  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 in order 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
Bi$_2$Se$_3$ and Bi$_2$Te$_3$ as examples of prototypical TI materials. We find
that the generalized gradient (GGA) and kinetic density functional (metaGGA)
produce displacements increasing the thickness of the TI slab, whereas we see
an opposite behavior in DFT computations using LDA. Accounting for van der
Waals (vdW) interactions overcomes the apparent over-relaxations and retraces
the atomic positions towards the bulk. Based on an intensive computational
study, we show that GGA with vdW treatment is the most appropriate method for
structural optimization. Electronic structures derived from GGA or metaGGA
employing experimental lattice parameters are also acceptable. In this regard,
we express a slight preference for metaGGA in terms of accuracy, but an overall
preference for GGA due to compensatory improvements in computability in
capturing TI behavior.

Computational Physics;Mesoscale and Nanoscale Physics