approximation (GGA) and kinetic density functional (metaGGA) increase the thickness of the TI slab, whereas we see the opposite behavior in DFT computations using LDA. Accounting for van der Waals (vdW) interactions overcomes the apparent over-relaxations and retraces the atomic positions toward the bulk. Based on a systematic computational study, we show that GGA with vdW treatment is an appropriate method for structural optimization. However, the vdW corrections recover the experimental bulk parameters, and do not influence the charge density implicitly. Thus, electronic structures derived from the base GGA functional, employing experimental lattice parameters, is sufficient.

• Received 23 July 2019
• Revised 12 December 2019
• Accepted 11 February 2020

DOI:https://doi.org/10.1103/PhysRevB.101.085140