Kekule Lattice in Graphdiyne: Coexistence of Phononic and Electronic Higher-Order Band Topology

TL;DR

This study reveals that graphdiyne exhibits coexistence of phononic and electronic higher-order topological states, demonstrating a unique interplay in a real 2D carbon material with tunable corner states.

Contribution

The paper uncovers the simultaneous existence of phononic and electronic higher-order topological insulator states in graphdiyne, a novel finding in a real material.

Findings

Graphdiyne is equivalent to the Kekule lattice.

It hosts 2D phononic and electronic SOTI states.

Topological corner states are tunable by edge and local potentials.

Abstract

The topological physics has been extensively studied in different kinds of bosonic and fermionic systems, ranging from artificial structures to natural materials. However, the coexistence of topological phonon and electron in one single material is seldom reported. Recently, graphdiyne is proposed to be a two-dimensional (2D) electronic second-order topological insulator (SOTI). In this work, based on density-functional tight-binding calculations, we found that graphdiyne is equivalent to the Kekule lattice, also realizing a 2D phononic SOTI in both out-of-plane and in-plane modes. Depending on edge terminations, the characterized topological corner states can be either inside or outside the bulk gap, which are tunable by local corner potential. Most remarkably, a unique selectivity of space and symmetry is revealed in electron-phonon coupling between the localized phononic and electronic topological corner states. Our results not only demonstrate the phononic higher-order band topology in a real carbon material, but also provide an opportunity to investigate the interplay between phononic and electronic higher-order topological states.