  The Abelian Higgs model is an appropriate field theoretic framework for the
description of superconductivity and its topological
excitations(Nielson-Olesen-Abrikosov vortex). Recently, C.-Y. Hou etl [ Phys.
Rev. lett.\textbf{98} 186809 (2007)]. show that such excitations exist in
graphene structures. In this paper, we show that a pseudo non-Abelian Higgs
field can also be generated in graphenelike systems. Introducing a non-Abelian
gauge field, we extend the chiral gauge theory for graphene constructed by R.
Jackiw and S.-Y. Pi [Phys. Rev. Lett. \textbf{98}, 266402 (2007)] to the
non-Abelian regime.
