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.
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