  We studied the thermal conductivity of graphene phononic crystal (GPnC), also
named as graphene nanomesh, by molecular dynamics simulations. The dependences
of thermal conductivity of GPnCs on both length and temperature are
investigated. It is found that the thermal conductivity of GPnCs is
significantly lower than that of graphene and can be efficiently tuned by
changing the porosity and period length. For example, the ratio of thermal
conductivity of GPnC to thermal conductivity of graphene can be changed from
0.1 to 0.01 when the porosity is changed from about 21% to 65%. The phonon
participation ratio spectra reveal that more phonon modes are localized in
GPnCs with larger porosity. Our results suggest that creating GPnCs is a
valuable method to efficiently manipulate the thermal conductivity of graphene.
