# Two-dimensional higher-order topology in monolayer graphdiyne

## TL;DR

This paper predicts monolayer graphdiyne as a two-dimensional higher-order topological insulator with unique corner charge phenomena, revealed through first-principles and tight-binding analyses, and links its topology to a three-dimensional counterpart.

## Contribution

It introduces monolayer graphdiyne as a new higher-order topological insulator candidate, emphasizing the importance of core orbital contributions for correct bulk topology characterization.

## Key findings

- Higher-order topology manifests in corner charge accumulation.
- Bulk topology is trivial when only $p_z$ orbitals are considered.
- Including $p_{x,y}$ and $s$ orbitals reveals nontrivial topology.

## Abstract

Based on first-principles calculations and tight-binding model analysis, we propose monolayer graphdiyne as a candidate material for a two-dimensional higher-order topological insulator protected by inversion symmetry. Despite the absence of chiral symmetry, the higher-order topology of monolayer graphdiyne is manifested in the filling anomaly and charge accumulation at two corners. Although its low energy band structure can be properly described by the tight-binding Hamiltonian constructed by using only the $p_z$ orbital of each atom, the corresponding bulk band topology is trivial. The nontrivial bulk topology can be correctly captured only when the contribution from the core levels derived from $p_{x,y}$ and $s$ orbitals are included, which is further confirmed by the Wilson loop calculations. We also show that the higher-order band topology of a monolayer graphdyine gives rise to the nontrivial band topology of the corresponding three-dimensional material, ABC-stacked graphdiyne, which hosts monopole nodal lines and hinge states.