Dirac Fermions in Graphene Nanodisk and Graphene Corner: Texture of Vortices with Unusual Winding Number

TL;DR

This paper investigates zero-energy states in graphene nanodisks and corners, revealing vortex textures with unusual winding numbers, including rare double-winding vortices, using Dirac theory and symmetry analysis.

Contribution

It introduces the analysis of vortex textures with unconventional winding numbers in graphene nanostructures based on Dirac theory and symmetry considerations.

Findings

Zero-energy states are classified by edge momentum and symmetry.

A vortex with winding number 2 emerges in the E representation.

Each zero-energy mode is a chiral edge mode.

Abstract

We analyze the zero-energy sector of the trigonal zigzag nanodisk and corner based on the Dirac theory of graphene. The zero-energy states are shown to be indexed by the edge momentum and grouped according to the irreducible representation of the trigonal symmetry group $C_{3v}$. Wave functions are explicitly constructed as holomorphic or antiholomorphic functions around the K or K' point. Each zero-energy mode is a chiral edge mode. We find a texture of magnetic vortices. It is intriguing that a vortex with the winding number $2$ emerges in the state belonging to the $E$ (doublet) representation. The realization of such a vortex is vary rare.