From Atomic Semimetal to Topological Nontrivial Insulator

TL;DR

This paper explores how increasing electron hopping strength in certain crystals can transform atomic metals into topologically non-trivial insulators, revealing new pathways for designing advanced electronic materials.

Contribution

It introduces a criterion for identifying atomic semimetals that can become topological insulators, including previously overlooked cases, and applies this to group-IV semiconductors.

Findings

Atomic (semi-)metals can become topological insulators with increased hopping.

The criterion identifies OAIs missed by existing methods.

Group-IV semiconductors are promising candidates for OAIs.

Abstract

Topological band insulators and (semi-) metals can arise out of atomic insulators when the hopping strength between electrons increases. Such topological phases are separated from the atomic insulator by a bulk gap closing. In this work, we show that in many (magnetic) space groups, the crystals with certain Wyckoff positions and orbitals being occupied must be semimetal or metals in the atomic limit, e.g. the hopping strength between electrons is infinite weak but not vanishing, which then are termed atomic (semi-)metals (ASMs). We derive a sufficient condition for realizing ASMs in spinless and spinful systems. Remarkably, we find that increasing the hopping strength between electrons may transform an ASM into an insulator with both symmetries and electron fillings of crystal are preserved. The induced insulators inevitably are topologically non-trivial and at least are obstructed atomic insulators (OAIs) that are labeled as trivial insulator in topological quantum chemistry website. Particularly, using silicon as an example, we show ASM criterion can discover the OAIs missed by the recently proposed criterion of filling enforced OAI. Our work not only establishes an efficient way to identify and design non-trivial insulators but also predicts that the group-IV elemental semiconductors are ideal candidate materials for OAI.