Graphyne as a second-order and real Chern topological insulator in two dimensions

TL;DR

This paper predicts that graphyne, a carbon allotrope, can host second-order and real Chern topological phases in two dimensions, characterized by unique edge and corner states, with potential for experimental realization.

Contribution

It identifies graphyne as a 2D second-order and real Chern topological insulator through first-principles calculations and theoretical analysis.

Findings

Graphyne exhibits a direct bulk band gap at three M points.

The bulk bands show a double band inversion characterized by a nontrivial real Chern number.

The topological phase transition involves a 2D Weyl semimetal phase.

Abstract

Higher-order topological phases and real topological phases are two emerging topics in topological states of matter, which have been attracting considerable research interest. However, it remains a challenge to find realistic materials that can realize these exotic phases. Here, based on first-principles calculations and theoretical analysis, we identify graphyne, the representative of the graphyne-family carbon allotropes, as a two-dimensional (2D) second-order topological insulator and a real Chern insulator. We show that graphyne has a direct bulk band gap at the three $M$ points, forming three valleys. The bulk bands feature a double band inversion, which is characterized by the nontrivial real Chern number enabled by the spacetime-inversion symmetry. The real Chern number is explicitly evaluated by both the Wilson-loop method and the parity approach, and we show that it dictates the existence of Dirac type edge bands and the topological corner states. Furthermore, we find that the topological phase transition in graphyne from the second-order topological insulator to a trivial insulator is mediated by a 2D Weyl semimetal phase. The robustness of the corner states against symmetry breaking and possible experimental detection methods are discussed.