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Two-dimensional (2D) graphene monolayer has been attached importance because of the fantastic physical properties. In this work, we conduct the atomistic simulations to evaluate the phonon behaviors in isotopically doped graphene with Sierpinski Carpet (SC) fractal structure. The thermal conductivities ( k ) with different fractal numbers are calculated by molecular dynamics simulation. The relationship between the  k  and the fractal number from 0 to 8 shows a first decreasing and then stable trend. The maximum reduction ratio of the  k  in SC fractal structures is 52.37%. Afterwards, we utilize the molecular dynamics simulation, phonon wave packet simulation and lattice dynamics simulation to investigate the phonon density of states (PDOS), energy transmission coefficient (ETC), phonon group velocity and participation ratio (PR) in SC fractal structures. In SC fractal structures, the PDOS increases in the low frequency region and the G-band will soften with the enhanced fractal number. We also observe that the isotopic doping atoms can lead to continuous reflected waves in SC fractal structure regions. Moreover, phonon modes in SC fractal structures possess the lower ETCs, phonon group velocities and PRs in comparison with the pristine graphene monolayer. Therefore, we attribute the lower  k  in SC fractal structures to the stronger phonon-impurity scattering and the increasing localized phonon modes.

Atomistic simulations of phonon behaviors in isotopically doped graphene with Sierpinski carpet fractal structure