# Topological Phase Transition in Layered XIn$_2$P$_2$ (X = Ca, Sr)

## TL;DR

This study uses relativistic first-principles calculations to explore how strain induces topological phase transitions in layered XIn$_2$P$_2$ (X=Ca, Sr), revealing a transition from semiconductors to topological insulators.

## Contribution

It demonstrates strain-induced topological phase transitions in layered XIn$_2$P$_2$, highlighting the formation of topological line-node semimetals and insulators through elastic strain engineering.

## Key findings

- Band inversion occurs under strain without SOC, forming a nodal ring.
- Including SOC opens a band gap, transforming the material into a topological insulator.
- Strain can tune the material from trivial semiconductor to topological insulator.

## Abstract

Based on fully relativistic first-principles calculations, we studied the topological properties of layered XIn$_2$P$_2$ (X = Ca, Sr). Band inversion can be induced by strain without SOC, forming one nodal ring in the k$_z$ = 0 plane, which is protected by the coexistence of time-reversal and mirror-reflection symmetry. Including SOC, a substantial band gap is opened along the nodal line and the line-node semimetal would evolve into a topological insulator. These results reveal a category of materials showing quantum phase transition from trivial semiconductor and topologically nontrivial insulator by the tuneable elastic strain engineering. Our investigations provide a new perspective about the formation of topological line-node semimetal under stain.