Topological obstructed atomic limit by annihilating Dirac fermions

TL;DR

This paper demonstrates that annihilating Dirac fermions induces a topological phase transition from a semi-metal to an Obstructed Atomic Limit insulator, characterized by non-trivial Zak phases and observable in materials like strained graphene.

Contribution

It reveals a novel topological transition mechanism driven by Dirac fermion annihilation, linking critical semi-metallic phases to Obstructed Atomic Limit insulators.

Findings

Transition from semi-metal to OAL insulator upon Dirac fermion annihilation

Non-trivial Zak phase due to phase branch-cuts in wave functions

Observation of the transition in materials like strained graphene and Sb/As

Abstract

We show that annihilating a pair of Dirac fermions implies a topological transition from the critical semi-metallic phase to an Obstructed Atomic Limit (OAL) insulator phase instead of a trivial insulator. This is shown to happen because of branch-cuts in the phase of the wave functions, leading to non trivial Zak phase along certain directions. To this end, we study their Z$_2$ invariant and also study the phase transition using Entanglement Entropy. We use low energy Hamiltonians and numerical result from model systems to show this effect. These transitions are observed in realistic materials including strained graphene and buckled honeycomb group-V (Sb/As).