Kaluza-Klein description of geometric phases in graphene

TL;DR

This paper introduces a novel geometric model using Kaluza-Klein theory to describe topological defects and quantum phases in graphene, linking geometry and quantum properties.

Contribution

It presents a new four-dimensional geometric framework for analyzing topological defects and quantum flux in graphene using Kaluza-Klein theory.

Findings

Model successfully describes topological defects in graphene

Links geometric deformation to quantum flux via extra dimension

Provides insights into topological quantum phases in graphene

Abstract

In this paper, we use the Kaluza-Klein approach to describe topological defects in a graphene layer. Using this approach, we propose a geometric model allowing to discuss the quantum flux in $K$-spin subspace. Within this model, the graphene layer with a topological defect is described by a four-dimensional metric, where the deformation produced by the topological defect is introduced via the three-dimensional part of metric tensor, while an Abelian gauge field is introduced via an extra dimension. We use this new geometric model to discuss the arising of topological quantum phases in a graphene layer with a topological defect.