  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.
