From atomic semimetal to topological nontrivial insulator

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 paper, we show that in many (magnetic) space groups, the crystals with certain Wyckoff positions and atomic orbitals being occupied must be semimetals in the atomic limit, e.g., the hopping strength between electrons is infinitesimal but not vanishing, which then are termed atomic semimetals (ASMs). We derive a sufficient condition for realizing ASMs in both spinless and spinful systems. Remarkably, with both symmetries and electron fillings of system preserved, increasing the hopping strength between electrons may transform an ASM into an insulator, and the induced insulators inevitably are topologically nontrivial. Particularly, using silicon as an example, we show the ASM criterion can discover the obstructed atomic insulators (OAIs) that are marked as trivial insulators on the topological quantum chemistry website. Our paper not only establishes an efficient way to identify and design topologically nontrivial insulators, but also predicts that the group-IV elemental semiconductors are ideal candidate materials for OAI.