# Three-dimensional real Chern insulator in bulk $\gamma$-graphyne

## TL;DR

This paper predicts that bulk γ-graphyne is a three-dimensional real Chern insulator with topological hinge modes, and demonstrates a phase transition to a nodal-line semimetal under compression, supported by first-principles calculations.

## Contribution

It identifies bulk γ-graphyne as a 3D real Chern insulator and analyzes its topological phase transition, providing a new material realization for this class of topological phases.

## Key findings

- γ-graphyne is a 3D real Chern insulator with hinge modes.
- Compression induces a transition to a nodal-line semimetal.
- Theoretical model captures the essential physics of the system.

## Abstract

The real Chern insulator state, featuring nontrivial real Chern number and second-order boundary modes, has been revealed in a few two-dimensional systems. The concept can be extended to three dimensions (3D), but a proper material realization is still lacking. Here, based on first-principles calculations and theoretical analysis, we identify the recently synthesized bulk ${\gamma}$-graphyne as a 3D real Chern insulator. Its nontrivial bulk topology leads to topological hinge modes spreading across the 1D edge Brillouin zone. Under compression of the interlayer distance, the system can undergo a topological phase transition into a real nodal-line semimetal, which hosts three bulk nodal rings and topological boundary modes on both surfaces and hinges. We also develop a minimal model which captures essential physics of the system.