Graphene with geometrically induced vorticity

TL;DR

This paper explores how geometrically induced gauge fields in graphene lead to vorticity in the Higgs field, resulting in fractionally charged vortices with zero modes, supported by index theorem analysis.

Contribution

It demonstrates the connection between geometric gauge fields and vorticity in the Higgs field in graphene, revealing fractional charge vortices and zero modes.

Findings

Identification of non-real Higgs fields with vorticity in graphene

Existence of fractionally charged vortices with zero modes

Six low-lying states in fullerene-like molecules

Abstract

At half filling, the electronic structure of graphene can be modelled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field, an everywhere-real Kekule modulation of the hopping matrix elements can correspond to a non-real Higgs field with non-trivial vorticity. This provides a natural setting for fractionally charged vortices with localized zero modes. For fullerene-like molecules we employ the index theorem to demonstrate the existence of six low-lying states that do not depend strongly on the Kekule-induced mass gap.