# Topological Weyl-like Phonons and Nodal Line Phonons in Graphene

## TL;DR

This paper predicts topological Weyl-like points and nodal lines in graphene's phonon spectrum using first-principles calculations, revealing non-trivial topological phononic states and edge modes that could lead to novel phononic phenomena.

## Contribution

It introduces the discovery of topological phononic Weyl-like points and nodal lines in graphene, a novel topological phononic feature in a 2D material.

## Key findings

- Identification of three type-I Weyl points and one type-II Weyl point in graphene
- Existence of a phononic nodal line with topological non-triviality
- Observation of topologically protected phononic edge states

## Abstract

By means of first-principles calculations and modeling analysis, we have predicted that the traditional 2D-graphene hosts the topological phononic Weyl-like points (PWs) and phononic nodal line (PNL) in its phonon spectrum. The phonon dispersion of graphene hosts three type-I PWs (both PW1 and PW2 at the BZ corners \emph{K} and \emph{K}', and PW3 locating along the $\Gamma$-\emph{K} line), one type-II PW4 locating along the $\Gamma$-\emph{M} line, and one PNL surrounding the centered $\Gamma$ point in the $q_{x,y}$ plane. The calculations further reveal that Berry curvatures are vanishingly zero throughout the whole BZ, except for the positions of these four pairs of Weyl-like phonons, at which the non-zero singular Berry curvatures appear with the Berry phase of $\pi$ or -$\pi$, confirming its topological non-trivial nature. The topologically protected non-trivial phononic edge states have been also evidenced along both the zigzag-edged and armchair-edged boundaries. These results would pave the ways for further studies of topological phononic properties of graphene, such as phononic destructive interference with a suppression of backscattering and intrinsic phononic quantum Hall-like effects.