# 2D and 3D topological phases in BiTe$X$ compounds

## TL;DR

This paper investigates the topological phases in BiTe$X$ compounds, revealing that certain layered structures exhibit quantum spin Hall and strong topological insulator phases, while others remain trivial, depending on composition and stacking.

## Contribution

It provides a detailed analysis of the topological properties of BiTe$X$ compounds, identifying conditions under which they exhibit nontrivial topological phases in 2D and 3D.

## Key findings

- Bi$_2$Te$_2$I$_2$ exhibits topological edge states and maintains $ ext{Z}_2$ invariance on BiTeI substrate.
- BiTeBr-based films are trivial insulators up to five layers thick.
- BiTeBr in 3D forms a strong topological insulator despite trivial 2D layers.

## Abstract

Recently, it was shown that quantum spin Hall insulator (QSHI) phase with a gap wide enough for practical applications can be realized in the ultra thin films constructed from two inversely stacked structural elements of trivial band insulator BiTeI. Here, we study the edge states in the free-standing Bi$_2$Te$_2$I$_2$ sextuple layer (SL) and the electronic structure of the Bi$_2$Te$_2$I$_2$ SL on the natural BiTeI substrate. We show that the topological properties of the Bi$_2$Te$_2$I$_2$ SL on this substrate keep $\mathbb Z_2$ invariant. We also demonstrate that ultra thin centrosymmetric films constructed in the similar manner but from related material BiTeBr are trivial band insulators up to five-SL film thickness. In contrast to Bi$_2$Te$_2$I$_2$ for which the stacking of nontrivial SLs in 3D limit gives a strong topological insulator (TI) phase, strong TI is realized in 3D Bi$_2$Te$_2$Br$_2$ in spite of the SL is trivial. For the last material of the BiTe$X$ ($X$=I,Br,Cl) series, BiTeCl, both 2D and 3D centrosymmetric phases are characterized by topologically trivial band structure.