# Importance of van der Waals interactions for ab initio studies of topological insulators

## TL;DR

This study demonstrates that accurately including van der Waals interactions in ab initio calculations is crucial for correctly modeling the structural and electronic properties of layered topological insulators like Bi2Se3 and Bi2Te3.

## Contribution

It systematically compares different vdW correction methods and establishes a framework for first-principles modeling of topological insulators and heterostructures.

## Key findings

- Semi-empirical vdW corrections yield accurate structural descriptions.
- Proper long-range vdW tail treatment matches experimental lattice constants.
- Bi2Te3 exhibits hexagonal warping affecting spin textures.

## Abstract

We investigate the lattice and electronic structures of the bulk and surface of the prototypical layered topological insulators Bi$_2$Se$_3$ and Bi$_2$Te$_3$ using ab initio density functional methods, and systematically compare the results of different methods of including van der Waals (vdW) interactions. We show that the methods utilizing semi-empirical energy corrections yield accurate descriptions of these materials, with the most precise results obtained by properly accounting for the long-range tail of the vdW interactions. The bulk lattice constants, distances between quintuple layers and the Dirac velocity of the topological surface states (TSS) are all in excellent agreement with experiment. In Bi$_2$Te$_3$, hexagonal warping of the energy dispersion leads to complex spin textures of the TSS at moderate energies, while in Bi$_2$Se$_3$ these states remain almost perfectly helical away from the Dirac point, showing appreciable signs of hexagonal warping at much higher energies, above the minimum of the bulk conduction band. Our results establish a framework for unified and systematic self-consistent first principles calculations of topological insulators in bulk, slab and interface geometries, and provides the necessary first step towards ab initio modeling of topological heterostructures.